importance of deductive and inductive reasoning in problem solving essay

Deductive and Inductive Reasoning Essay

Inductive and deductive reasoning: essay introduction, deductive approach, inductive approach, inductive vs deductive: essay conclusion, reference list.

There are different types of reasoning, most of which are explained in psychology books and articles. This paper discusses two types of reasoning – deductive and inductive reasoning using cognitive research. The inductive and deductive reasoning essay you read focuses on teaching science and technical courses in High Schools. It explores cases of science and mathematical teaching in schools.

Deductive reasoning is a logical process where conclusions are made from general cases. General cases are studied, after which conclusions are made as they apply to a certain case (Byrne, Evans and Newstead, 2019). In the context of this deductive reasoning essay, an argument from analogy is one of the examples under deductive reasoning. The rule underlying this module is that in the case where P and Q are similar and have properties a, b, and c, object P has an extra property, “x.” Therefore, Q will automatically have the same extra property, “x,” as the two are similar (Dew Jr and Foreman, 2020).

Most high school students in the United States do come across the argument from the analogy model of deductive reasoning while studying science subjects. Nonetheless, most students do not realize the applicability of this rule. They apply the rule unconsciously. Therefore, high school students should learn about this model of reasoning. This will help them know certain instances under which they should apply this rule when making arguments in science subjects (National Academies of Sciences, Engineering, and Medicine, 2019).

Researches conducted on analogies give a clear way of explaining why student reports have added ideas. While studying scientific subjects, students do make productive analogies. They apply scientific principles, for instance, energy conservation principles, to different settings.

Unproductive analogies are also made by students, for example, in experiments between temperature and heat. Research that compares different forms of analogies gained from visual and animated representations. Such studies distinguish the functions of different brain parts. It emphasizes the benefits of activating correct pathways for specific learning forms. Research on analogies emphasizes on the selection and inclusion of right analogies in the reports. It also encourages the analysis of different analogies (Vygotsky, 2020).

Argument from analogy is one of the tools that students can use to advance reasonable arguments in different science subjects. This is according to a study that was conducted to ascertain the model that can be used by high school students in when solving problems in genetics. Different questions and student-teacher engagements were used to reach the conclusion (Choden and Kijkuakul, 2020).

The major problems in the teaching of science subjects are the lapses in communication. More often, students and teachers in science classrooms rarely share similar purpose on either the subject or the activity. At times, teachers and students assign different meanings to the same concept. This happens in cases where the two have different levels of understanding about the science concepts because most of these concepts are technical (Choden and Kijkuakul, 2020).

In order to improve the understanding of science subjects, students are required to use different approaches. For students to use analogy, they must have an understanding of the concept in question first. The concept is the most important thing as arguments derived from the subject will be concrete when the concept is well grasped.

More models should be used by science teachers in the science classes. The real nature of the models or analogs used for teaching are better understood when they are realistic. Analogs are forms of human interventions in learning. They should be used carefully as poor use may result in mal understanding of the real meaning. Analogs have an aspect of practicality which leaves images in the minds of students.

When used well, a constructive learning environment will be attained. Analogies should be used in a way that students can easily capture or map. Students should also be given room to make suggestions of improving the analogies used by their teachers. Imperfect analogies expose difficulties that arise in describing and explaining scientific ideas that are mostly of an abstract nature (Newton, 2022).

According to Oaksford and Chater (2020), inductive reasoning entails taking certain examples and using the examples to develop a general principle. It cannot be utilized in proving a concept. In inductive reasoning, solutions to problems can be reached even when the person offering the solution does not have general knowledge about the world.

An example of deductive reasoning is the case of ‘Rex the dog’. In this case, a child can make a deduction that is logical when Rex barks even at times when barking itself is an unfamiliar activity. If the child was told that Rex is a cat and that all cats bark, the child would respond with a “yes” when asked whether Rex barks. This is even when Rex does not bark. Under this reasoning, logical deductions are counterfactual in that they are not made in line with the beliefs of the real world (Pellegrino and Glaser, 2021).

On the other hand, inductive reasoning is one of the oldest learning models. Inductive reasoning develops with time as students grow. However, this reasoning has not been fully utilized in schools. It carries many cognitive skills within it. Inductive thinking is used in creative arts in high schools. In creative art subjects, students are expected to build on their learned ideas. The knowledge learned is applied in different contexts. This is the real goal of inductive reasoning (Csapó, 2020).

For the purposes of the inductive reasoning essay, research has revealed that deductive reasoning can be applied in two performance contexts. This includes the school knowledge application and the applicable knowledge context. School knowledge is the knowledge that is acquired at school. This knowledge is mostly applied in situations that are related to schoolwork.

It is applied in a similar context in which it was acquired. This knowledge or reasoning is what the students apply in handling assignments, tests, and examinations in school. It is used to grade students and determine student careers in schools. Applicable knowledge can be easily applied in situations that differ from the context in which the command was acquired (Csapó, 2020).

Research conducted in the United States revealed that the skills students acquire at the elementary level are insufficient. Elementary mathematics teaching lacks a conceptual explanation to the students. When these students get to high school, they need a basis upon which they can understand mathematical formulas and measurements. Therefore, teachers are forced to introduce these students to a higher level of thinking.

The tasks in high school mathematics that require deep thinking are also called high cognitive demand tasks. At this level of thinking, students can understand complex mathematical concepts and apply them correctly. Thus, students are introduced to inductive reasoning (Brahier, 2020).

Students will mostly have a tough time at the introductory to inductive reasoning. Students will get a grasp of concepts, mostly mathematical ones. However, it will take longer for students to develop application skills. Mathematical concepts will be understood by students within a short span.

However, applying the concepts to solve different mathematical problems is another problem. Just like for the two types of knowledge, it has always been hard for students from high school to apply the school concept in the real world. Students acquire the inside, but in most cases, they reserve it for schoolwork only.

When students do not get good tutoring, gaining the transition required to achieve the real concepts becomes difficult. This idea further destroys them and may even cause a total failure to understand and apply inductive reasoning (Van Vo and Csapó, 2022).

The transition from elementary school to high school includes psychological changes. These changes need to be molded by introducing the student to detailed thinking. This gradual process begins with slowly ushering the students to simple concepts. This simple concept builds slowly, and complexity is introduced gradually.

The students’ minds grow as they get used to the hard concepts. Later, the students become more creative and critical in thinking and understanding concepts (Hayes et al., 2019).

Inductive and deductive reasoning are two types of reasoning that borrow from one another. The use of logical conclusion applies in both of them. They are very useful, especially in teaching mathematics and science courses.

Brahier, D. (2020) Teaching secondary and middle school mathematics . Abingdon: Routledge.

Byrne, R.M., Evans, J.S.B. and Newstead, S.E. (2019) Human reasoning: the psychology of deduction . London: Psychology Press.

Choden, T. and Kijkuakul, S. (2020) ‘Blending problem based learning with scientific argumentation to enhance students’ understanding of basic genetics’, International Journal of Instruction , 13(1), pp. 445-462.

Csapó, B. (2020) ‘Development of inductive reasoning in students across school grade levels’, Thinking Skills and Creativity , 37, pp. 1-15.

Dew Jr, J.K. and Foreman, M.W. (2020) How do we know?: an introduction to epistemology . Westmont: InterVarsity Press.

Hayes, B.K. et al. (2019) ‘The diversity effect in inductive reasoning depends on sampling assumptions’, Psychonomic Bulletin & Review , 26, pp.1043-1050.

National Academies of Sciences, Engineering, and Medicine (2019) Science and engineering for grades 6-12: investigation and design at the center . Washington, D.C.: National Academies Press.

Newton, D.P. (2022) A practical guide to teaching science in the secondary school . Milton Park: Taylor & Francis.

Oaksford, M. and Chater, N. (2020) ‘New paradigms in the psychology of reasoning’, Annual Review of Psychology , 71, pp. 305-330.

Pellegrino, J.W. and Glaser, R. (2021) ‘Components of inductive reasoning’, In Aptitude, learning, and instruction (pp. 177-218). Abingdon: Routledge.

Upmeier zu Belzen, A., Engelschalt, P. and Krüger, D. (2021) ‘Modeling as scientific reasoning – the role of abductive reasoning for modeling competence’, Education Sciences , 11(9), pp. 1-11.

Van Vo, D. and Csapó, B. (2022) ‘Exploring students’ science motivation across grade levels and the role of inductive reasoning in science motivation’, European Journal of Psychology of Education , 37(3), pp. 807-829.

Vygotsky, L.S. (2020) Educational psychology . Boca Raton: CRC Press.

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Essay about Inductive and Deductive Reasoning

The two basic strategies of reasoning are frequently referred to as deductive and inductive approaches in logic. Deductive reasoning operates from the broadest to the narrowest level of abstraction. Inductive reasoning moves from individual facts to overall workload and ideas in the other direction. In the article, “A Problem in Logic,” the author compares and contrasts deductive and inductive reasoning. The major difference between inductive and deductive deductive reasoning is that inductive reasoning aims to improve a hypothesis, while deductive reasoning seeks to test an established theory. Inductive reasoning leads from particular observations to wide assumptions, while deductive reasoning leads from particular examples to broad generalizations.

Deductive reasoning is a type of argument in which the reality of the input statements practically guarantees the truth of the output assertion, as long as the reasoning is done correctly. The following are some of the benefits of using a deductive approach: Explaining causal links between research variables is possible. Determination of concepts is possible. To some level, it is possible to generalize study findings. The passage states, “Deductive reasoning usually involves moving from certain general statements or premises to new conclusions and new knowledge about a specific situation.” A syllogism is one of the most common patterns of logical reasoning. A logical conclusion is formed when two statements, a major and a minor statement. The two correct statements imply that the claim will most likely be valid for all other premises in that group. Deductive reasoning is a valuable skill that can help anyone think critically and make smarter business decisions. This mental tool allows experts to reach conclusions based on assumptions that are generally supported or by transforming a sweeping statement into a more precise concept or activity. 

Inductive reasoning is how people develop their knowledge of the world in everyday life. The scientific process is also built on inductive reasoning: scientists collect evidence through observation and experiment, make predictions based on that data, and then verify those ideas deeper. The article provides, “The inductive process consists of moving from the specific to the general.” Inductive reasoning enables for the result to be untrue even if all of the facts of a statement are accurate. The scientific technique allows for inductive reasoning. It is used by scientists to generate theories and ideas. They may use logic and reasoning to apply theories to specific circumstances.

To arrive at a confirmed conclusion, deductive reasoning employs given knowledge, premises, or established basic principles. Inductive logic or reasoning, on the other hand, includes forming patterns based on actions seen in specific circumstances. There are two types of deductive arguments: valid and invalid. The passage mentions, “Today, when scientists use formulas to solve problems, they rely on inductive reasoning, while detectives shot on the trail of Ramona-the-bank-robber would be more likely to use deductive reasoning.” Inductive reasoning accumulates distinct occurrences to arrive at reality or principles. Deductive reasoning progresses from truth or standards to specific examples. Many people need to understand the rules and then employ them deductively, yet those who learn grammar almost naturally by becoming teachable about how communication works employ an inductive reasoning to grammar.

There are two main notions that influence how grammar should be taught. Inductive and deductive reasoning are terms used to describe how one comes to a conclusion about what is true or likely. Inductive reasoning, often known as the scientific method, involves making an observation and comparing it to multiple examples of similar conditions. In deductive reasoning, one starts with an acknowledged truth and looks for multiple examples of it elsewhere. When carrying out research, these two styles of reasoning have an entirely different "feel" to them. By its very essence, inductive reasoning is more open-ended and experimental, especially in the beginning. Deductive reasoning is a type of reasoning that focuses on verifying or proving assumptions. Even though a study appears to be entirely deductive, most scientific research projects include both inductive and deductive thinking processes at some point.

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Inductive vs Deductive Reasoning | Difference & Examples

Published on 4 May 2022 by Raimo Streefkerk . Revised on 10 October 2022.

The main difference between inductive and deductive reasoning is that inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory .

Inductive reasoning moves from specific observations to broad generalisations , and deductive reasoning the other way around.

Both approaches are used in various types of research , and it’s not uncommon to combine them in one large study.

Table of contents

Inductive research approach, deductive research approach, combining inductive and deductive research, frequently asked questions about inductive vs deductive reasoning.

When there is little to no existing literature on a topic, it is common to perform inductive research because there is no theory to test. The inductive approach consists of three stages:

• A low-cost airline flight is delayed
• Dogs A and B have fleas
• Elephants depend on water to exist
• Another 20 flights from low-cost airlines are delayed
• All observed dogs have fleas
• All observed animals depend on water to exist
• Low-cost airlines always have delays
• All dogs have fleas
• All biological life depends on water to exist

Limitations of an inductive approach

A conclusion drawn on the basis of an inductive method can never be proven, but it can be invalidated.

Example You observe 1,000 flights from low-cost airlines. All of them experience a delay, which is in line with your theory. However, you can never prove that flight 1,001 will also be delayed. Still, the larger your dataset, the more reliable the conclusion.

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When conducting deductive research , you always start with a theory (the result of inductive research). Reasoning deductively means testing these theories. If there is no theory yet, you cannot conduct deductive research.

The deductive research approach consists of four stages:

• If passengers fly with a low-cost airline, then they will always experience delays
• All pet dogs in my apartment building have fleas
• All land mammals depend on water to exist
• Collect flight data of low-cost airlines
• Test all dogs in the building for fleas
• Study all land mammal species to see if they depend on water
• 5 out of 100 flights of low-cost airlines are not delayed
• 10 out of 20 dogs didn’t have fleas
• All land mammal species depend on water
• 5 out of 100 flights of low-cost airlines are not delayed = reject hypothesis
• 10 out of 20 dogs didn’t have fleas = reject hypothesis
• All land mammal species depend on water = support hypothesis

Limitations of a deductive approach

The conclusions of deductive reasoning can only be true if all the premises set in the inductive study are true and the terms are clear.

• All dogs have fleas (premise)
• Benno is a dog (premise)
• Benno has fleas (conclusion)

Many scientists conducting a larger research project begin with an inductive study (developing a theory). The inductive study is followed up with deductive research to confirm or invalidate the conclusion.

In the examples above, the conclusion (theory) of the inductive study is also used as a starting point for the deductive study.

Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

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Inductive VS Deductive Reasoning – The Meaning of Induction and Deduction, with Argument Examples

If you're conducting research on a topic, you'll use various strategies and methods to gather information and come to a conclusion.

Two of those methods are inductive and deductive reasoning.

So what's the difference between inductive and deductive reasoning, when should you use each method, and is one better than the other?

We'll answer those questions and give you some examples of both types of reasoning in this article.

What is Inductive Reasoning?

The method behind inductive reasoning.

When you're using inductive reasoning to conduct research, you're basing your conclusions off your observations. You gather information - from talking to people, reading old newspapers, observing people, animals, or objects in their natural habitat, and so on.

Inductive reasoning helps you take these observations and form them into a theory. So you're starting with some more specific information (what you've seen/heard) and you're using it to form a more general theory about the way things are.

What does the inductive reasoning process look like?

You can think of this process as a reverse funnel – starting with more specifics and getting broader as you reach your conclusions (theory).

Some people like to think of it as a "bottom up" approach (meaning you're starting at the bottom with the info and are going up to the top where the theory forms).

Here's an example of an inductive argument:

Observation (premise): My Welsh Corgis were incredibly stubborn and independent (specific observation of behavior). Observation (premise): My neighbor's Corgis are the same way (another specific observation of behavior). Theory: All Welsh Corgis are incredibly stubborn and independent (general statement about the behavior of Corgis).

As you can see, I'm basing my theory on my observations of the behavior of a number of Corgis. Since I only have a small amount of data, my conclusion or theory will be quite weak.

If I was able to observe the behavior of 1000 Corgis (omg that would be amazing), my conclusion would be stronger – but still not certain. Because what if 10 of them were extremely well-behaved and obedient? Or what if the 1001st Corgi was?

So, as you can see, I can make a general statement about Corgis being stubborn, but I can't say that ALL of them are.

What can you conclude with inductive reasoning?

As I just discussed, one of the main things to know about inductive reasoning is that any conclusions you make from inductive research will not be 100% certain or confirmed.

Let's talk about the language we use to describe inductive arguments and conclusions. You can have a strong argument (if your premise(s) are true, meaning your conclusion is probably true). And that argument becomes cogent if the conclusion ends up being true.

Still, even if the premises of your argument are true, and that means that your conclusion is probably true, or likely true, or true much of the time – it's not certain.

And – weirdly enough – your conclusion can still be false even if all your premises are true (my Corgis were stubborn, my neighbor's corgis were stubborn, perhaps a friend's Corgis and the Queen of England's Corgis were stubborn...but that doesn't guarantee that all Corgis are stubborn).

How to make your inductive arguments stronger

If you want to make sure your inductive arguments are as strong as possible, there are a couple things you can do.

First of all, make sure you have a large data set to work with. The larger your sample size, the stronger (and more certain/conclusive) your results will be. Again, thousands of Corgis are better than four (I mean, always, amiright?).

Second, make sure you're taking a random and representative sample of the population you're studying. So, for example, don't just study Corgi puppies (cute as they may be). Or show Corgis (theoretically they're better trained). You'd want to make sure you looked at Corgis from all walks of life and of all ages.

If you want to dig deeper into inductive reasoning, look into the three different types – generalization, analogy, and causal inference. You can also look into the two main methods of inductive reasoning, enumerative and eliminative. But those things are a bit out of the scope of this beginner's guide. :)

What is Deductive Reasoning?

The method behind deductive reasoning.

In order to use deductive reasoning, you have to have a theory to begin with. So inductive reasoning usually comes before deductive in your research process.

Once you have a theory, you'll want to test it to see if it's valid and your conclusions are sound. You do this by performing experiments and testing your theory, narrowing down your ideas as the results come in. You perform these tests until only valid conclusions remain.

What does the deductive reasoning process look like?

You can think of this as a proper funnel – you start with the broad open top end of the funnel and get more specific and narrower as you conduct your deductive research.

Some people like to think of this as a "top down" approach (meaning you're starting at the top with your theory, and are working your way down to the bottom/specifics). I think it helps to think of this as " reductive " reasoning – you're reducing your theories and hypotheses down into certain conclusions.

Here's an example of a deductive argument:

We'll use a classic example of deductive reasoning here – because I used to study Greek Archaeology, history, and language:

Theory: All men are mortal Premise: Socrates is a man Conclusion: Therefore, Socrates is mortal

As you can see here, we start off with a general theory – that all men are mortal. (This is assuming you don't believe in elves, fairies, and other beings...)

Then we make an observation (develop a premise) about a particular example of our data set (Socrates). That is, we say that he is a man, which we can establish as a fact.

Finally, because Socrates is a man, and based on our theory, we conclude that Socrates is therefore mortal (since all men are mortal, and he's a man).

You'll notice that deductive reasoning relies less on information that could be biased or uncertain. It uses facts to prove the theory you're trying to prove. If any of your facts lead to false premises, then the conclusion is invalid. And you start the process over.

What can you conclude with deductive reasoning?

Deductive reasoning gives you a certain and conclusive answer to your original question or theory. A deductive argument is only valid if the premises are true. And the arguments are sound when the conclusion, following those valid arguments, is true.

To me, this sounds a bit more like the scientific method. You have a theory, test that theory, and then confirm it with conclusive/valid results.

To boil it all down, in deductive reasoning:

"If all premises are true, the terms are clear , and the rules of deductive logic are followed, then the conclusion reached is necessarily true ." ( Source )

So Does Sherlock Holmes Use Inductive or Deductive Reasoning?

Sherlock Holmes is famous for using his deductive reasoning to solve crimes. But really, he mostly uses inductive reasoning. Now that we've gone through what inductive and deductive reasoning are, we can see why this is the case.

Let's say Sherlock Holmes is called in to work a case where a woman was found dead in her bed, under the covers, and appeared to be sleeping peacefully. There are no footprints in the carpet, no obvious forced entry, and no immediately apparent signs of struggle, injury, and so on.

Sherlock observes all this as he looks in, and then enters the room. He walks around the crime scene making observations and taking notes. He might talk to anyone who lives with her, her neighbors, or others who might have information that could help him out.

Then, once he has all the info he needs, he'll come to a conclusion about how the woman died.

That pretty clearly sounds like an inductive reasoning process to me.

Now you might say - what if Sherlock found the "smoking gun" so to speak? Perhaps this makes his arguments and process seem more deductive.

But still, remember how he gets to his conclusions: starting with observations and evidence, processing that evidence to come up with a hypothesis, and then forming a theory (however strong/true-seeming) about what happened.

How to Use Inductive and Deductive Reasoning Together

As you might be able to tell, researchers rarely just use one of these methods in isolation. So it's not that deductive reasoning is better than inductive reasoning, or vice versa – they work best when used in tandem.

Often times, research will begin inductively. The researcher will make their observations, take notes, and come up with a theory that they want to test.

Then, they'll come up with ways to definitively test that theory. They'll perform their tests, sort through the results, and deductively come to a sure conclusion.

So if you ever hear someone say "I deduce that x happened", they better make sure they're working from facts and not just observations. :)

TL;DR: Inductive vs Deductive Reasoning – What are the Main Differences?

Inductive reasoning:.

• Based on observations, conversations, stuff you've read
• Starts with information/evidence and works towards a broader theory
• Arguments can be strong and cogent, but never valid or sound (that is, certain)
• Premises can all be true, but conclusion doesn't have to be true

Deductive reasoning:

• Based on testing a theory, narrowing down the results, and ending with a conclusion
• Starts with a broader theory and works towards certain conclusion
• Arguments can be valid/invalid or sound/unsound, because they're based on facts
• If premises are true, conclusion has to be true

And here's a cool and helpful chart if you're a visual learner:

That's about it!

Now, if you need to conduct some research, you should have a better idea of where to start – and where to go from there.

Just remember that induction is all about observing, hypothesizing, and forming a theory. Deducing is all about taking that (or any) theory, boiling it down, and testing until a certain conclusion(s) is all that remains.

Happy reasoning!

Former archaeologist, current editor and podcaster, life-long world traveler and learner.

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The Problem of Induction

We generally think that the observations we make are able to justify some expectations or predictions about observations we have not yet made, as well as general claims that go beyond the observed. For example, the observation that bread of a certain appearance has thus far been nourishing seems to justify the expectation that the next similar piece of bread I eat will also be nourishing, as well as the claim that bread of this sort is generally nourishing. Such inferences from the observed to the unobserved, or to general laws, are known as “inductive inferences”.

The original source of what has become known as the “problem of induction” is in Book 1, part iii, section 6 of A Treatise of Human Nature by David Hume, published in 1739 (Hume 1739). In 1748, Hume gave a shorter version of the argument in Section iv of An enquiry concerning human understanding (Hume 1748). Throughout this article we will give references to the Treatise as “T”, and the Enquiry as “E”.

Hume asks on what grounds we come to our beliefs about the unobserved on the basis of inductive inferences. He presents an argument in the form of a dilemma which appears to rule out the possibility of any reasoning from the premises to the conclusion of an inductive inference. There are, he says, two possible types of arguments, “demonstrative” and “probable”, but neither will serve. A demonstrative argument produces the wrong kind of conclusion, and a probable argument would be circular. Therefore, for Hume, the problem remains of how to explain why we form any conclusions that go beyond the past instances of which we have had experience (T. 1.3.6.10). Hume stresses that he is not disputing that we do draw such inferences. The challenge, as he sees it, is to understand the “foundation” of the inference—the “logic” or “process of argument” that it is based upon (E. 4.2.21). The problem of meeting this challenge, while evading Hume’s argument against the possibility of doing so, has become known as “the problem of induction”.

Hume’s argument is one of the most famous in philosophy. A number of philosophers have attempted solutions to the problem, but a significant number have embraced his conclusion that it is insoluble. There is also a wide spectrum of opinion on the significance of the problem. Some have argued that Hume’s argument does not establish any far-reaching skeptical conclusion, either because it was never intended to, or because the argument is in some way misformulated. Yet many have regarded it as one of the most profound philosophical challenges imaginable since it seems to call into question the justification of one of the most fundamental ways in which we form knowledge. Bertrand Russell, for example, expressed the view that if Hume’s problem cannot be solved, “there is no intellectual difference between sanity and insanity” (Russell 1946: 699).

In this article, we will first examine Hume’s own argument, provide a reconstruction of it, and then survey different responses to the problem which it poses.

1. Hume’s Problem

2. reconstruction, 3.1 synthetic a priori, 3.2 the nomological-explanatory solution, 3.3 bayesian solution, 3.4 partial solutions, 3.5 the combinatorial approach, 4.1 inductive justifications of induction, 4.2 no rules, 5.1 postulates and hinges, 5.2 ordinary language dissolution, 5.3 pragmatic vindication of induction, 5.4 formal learning theory, 5.5 meta-induction, 6. living with inductive skepticism, other internet resources, related entries.

Hume introduces the problem of induction as part of an analysis of the notions of cause and effect. Hume worked with a picture, widespread in the early modern period, in which the mind was populated with mental entities called “ideas”. Hume thought that ultimately all our ideas could be traced back to the “impressions” of sense experience. In the simplest case, an idea enters the mind by being “copied” from the corresponding impression (T. 1.1.1.7/4). More complex ideas are then created by the combination of simple ideas (E. 2.5/19). Hume took there to be a number of relations between ideas, including the relation of causation (E. 3.2). (For more on Hume’s philosophy in general, see Morris & Brown 2014).

For Hume, the relation of causation is the only relation by means of which “we can go beyond the evidence of our memory and senses” (E. 4.1.4, T. 1.3.2.3/74). Suppose we have an object present to our senses: say gunpowder. We may then infer to an effect of that object: say, the explosion. The causal relation links our past and present experience to our expectations about the future (E. 4.1.4/26).

Hume argues that we cannot make a causal inference by purely a priori means (E. 4.1.7). Rather, he claims, it is based on experience, and specifically experience of constant conjunction. We infer that the gunpowder will explode on the basis of past experience of an association between gunpowder and explosions.

Hume wants to know more about the basis for this kind of inference. If such an inference is made by a “chain of reasoning” (E. 4.2.16), he says, he would like to know what that reasoning is. In general, he claims that the inferences depend on a transition of the form:

I have found that such an object has always been attended with such an effect, and I foresee, that other objects, which are, in appearance, similar, will be attended with similar effects . (E. 4.2.16)

In the Treatise , Hume says that

if Reason determin’d us, it would proceed upon that principle that instances, of which we have had no experience, must resemble those, of which we have had experience, and that the course of nature continues always uniformly the same . (T. 1.3.6.4)

For convenience, we will refer to this claim of similarity or resemblance between observed and unobserved regularities as the “Uniformity Principle (UP)”. Sometimes it is also called the “Resemblance Principle”, or the “Principle of Uniformity of Nature”.

Hume then presents his famous argument to the conclusion that there can be no reasoning behind this principle. The argument takes the form of a dilemma. Hume makes a distinction between relations of ideas and matters of fact. Relations of ideas include geometric, algebraic and arithmetic propositions, “and, in short, every affirmation, which is either intuitively or demonstratively certain”. “Matters of fact”, on the other hand are empirical propositions which can readily be conceived to be other than they are. Hume says that

All reasonings may be divided into two kinds, namely, demonstrative reasoning, or that concerning relations of ideas, and moral reasoning, or that concerning matter of fact and existence. (E. 4.2.18)

Hume considers the possibility of each of these types of reasoning in turn, and in each case argues that it is impossible for it to supply an argument for the Uniformity Principle.

First, Hume argues that the reasoning cannot be demonstrative, because demonstrative reasoning only establishes conclusions which cannot be conceived to be false. And, he says,

it implies no contradiction that the course of nature may change, and that an object seemingly like those which we have experienced, may be attended with different or contrary effects. (E. 4.2.18)

It is possible, he says, to clearly and distinctly conceive of a situation where the unobserved case does not follow the regularity so far observed (E. 4.2.18, T. 1.3.6.5/89).

Second, Hume argues that the reasoning also cannot be “such as regard matter of fact and real existence”. He also calls this “probable” reasoning. All such reasoning, he claims, “proceed upon the supposition, that the future will be conformable to the past”, in other words on the Uniformity Principle (E. 4.2.19).

Therefore, if the chain of reasoning is based on an argument of this kind it will again be relying on this supposition, “and taking that for granted, which is the very point in question”. (E. 4.2.19, see also T. 1.3.6.7/90). The second type of reasoning then fails to provide a chain of reasoning which is not circular.

In the Treatise version, Hume concludes

Thus, not only our reason fails us in the discovery of the ultimate connexion of causes and effects, but even after experience has inform’d us of their constant conjunction , ’tis impossible for us to satisfy ourselves by our reason, why we shou’d extend that experience beyond those particular instances, which have fallen under our observation. (T. 1.3.6.11/91–2)

The conclusion then is that our tendency to project past regularities into the future is not underpinned by reason. The problem of induction is to find a way to avoid this conclusion, despite Hume’s argument.

After presenting the problem, Hume does present his own “solution” to the doubts he has raised (E. 5, T. 1.3.7–16). This consists of an explanation of what the inductive inferences are driven by, if not reason. In the Treatise Hume raises the problem of induction in an explicitly contrastive way. He asks whether the transition involved in the inference is produced

by means of the understanding or imagination; whether we are determin’d by reason to make the transition, or by a certain association and relation of perceptions? (T. 1.3.6.4)

And he goes on to summarize the conclusion by saying

When the mind, therefore, passes from the idea or impression of one object to the idea or belief of another, it is not determin’d by reason, but by certain principles, which associate together the ideas of these objects, and unite them in the imagination. (T. 1.3.6.12)

Thus, it is the imagination which is taken to be responsible for underpinning the inductive inference, rather than reason.

In the Enquiry , Hume suggests that the step taken by the mind,

which is not supported by any argument, or process of the understanding … must be induced by some other principle of equal weight and authority. (E. 5.1.2)

That principle is “custom” or “habit”. The idea is that if one has seen similar objects or events constantly conjoined, then the mind is inclined to expect a similar regularity to hold in the future. The tendency or “propensity” to draw such inferences, is the effect of custom:

… having found, in many instances, that any two kinds of objects, flame and heat, snow and cold, have always been conjoined together; if flame or snow be presented anew to the senses, the mind is carried by custom to expect heat or cold, and to believe , that such a quality does exist and will discover itself upon a nearer approach. This belief is the necessary result of of placing the mind in such circumstances. It is an operation of the soul, when we are so situated, as unavoidable as to feel the passion of love, when we receive benefits; or hatred, when we meet with injuries. All these operations are a species of natural instincts, which no reasoning or process of the thought and understanding is able, either to produce, or to prevent. (E. 5.1.8)

Hume argues that the fact that these inferences do follow the course of nature is a kind of “pre-established harmony” (E. 5.2.21). It is a kind of natural instinct, which may in fact be more effective in making us successful in the world, than if we relied on reason to make these inferences.

Hume’s argument has been presented and formulated in many different versions. There is also an ongoing lively discussion over the historical interpretation of what Hume himself intended by the argument. It is therefore difficult to provide an unequivocal and uncontroversial reconstruction of Hume’s argument. Nonetheless, for the purposes of organizing the different responses to Hume’s problem that will be discussed in this article, the following reconstruction will serve as a useful starting point.

Hume’s argument concerns specific inductive inferences such as:

All observed instances of A have been B .

The next instance of A will be B .

Let us call this “inference I ”. Inferences which fall under this type of schema are now often referred to as cases of “simple enumerative induction”.

Hume’s own example is:

All observed instances of bread (of a particular appearance) have been nourishing.

The next instance of bread (of that appearance) will be nourishing.

Hume’s argument then proceeds as follows (premises are labeled as P, and subconclusions and conclusions as C):

Consequences:

There have been different interpretations of what Hume means by “demonstrative” and “probable” arguments. Sometimes “demonstrative” is equated with “deductive”, and probable with “inductive” (e.g., Salmon 1966). Then the first horn of Hume’s dilemma would eliminate the possibility of a deductive argument, and the second would eliminate the possibility of an inductive argument. However, under this interpretation, premise P3 would not hold, because it is possible for the conclusion of a deductive argument to be a non-necessary proposition. Premise P3 could be modified to say that a demonstrative (deductive) argument establishes a conclusion that cannot be false if the premises are true. But then it becomes possible that the supposition that the future resembles the past, which is not a necessary proposition, could be established by a deductive argument from some premises, though not from a priori premises (in contradiction to conclusion C1 ).

Another common reading is to equate “demonstrative” with “deductively valid with a priori premises”, and “probable” with “having an empirical premise” (e.g., Okasha 2001). This may be closer to the mark, if one thinks, as Hume seems to have done, that premises which can be known a priori cannot be false, and hence are necessary. If the inference is deductively valid, then the conclusion of the inference from a priori premises must also be necessary. What the first horn of the dilemma then rules out is the possibility of a deductively valid argument with a priori premises, and the second horn rules out any argument (deductive or non-deductive), which relies on an empirical premise.

However, recent commentators have argued that in the historical context that Hume was situated in, the distinction he draws between demonstrative and probable arguments has little to do with whether or not the argument has a deductive form (Owen 1999; Garrett 2002). In addition, the class of inferences that establish conclusions whose negation is a contradiction may include not just deductively valid inferences from a priori premises, but any inferences that can be drawn using a priori reasoning (that is, reasoning where the transition from premises to the conclusion makes no appeal to what we learn from observations). It looks as though Hume does intend the argument of the first horn to rule out any a priori reasoning, since he says that a change in the course of nature cannot be ruled out “by any demonstrative argument or abstract reasoning a priori ” (E. 5.2.18). On this understanding, a priori arguments would be ruled out by the first horn of Hume’s dilemma, and empirical arguments by the second horn. This is the interpretation that I will adopt for the purposes of this article.

In Hume’s argument, the UP plays a central role. As we will see in section 4.2 , various authors have been doubtful about this principle. Versions of Hume’s argument have also been formulated which do not make reference to the UP. Rather they directly address the question of what arguments can be given in support of the transition from the premises to the conclusion of the specific inductive inference I . What arguments could lead us, for example, to infer that the next piece of bread will nourish from the observations of nourishing bread made so far? For the first horn of the argument, Hume’s argument can be directly applied. A demonstrative argument establishes a conclusion whose negation is a contradiction. The negation of the conclusion of the inductive inference is not a contradiction. It is not a contradiction that the next piece of bread is not nourishing. Therefore, there is no demonstrative argument for the conclusion of the inductive inference. In the second horn of the argument, the problem Hume raises is a circularity. Even if Hume is wrong that all inductive inferences depend on the UP, there may still be a circularity problem, but as we shall see in section 4.1 , the exact nature of the circularity needs to be carefully considered. But the main point at present is that the Humean argument is often formulated without invoking the UP.

Since Hume’s argument is a dilemma, there are two main ways to resist it. The first is to tackle the first horn and to argue that there is after all a demonstrative argument –here taken to mean an argument based on a priori reasoning—that can justify the inductive inference. The second is to tackle the second horn and to argue that there is after all a probable (or empirical) argument that can justify the inductive inference. We discuss the different variants of these two approaches in sections 3 and 4 .

There are also those who dispute the consequences of the dilemma. For example, some scholars have denied that Hume should be read as invoking a premise such premise P8 at all. The reason, they claim, is that he was not aiming for an explicitly normative conclusion about justification such as C5 . Hume certainly is seeking a “chain of reasoning” from the premises of the inductive inference to the conclusion, and he thinks that an argument for the UP is necessary to complete the chain. However, one could think that there is no further premise regarding justification, and so the conclusion of his argument is simply C4 : there is no chain of reasoning from the premises to the conclusion of an inductive inference. Hume could then be, as Don Garrett and David Owen have argued, advancing a “thesis in cognitive psychology”, rather than making a normative claim about justification (Owen 1999; Garrett 2002). The thesis is about the nature of the cognitive process underlying the inference. According to Garrett, the main upshot of Hume’s argument is that there can be no reasoning process that establishes the UP. For Owen, the message is that the inference is not drawn through a chain of ideas connected by mediating links, as would be characteristic of the faculty of reason.

There are also interpreters who have argued that Hume is merely trying to exclude a specific kind of justification of induction, based on a conception of reason predominant among rationalists of his time, rather than a justification in general (Beauchamp & Rosenberg 1981; Baier 2009). In particular, it has been claimed that it is “an attempt to refute the rationalist belief that at least some inductive arguments are demonstrative” (Beauchamp & Rosenberg 1981: xviii). Under this interpretation, premise P8 should be modified to read something like:

• If there is no chain of reasoning based on demonstrative arguments from the premises to the conclusion of inference I , then inference I is not justified.

Such interpretations do however struggle with the fact that Hume’s argument is explicitly a two-pronged attack, which concerns not just demonstrative arguments, but also probable arguments.

The question of how expansive a normative conclusion to attribute to Hume is a complex one. It depends in part on the interpretation of Hume’s own solution to his problem. As we saw in section 1 , Hume attributes the basis of inductive inference to principles of the imagination in the Treatise, and in the Enquiry to “custom”, “habit”, conceived as a kind of natural instinct. The question is then whether this alternative provides any kind of justification for the inference, even if not one based on reason. On the face of it, it looks as though Hume is suggesting that inductive inferences proceed on an entirely arational basis. He clearly does not think that they do not succeed in producing good outcomes. In fact, Hume even suggests that this operation of the mind may even be less “liable to error and mistake” than if it were entrusted to “the fallacious deductions of our reason, which is slow in its operations” (E. 5.2.22). It is also not clear that he sees the workings of the imagination as completely devoid of rationality. For one thing, Hume talks about the imagination as governed by principles . Later in the Treatise , he even gives “rules” and “logic” for characterizing what should count as a good causal inference (T. 1.3.15). He also clearly sees it as possible to distinguish between better forms of such “reasoning”, as he continues to call it. Thus, there may be grounds to argue that Hume was not trying to argue that inductive inferences have no rational foundation whatsoever, but merely that they do not have the specific type of rational foundation which is rooted in the faculty of Reason.

All this indicates that there is room for debate over the intended scope of Hume’s own conclusion. And thus there is also room for debate over exactly what form a premise (such as premise P8 ) that connects the rest of his argument to a normative conclusion should take. No matter who is right about this however, the fact remains that Hume has throughout history been predominantly read as presenting an argument for inductive skepticism.

There are a number of approaches which effectively, if not explicitly, take issue with premise P8 and argue that providing a chain of reasoning from the premises to the conclusion is not a necessary condition for justification of an inductive inference. According to this type of approach, one may admit that Hume has shown that inductive inferences are not justified in the sense that we have reasons to think their conclusions true, but still think that weaker kinds of justification of induction are possible ( section 5 ). Finally, there are some philosophers who do accept the skeptical conclusion C5 and attempt to accommodate it. For example, there have been attempts to argue that inductive inference is not as central to scientific inquiry as is often thought ( section 6 ).

3. Tackling the First Horn of Hume’s Dilemma

The first horn of Hume’s argument, as formulated above, is aimed at establishing that there is no demonstrative argument for the UP. There are several ways people have attempted to show that the first horn does not definitively preclude a demonstrative or a priori argument for inductive inferences. One possible escape route from the first horn is to deny premise P3 , which amounts to admitting the possibility of synthetic a priori propositions ( section 3.1 ). Another possibility is to attempt to provide an a priori argument that the conclusion of the inference is probable, though not certain. The first horn of Hume’s dilemma implies that there cannot be a demonstrative argument to the conclusion of an inductive inference because it is possible to conceive of the negation of the conclusion. For instance, it is quite possible to imagine that the next piece of bread I eat will poison me rather than nourish me. However, this does not rule out the possibility of a demonstrative argument that establishes only that the bread is highly likely to nourish, not that it definitely will. One might then also challenge premise P8 , by saying that it is not necessary for justification of an inductive inference to have a chain of reasoning from its premises to its conclusion. Rather it would suffice if we had an argument from the premises to the claim that the conclusion is probable or likely. Then an a priori justification of the inductive inference would have been provided. There have been attempts to provide a priori justifications for inductive inference based on Inference to the Best Explanation ( section 3.2 ). There are also attempts to find an a priori solution based on probabilistic formulations of inductive inference, though many now think that a purely a priori argument cannot be found because there are empirical assumptions involved (sections 3.3 - 3.5 ).

As we have seen in section 1 , Hume takes demonstrative arguments to have conclusions which are “relations of ideas”, whereas “probable” or “moral” arguments have conclusions which are “matters of fact”. Hume’s distinction between “relations of ideas” and “matters of fact” anticipates the distinction drawn by Kant between “analytic” and “synthetic” propositions (Kant 1781). A classic example of an analytic proposition is “Bachelors are unmarried men”, and a synthetic proposition is “My bike tyre is flat”. For Hume, demonstrative arguments, which are based on a priori reasoning, can establish only relations of ideas, or analytic propositions. The association between a prioricity and analyticity underpins premise P3 , which states that a demonstrative argument establishes a conclusion whose negation is a contradiction.

One possible response to Hume’s problem is to deny premise P3 , by allowing the possibility that a priori reasoning could give rise to synthetic propositions. Kant famously argued in response to Hume that such synthetic a priori knowledge is possible (Kant 1781, 1783). He does this by a kind of reversal of the empiricist programme espoused by Hume. Whereas Hume tried to understand how the concept of a causal or necessary connection could be based on experience, Kant argued instead that experience only comes about through the concepts or “categories” of the understanding. On his view, one can gain a priori knowledge of these concepts, including the concept of causation, by a transcendental argument concerning the necessary preconditions of experience. A more detailed account of Kant’s response to Hume can be found in de Pierris and Friedman 2013.

The “Nomological-explanatory” solution, which has been put forward by Armstrong, BonJour and Foster (Armstrong 1983; BonJour 1998; Foster 2004) appeals to the principle of Inference to the Best Explanation (IBE). According to IBE, we should infer that the hypothesis which provides the best explanation of the evidence is probably true. Proponents of the Nomological-Explanatory approach take Inference to the Best Explanation to be a mode of inference which is distinct from the type of “extrapolative” inductive inference that Hume was trying to justify. They also regard it as a type of inference which although non-deductive, is justified a priori . For example, Armstrong says “To infer to the best explanation is part of what it is to be rational. If that is not rational, what is?” (Armstrong 1983: 59).

The a priori justification is taken to proceed in two steps. First, it is argued that we should recognize that certain observed regularities require an explanation in terms of some underlying law. For example, if a coin persistently lands heads on repeated tosses, then it becomes increasingly implausible that this occurred just because of “chance”. Rather, we should infer to the better explanation that the coin has a certain bias. Saying that the coin lands heads not only for the observed cases, but also for the unobserved cases, does not provide an explanation of the observed regularity. Thus, mere Humean constant conjunction is not sufficient. What is needed for an explanation is a “non-Humean, metaphysically robust conception of objective regularity” (BonJour 1998), which is thought of as involving actual natural necessity (Armstrong 1983; Foster 2004).

Once it has been established that there must be some metaphysically robust explanation of the observed regularity, the second step is to argue that out of all possible metaphysically robust explanations, the “straight” inductive explanation is the best one, where the straight explanation extrapolates the observed frequency to the wider population. For example, given that a coin has some objective chance of landing heads, the best explanation of the fact that \(m/n\) heads have been so far observed, is that the objective chance of the coin landing heads is \(m/n\). And this objective chance determines what happens not only in observed cases but also in unobserved cases.

The Nomological-Explanatory solution relies on taking IBE as a rational, a priori form of inference which is distinct from inductive inferences like inference I . However, one might alternatively view inductive inferences as a special case of IBE (Harman 1968), or take IBE to be merely an alternative way of characterizing inductive inference (Henderson 2014). If either of these views is right, IBE does not have the necessary independence from inductive inference to provide a non-circular justification of it.

One may also object to the Nomological-Explanatory approach on the grounds that regularities do not necessarily require an explanation in terms of necessary connections or robust metaphysical laws. The viability of the approach also depends on the tenability of a non-Humean conception of laws. There have been several serious attempts to develop such an account (Armstrong 1983; Tooley 1977; Dretske 1977), but also much criticism (see J. Carroll 2016).

Another critical objection is that the Nomological-Explanatory solution simply begs the question, even if it is taken to be legitimate to make use of IBE in the justification of induction. In the first step of the argument we infer to a law or regularity which extends beyond the spatio-temporal region in which observations have been thus far made, in order to predict what will happen in the future. But why could a law that only applies to the observed spatio-temporal region not be an equally good explanation? The main reply seems to be that we can see a priori that laws with temporal or spatial restrictions would be less good explanations. Foster argues that the reason is that this would introduce more mysteries:

For it seems to me that a law whose scope is restricted to some particular period is more mysterious, inherently more puzzling, than one which is temporally universal. (Foster 2004)

Another way in which one can try to construct an a priori argument that the premises of an inductive inference make its conclusion probable, is to make use of the formalism of probability theory itself. At the time Hume wrote, probabilities were used to analyze games of chance. And in general, they were used to address the problem of what we would expect to see, given that a certain cause was known to be operative. This is the so-called problem of “direct inference”. However, the problem of induction concerns the “inverse” problem of determining the cause or general hypothesis, given particular observations.

One of the first and most important methods for tackling the “inverse” problem using probabilities was developed by Thomas Bayes. Bayes’s essay containing the main results was published after his death in 1764 (Bayes 1764). However, it is possible that the work was done significantly earlier and was in fact written in direct response to the publication of Hume’s Enquiry in 1748 (see Zabell 1989: 290–93, for discussion of what is known about the history).

We will illustrate the Bayesian method using the problem of drawing balls from an urn. Suppose that we have an urn which contains white and black balls in an unknown proportion. We draw a sample of balls from the urn by removing a ball, noting its color, and then putting it back before drawing again.

Consider first the problem of direct inference. Given the proportion of white balls in the urn, what is the probability of various outcomes for a sample of observations of a given size? Suppose the proportion of white balls in the urn is \(\theta = 0.6\). The probability of drawing one white ball in a sample of one is then \(p(W; \theta = 0.6) = 0.6\). We can also compute the probability for other outcomes, such as drawing two white balls in a sample of two, using the rules of the probability calculus (see section 1 of Hájek 2011). Generally, the probability that \(n_w\) white balls are drawn in a sample of size N , is given by the binomial distribution:

This is a specific example of a “sampling distribution”, \(p(E\mid H)\), which gives the probability of certain evidence E in a sample, on the assumption that a certain hypothesis H is true. Calculation of the sampling distribution can in general be done a priori , given the rules of the probability calculus.

However, the problem of induction is the inverse problem. We want to infer not what the sample will be like, with a known hypothesis, rather we want to infer a hypothesis about the general situation or population, based on the observation of a limited sample. The probabilities of the candidate hypotheses can then be used to inform predictions about further observations. In the case of the urn, for example, we want to know what the observation of a particular sample frequency of white balls, \(\frac{n_w}{N}\), tells us about \(\theta\), the proportion of white balls in the urn.

The idea of the Bayesian approach is to assign probabilities not only to the events which constitute evidence, but also to hypotheses. One starts with a “prior probability” distribution over the relevant hypotheses \(p(H)\). On learning some evidence E , the Bayesian updates the prior \(p(H)\) to the conditional probability \(p(H\mid E)\). This update rule is called the “rule of conditionalisation”. The conditional probability \(p(H\mid E)\) is known as the “posterior probability”, and is calculated using Bayes’ rule:

Here the sampling distribution can be taken to be a conditional probability \(p(E\mid H)\), which is known as the “likelihood” of the hypothesis H on evidence E .

One can then go on to compute the predictive distribution for as yet unobserved data \(E'\), given observations E . The predictive distribution in a Bayesian approach is given by

where the sum becomes an integral in cases where H is a continuous variable.

For the urn example, we can compute the posterior probability \(p(\theta\mid n_w)\) using Bayes’ rule, and the likelihood given by the binomial distribution above. In order to do so, we also need to assign a prior probability distribution to the parameter \(\theta\). One natural choice, which was made early on by Bayes himself and by Laplace, is to put a uniform prior over the parameter \(\theta\). Bayes’ own rationale for this choice was that then if you work out the probability of each value for the number of whites in the sample based only on the prior, before any data is observed, all those probabilities are equal. Laplace had a different justification, based on the Principle of Indifference. This principle states that if you don’t have any reason to favor one hypothesis over another, you should assign them all equal probabilities.

With the choice of uniform prior, the posterior probability and predictive distribution can be calculated. It turns out that the probability that the next ball will be white, given that \(n_w\) of N draws were white, is given by

This is Laplace’s famous “rule of succession” (1814). Suppose on the basis of observing 90 white balls out of 100, we calculate by the rule of succession that the probability of the next ball being white is \(91/102=0.89\). It is quite conceivable that the next ball might be black. Even in the case, where all 100 balls have been white, so that the probability of the next ball being white is 0.99, there is still a small probability that the next ball is not white. What the probabilistic reasoning supplies then is not an argument to the conclusion that the next ball will be a certain color, but an argument to the conclusion that certain future observations are very likely given what has been observed in the past.

Overall, the Bayes-Laplace argument in the urn case provides an example of how probabilistic reasoning can take us from evidence about observations in the past to a prediction for how likely certain future observations are. The question is what kind of solution, if any, this type of calculation provides to the problem of induction. At first sight, since it is just a mathematical calculation, it looks as though it does indeed provide an a priori argument from the premises of an inductive inference to the proposition that a certain conclusion is probable.

However, in order to establish this definitively, one would need to argue that all the components and assumptions of the argument are a priori and this requires further examination of at least three important issues.

First, the Bayes-Laplace argument relies on the rules of the probability calculus. What is the status of these rules? Does following them amount to a priori reasoning? The answer to this depends in part on how probability itself is interpreted. Broadly speaking, there are prominent interpretations of probability according to which the rules plausibly have a priori status and could form the basis of a demonstrative argument. These include the classical interpretation originally developed by Laplace (1814), the logical interpretation (Keynes (1921), Johnson (1921), Jeffreys (1939), Carnap (1950), Cox (1946, 1961), and the subjectivist interpretation of Ramsey (1926), Savage (1954), and de Finetti (1964). Attempts to argue for a probabilistic a priori solution to the problem of induction have been primarily associated with these interpretations.

Secondly, in the case of the urn, the Bayes-Laplace argument is based on a particular probabilistic model—the binomial model. This involves the assumption that there is a parameter describing an unknown proportion \(\theta\) of balls in the urn, and that the data amounts to independent draws from a distribution over that parameter. What is the basis of these assumptions? Do they generalize to other cases beyond the actual urn case—i.e., can we see observations in general as analogous to draws from an “Urn of Nature”? There has been a persistent worry that these types of assumptions, while reasonable when applied to the case of drawing balls from an urn, will not hold for other cases of inductive inference. Thus, the probabilistic solution to the problem of induction might be of relatively limited scope. At the least, there are some assumptions going into the choice of model here that need to be made explicit. Arguably the choice of model introduces empirical assumptions, which would mean that the probabilistic solution is not an a priori one.

Thirdly, the Bayes-Laplace argument relies on a particular choice of prior probability distribution. What is the status of this assignment, and can it be based on a priori principles? Historically, the Bayes-Laplace choice of a uniform prior, as well as the whole concept of classical probability, relied on the Principle of Indifference. This principle has been regarded by many as an a priori principle. However, it has also been subjected to much criticism on the grounds that it can give rise to inconsistent probability assignments (Bertrand 1888; Borel 1909; Keynes 1921). Such inconsistencies are produced by there being more than one way to carve up the space of alternatives, and different choices give rise to conflicting probability assignments. One attempt to rescue the Principle of Indifference has been to appeal to explanationism, and argue that the principle should be applied only to the carving of the space at “the most explanatorily basic level”, where this level is identified according to an a priori notion of explanatory priority (Huemer 2009).

The quest for an a priori argument for the assignment of the prior has been largely abandoned. For many, the subjectivist foundations developed by Ramsey, de Finetti and Savage provide a more satisfactory basis for understanding probability. From this point of view, it is a mistake to try to introduce any further a priori constraints on the probabilities beyond those dictated by the probability rules themselves. Rather the assignment of priors may reflect personal opinions or background knowledge, and no prior is a priori an unreasonable choice.

So far, we have considered probabilistic arguments which place probabilities over hypotheses in a hypothesis space as well as observations. There is also a tradition of attempts to determine what probability distributions we should have, given certain observations, from the starting point of a joint probability distribution over all the observable variables. One may then postulate axioms directly on this distribution over observables, and examine the consequences for the predictive distribution. Much of the development of inductive logic, including the influential programme by Carnap, proceeded in this manner (Carnap 1950, 1952).

This approach helps to clarify the role of the assumptions behind probabilistic models. One assumption that one can make about the observations is that they are “exchangeable”. This means that the joint distribution of the random variables is invariant under permutations. Informally, this means that the order of the observations does not affect the probability. For instance, in the urn case, this would mean that drawing first a white ball and then a black ball is just as probable as first drawing a black and then a white. De Finetti proved a general representation theorem that if the joint probability distribution of an infinite sequence of random variables is assumed to be exchangeable, then it can be written as a mixture of distribution functions from each of which the data behave as if they are independent random draws (de Finetti 1964). In the case of the urn example, the theorem shows that it is as if the data are independent random draws from a binomial distribution over a parameter \(\theta\), which itself has a prior probability distribution.

The assumption of exchangeability may be seen as a natural formalization of Hume’s assumption that the past resembles the future. This is intuitive because assuming exchangeability means thinking that the order of observations, both past and future, does not matter to the probability assignments.

However, the development of the programme of inductive logic revealed that many generalizations are possible. For example, Johnson proposed to assume an axiom he called the “sufficientness postulate”. This states that outcomes can be of a number of different types, and that the conditional probability that the next outcome is of type i depends only on the number of previous trials and the number of previous outcomes of type i (Johnson 1932). Assuming the sufficientness postulate for three or more types gives rise to a general predictive distribution corresponding to Carnap’s “continuum of inductive methods” (Carnap 1952). This predictive distribution takes the form:

for some positive number k . This reduces to Laplace’s rule of succession when \(t=2\) and \(k=1\).

Generalizations of the notion of exchangeability, such as “partial exchangeability” and “Markov exchangeability”, have been explored, and these may be thought of as forms of symmetry assumption (Zabell 1988; Skyrms 2012). As less restrictive axioms on the probabilities for observables are assumed, the result is that there is no longer a unique result for the probability of a prediction, but rather a whole class of possible probabilities, mapped out by a generalized rule of succession such as the above. Therefore, in this tradition, as in the Bayes-Laplace approach, we have moved away from producing an argument which produces a unique a priori probabilistic answer to Hume’s problem.

One might think then that the assignment of the prior, or the relevant corresponding postulates on the observable probability distribution, is precisely where empirical assumptions enter into inductive inferences. The probabilistic calculations are empirical arguments, rather than a priori ones. If this is correct, then the probabilistic framework has not in the end provided an a priori solution to the problem of induction, but it has rather allowed us to clarify what could be meant by Hume’s claim that inductive inferences rely on the Uniformity Principle.

Some think that although the problem of induction is not solved, there is in some sense a partial solution, which has been called a “logical solution”. Howson, for example, argues that “ Inductive reasoning is justified to the extent that it is sound, given appropriate premises ” (Howson 2000: 239, his emphasis). According to this view, there is no getting away from an empirical premise for inductive inferences, but we might still think of Bayesian conditioning as functioning like a kind of logic or “consistency constraint” which “generates predictions from the assumptions and observations together” (Romeijn 2004: 360). Once we have an empirical assumption, instantiated in the prior probability, and the observations, Bayesian conditioning tells us what the resulting predictive probability distribution should be.

The idea of a partial solution also arises in the context of the learning theory that grounds contemporary machine learning. Machine learning is a field in computer science concerned with algorithms that learn from experience. Examples are algorithms which can be trained to recognise or classify patterns in data. Learning theory concerns itself with finding mathematical theorems which guarantee the performance of algorithms which are in practical use. In this domain, there is a well-known finding that learning algorithms are only effective if they have ‘inductive bias’ — that is, if they make some a priori assumptions about the domain they are employed upon (Mitchell 1997).

The idea is also given formal expression in the so-called ‘No-Free-Lunch theorems’ (Wolpert 1992, 1996, 1997). These can be interpreted as versions of the argument in Hume’s first fork since they establish that there can be no contradiction in the algorithm not performing well, since there are a priori possible situations in which it does not (Sterkenburg and Grünwald 2021:9992). Given Hume’s premise P3 , this rules out a demonstrative argument for its good performance.

Premise P3 can perhaps be challenged on the grounds that a priori justifications can also be given for contingent propositions. Even though an inductive inference can fail in some possible situations, it could still be reasonable to form an expectation of reliability if we spread our credence equally over all the possibilities and have reason to think (or at least no reason to doubt) that the cases where inductive inference is unreliable require a ‘very specific arrangement of things’ and thus form a small fraction of the total space of possibilities (White 2015). The No-Free-Lunch theorems make difficulties for this approach since they show that if we put a uniform distribution over all logically possible sequences of future events, any learning algorithm is expected to have a generalisation error of 1/2, and hence to do no better than guessing at random (Schurz 2021b).

The No-Free-Lunch theorems may be seen as fundamental limitations on justifying learning algorithms when these algorithms are seen as ‘purely data-driven’ — that is as mappings from possible data to conclusions. However, learning algorithms may also be conceived as functions not only of input data, but also of a particular model (Sterkenburg and Grünwald 2021). For example, the Bayesian ‘algorithm’ gives a universal recipe for taking a particular model and prior and updating on the data. A number of theorems in learning theory provide general guarantees for the performance of such recipes. For instance, there are theorems which guarantee convergence of the Bayesian algorithm (Ghosal, Ghosh and van der Vaart 2000, Ghosal, Lember and van der Vaart 2008). In each instantiation, this convergence is relative to a particular specific prior. Thus, although the considerations first raised by Hume, and later instantiated in the No-Free-Lunch theorems, preclude any universal model-independent justification for learning algorithms, it does not rule out partial justifications in the form of such general a priori ‘model-relative’ learning guarantees (Sterkenburg and Grünwald 2021).

An alternative attempt to use probabilistic reasoning to produce an a priori justification for inductive inferences is the so-called “combinatorial” solution. This was first put forward by Donald C. Williams (1947) and later developed by David Stove (1986).

Like the Bayes-Laplace argument, the solution relies heavily on the idea that straightforward a priori calculations can be done in a “direct inference” from population to sample. As we have seen, given a certain population frequency, the probability of getting different frequencies in a sample can be calculated straightforwardly based on the rules of the probability calculus. The Bayes-Laplace argument relied on inverting the probability distribution using Bayes’ rule to get from the sampling distribution to the posterior distribution. Williams instead proposes that the inverse inference may be based on a certain logical syllogism: the proportional (or statistical) syllogism.

The proportional, or statistical syllogism, is the following:

• Of all the things that are M , \(m/n\) are P .

Therefore, a is P , with probability \(m/n\).

For example, if 90% of rabbits in a population are white and we observe a rabbit a , then the proportional syllogism says that we infer that a is white with a probability of 90%. Williams argues that the proportional syllogism is a non-deductive logical syllogism, which effectively interpolates between the syllogism for entailment

• All M s are P

Therefore, a is P .

And the syllogism for contradiction

Therefore, a is not P .

This syllogism can be combined with an observation about the behavior of increasingly large samples. From calculations of the sampling distribution, it can be shown that as the sample size increases, the probability that the sample frequency is in a range which closely approximates the population frequency also increases. In fact, Bernoulli’s law of large numbers states that the probability that the sample frequency approximates the population frequency tends to one as the sample size goes to infinity. Williams argues that such results support a “general over-all premise, common to all inductions, that samples ‘match’ their populations” (Williams 1947: 78).

We can then apply the proportional syllogism to samples from a population, to get the following argument:

• Most samples match their population
• S is a sample.

Therefore, S matches its population, with high probability.

This is an instance of the proportional syllogism, and it uses the general result about samples matching populations as the first major premise.

The next step is to argue that if we observe that the sample contains a proportion of \(m/n\) F s, then we can conclude that since this sample with high probability matches its population, the population, with high probability, has a population frequency that approximates the sample frequency \(m/n\). Both Williams and Stove claim that this amounts to a logical a priori solution to the problem of induction.

A number of authors have expressed the view that the Williams-Stove argument is only valid if the sample S is drawn randomly from the population of possible samples—i.e., that any sample is as likely to be drawn as any other (Brown 1987; Will 1948; Giaquinto 1987). Sometimes this is presented as an objection to the application of the proportional syllogism. The claim is that the proportional syllogism is only valid if a is drawn randomly from the population of M s. However, the response has been that there is no need to know that the sample is randomly drawn in order to apply the syllogism (Maher 1996; Campbell 2001; Campbell & Franklin 2004). Certainly if you have reason to think that your sampling procedure is more likely to draw certain individuals than others—for example, if you know that you are in a certain location where there are more of a certain type—then you should not apply the proportional syllogism. But if you have no such reasons, the defenders claim, it is quite rational to apply it. Certainly it is always possible that you draw an unrepresentative sample—meaning one of the few samples in which the sample frequency does not match the population frequency—but this is why the conclusion is only probable and not certain.

The more problematic step in the argument is the final step, which takes us from the claim that samples match their populations with high probability to the claim that having seen a particular sample frequency, the population from which the sample is drawn has frequency close to the sample frequency with high probability. The problem here is a subtle shift in what is meant by “high probability”, which has formed the basis of a common misreading of Bernouilli’s theorem. Hacking (1975: 156–59) puts the point in the following terms. Bernouilli’s theorem licenses the claim that much more often than not, a small interval around the sample frequency will include the true population frequency. In other words, it is highly probable in the sense of “usually right” to say that the sample matches its population. But this does not imply that the proposition that a small interval around the sample will contain the true population frequency is highly probable in the sense of “credible on each occasion of use”. This would mean that for any given sample, it is highly credible that the sample matches its population. It is quite compatible with the claim that it is “usually right” that the sample matches its population to say that there are some samples which do not match their populations at all. Thus one cannot conclude from Bernouilli’s theorem that for any given sample frequency, we should assign high probability to the proposition that a small interval around the sample frequency will contain the true population frequency. But this is exactly the slide that Williams makes in the final step of his argument. Maher (1996) argues in a similar fashion that the last step of the Williams-Stove argument is fallacious. In fact, if one wants to draw conclusions about the probability of the population frequency given the sample frequency, the proper way to do so is by using the Bayesian method described in the previous section. But, as we there saw, this requires the assignment of prior probabilities, and this explains why many people have thought that the combinatorial solution somehow illicitly presupposed an assumption like the principle of indifference. The Williams-Stove argument does not in fact give us an alternative way of inverting the probabilities which somehow bypasses all the issues that Bayesians have faced.

4. Tackling the Second Horn of Hume’s Dilemma

So far we have considered ways in which the first horn of Hume’s dilemma might be tackled. But it is of course also possible to take on the second horn instead.

One may argue that a probable argument would not, despite what Hume says, be circular in a problematic way (we consider responses of this kind in section 4.1 ). Or, one might attempt to argue that probable arguments are not circular at all ( section 4.2 ).

One way to tackle the second horn of Hume’s dilemma is to reject premise P6 , which rules out circular arguments. Some have argued that certain kinds of circular arguments would provide an acceptable justification for the inductive inference. Since the justification would then itself be an inductive one, this approach is often referred to as an “inductive justification of induction”.

First we should examine how exactly the Humean circularity supposedly arises. Take the simple case of enumerative inductive inference that follows the following pattern ( X ):

Most observed F s have been G s

Therefore: Most F s are G s.

Hume claims that such arguments presuppose the Uniformity Principle (UP). According to premises P7 and P8 , this supposition also needs to be supported by an argument in order that the inductive inference be justified. A natural idea is that we can argue for the Uniformity Principle on the grounds that “it works”. We know that it works, because past instances of arguments which relied upon it were found to be successful. This alone however is not sufficient unless we have reason to think that such arguments will also be successful in the future. That claim must itself be supported by an inductive argument ( S ):

Most arguments of form X that rely on UP have succeeded in the past.

Therefore, most arguments of form X that rely on UP succeed.

But this argument itself depends on the UP, which is the very supposition which we were trying to justify.

As we have seen in section 2 , some reject Hume’s claim that all inductive inferences presuppose the UP. However, the argument that basing the justification of the inductive inference on a probable argument would result in circularity need not rely on this claim. The circularity concern can be framed more generally. If argument S relies on something which is already presupposed in inference X , then argument S cannot be used to justify inference X . The question though is what precisely the something is.

Some authors have argued that in fact S does not rely on any premise or even presupposition that would require us to already know the conclusion of X . S is then not a “premise circular” argument. Rather, they claim, it is “rule-circular”—it relies on a rule of inference in order to reach the conclusion that that very rule is reliable. Suppose we adopt the rule R which says that when it is observed that most F s are G s, we should infer that most F s are G s. Then inference X relies on rule R . We want to show that rule R is reliable. We could appeal to the fact that R worked in the past, and so, by an inductive argument, it will also work in the future. Call this argument S *:

Most inferences following rule R have been successful

Therefore, most inferences following R are successful.

Since this argument itself uses rule R , using it to establish that R is reliable is rule-circular.

Some authors have then argued that although premise-circularity is vicious, rule-circularity is not (Cleve 1984; Papineau 1992). One reason for thinking rule-circularity is not vicious would be if it is not necessary to know or even justifiably believe that rule R is reliable in order to move to a justified conclusion using the rule. This is a claim made by externalists about justification (Cleve 1984). They say that as long as R is in fact reliable, one can form a justified belief in the conclusion of an argument relying on R , as long as one has justified belief in the premises.

If one is not persuaded by the externalist claim, one might attempt to argue that rule circularity is benign in a different fashion. For example, the requirement that a rule be shown to be reliable without any rule-circularity might appear unreasonable when the rule is of a very fundamental nature. As Lange puts it:

It might be suggested that although a circular argument is ordinarily unable to justify its conclusion, a circular argument is acceptable in the case of justifying a fundamental form of reasoning. After all, there is nowhere more basic to turn, so all that we can reasonably demand of a fundamental form of reasoning is that it endorse itself. (Lange 2011: 56)

Proponents of this point of view point out that even deductive inference cannot be justified deductively. Consider Lewis Carroll’s dialogue between Achilles and the Tortoise (Carroll 1895). Achilles is arguing with a Tortoise who refuses to perform modus ponens . The Tortoise accepts the premise that p , and the premise that p implies q but he will not accept q . How can Achilles convince him? He manages to persuade him to accept another premise, namely “if p and p implies q , then q ”. But the Tortoise is still not prepared to infer to q . Achilles goes on adding more premises of the same kind, but to no avail. It appears then that modus ponens cannot be justified to someone who is not already prepared to use that rule.

It might seem odd if premise circularity were vicious, and rule circularity were not, given that there appears to be an easy interchange between rules and premises. After all, a rule can always, as in the Lewis Carroll story, be added as a premise to the argument. But what the Carroll story also appears to indicate is that there is indeed a fundamental difference between being prepared to accept a premise stating a rule (the Tortoise is happy to do this), and being prepared to use that rule (this is what the Tortoise refuses to do).

Suppose that we grant that an inductive argument such as S (or S *) can support an inductive inference X without vicious circularity. Still, a possible objection is that the argument simply does not provide a full justification of X . After all, less sane inference rules such as counterinduction can support themselves in a similar fashion. The counterinductive rule is CI:

Most observed A s are B s.

Therefore, it is not the case that most A s are B s.

Consider then the following argument CI*:

Most CI arguments have been unsuccessful

Therefore, it is not the case that most CI arguments are unsuccessful, i.e., many CI arguments are successful.

This argument therefore establishes the reliability of CI in a rule-circular fashion (see Salmon 1963).

Argument S can be used to support inference X , but only for someone who is already prepared to infer inductively by using S . It cannot convince a skeptic who is not prepared to rely upon that rule in the first place. One might think then that the argument is simply not achieving very much.

The response to these concerns is that, as Papineau puts it, the argument is “not supposed to do very much” (Papineau 1992: 18). The fact that a counterinductivist counterpart of the argument exists is true, but irrelevant. It is conceded that the argument cannot persuade either a counterinductivist, or a skeptic. Nonetheless, proponents of the inductive justification maintain that there is still some added value in showing that inductive inferences are reliable, even when we already accept that there is nothing problematic about them. The inductive justification of induction provides a kind of important consistency check on our existing beliefs.

It is possible to go even further in an attempt to dismantle the Humean circularity. Maybe inductive inferences do not even have a rule in common. What if every inductive inference is essentially unique? This can be seen as rejecting Hume’s premise P5 . Okasha, for example, argues that Hume’s circularity problem can be evaded if there are “no rules” behind induction (Okasha 2005a,b). Norton puts forward the similar idea that all inductive inferences are material, and have nothing formal in common (Norton 2003, 2010, 2021).

Proponents of such views have attacked Hume’s claim that there is a UP on which all inductive inferences are based. There have long been complaints about the vagueness of the Uniformity Principle (Salmon 1953). The future only resembles the past in some respects, but not others. Suppose that on all my birthdays so far, I have been under 40 years old. This does not give me a reason to expect that I will be under 40 years old on my next birthday. There seems then to be a major lacuna in Hume’s account. He might have explained or described how we draw an inductive inference, on the assumption that it is one we can draw. But he leaves untouched the question of how we distinguish between cases where we extrapolate a regularity legitimately, regarding it as a law, and cases where we do not.

Nelson Goodman is often seen as having made this point in a particularly vivid form with his “new riddle of induction” (Goodman 1955: 59–83). Suppose we define a predicate “grue” in the following way. An object is “grue” when it is green if observed before time t and blue otherwise. Goodman considers a thought experiment in which we observe a bunch of green emeralds before time t . We could describe our results by saying all the observed emeralds are green. Using a simple enumerative inductive schema, we could infer from the result that all observed emeralds are green, that all emeralds are green. But equally, we could describe the same results by saying that all observed emeralds are grue. Then using the same schema, we could infer from the result that all observed emeralds are grue, that all emeralds are grue. In the first case, we expect an emerald observed after time t to be green, whereas in the second, we expect it to be blue. Thus the two predictions are incompatible. Goodman claims that what Hume omitted to do was to give any explanation for why we project predicates like “green”, but not predicates like “grue”. This is the “new riddle”, which is often taken to be a further problem of induction that Hume did not address.

One moral that could be taken from Goodman is that there is not one general Uniformity Principle that all probable arguments rely upon (Sober 1988; Norton 2003; Okasha 2001, 2005a,b, Jackson 2019). Rather each inductive inference presupposes some more specific empirical presupposition. A particular inductive inference depends on some specific way in which the future resembles the past. It can then be justified by another inductive inference which depends on some quite different empirical claim. This will in turn need to be justified—by yet another inductive inference. The nature of Hume’s problem in the second horn is thus transformed. There is no circularity. Rather there is a regress of inductive justifications, each relying on their own empirical presuppositions (Sober 1988; Norton 2003; Okasha 2001, 2005a,b).

One way to put this point is to say that Hume’s argument rests on a quantifier shift fallacy (Sober 1988; Okasha 2005a). Hume says that there exists a general presupposition for all inductive inferences, whereas he should have said that for each inductive inference, there is some presupposition. Different inductive inferences then rest on different empirical presuppositions, and the problem of circularity is evaded.

What will then be the consequence of supposing that Hume’s problem should indeed have been a regress, rather than a circularity? Here different opinions are possible. On the one hand, one might think that a regress still leads to a skeptical conclusion (Schurz and Thorn 2020). So although the exact form in which Hume stated his problem was not correct, the conclusion is not substantially different (Sober 1988). Another possibility is that the transformation mitigates or even removes the skeptical problem. For example, Norton argues that the upshot is a dissolution of the problem of induction, since the regress of justifications benignly terminates (Norton 2003). And Okasha more mildly suggests that even if the regress is infinite, “Perhaps infinite regresses are less bad than vicious circles after all” (Okasha 2005b: 253).

Any dissolution of Hume’s circularity does not depend only on arguing that the UP should be replaced by empirical presuppositions which are specific to each inductive inference. It is also necessary to establish that inductive inferences share no common rules—otherwise there will still be at least some rule-circularity. Okasha suggests that the Bayesian model of belief-updating is an illustration how induction can be characterized in a rule-free way, but this is problematic, since in this model all inductive inferences still share the common rule of Bayesian conditionalisation. Norton’s material theory of induction postulates a rule-free characterization of induction, but it is not clear whether it really can avoid any role for general rules (Achinstein 2010, Kelly 2010, Worrall 2010).

5. Alternative Conceptions of Justification

Hume is usually read as delivering a negative verdict on the possibility of justifying inference I , via a premise such as P8 , though as we have seen in section section 2 , some have questioned whether Hume is best interpreted as drawing a conclusion about justification of inference I at all. In this section we examine approaches which question in different ways whether premise P8 really does give a valid necessary condition for justification of inference I and propose various alternative conceptions of justification.

One approach has been to turn to general reflection on what is even needed for justification of an inference in the first place. For example, Wittgenstein raised doubts over whether it is even meaningful to ask for the grounds for inductive inferences.

If anyone said that information about the past could not convince him that something would happen in the future, I should not understand him. One might ask him: what do you expect to be told, then? What sort of information do you call a ground for such a belief? … If these are not grounds, then what are grounds?—If you say these are not grounds, then you must surely be able to state what must be the case for us to have the right to say that there are grounds for our assumption…. (Wittgenstein 1953: 481)

One might not, for instance, think that there even needs to be a chain of reasoning in which each step or presupposition is supported by an argument. Wittgenstein took it that there are some principles so fundamental that they do not require support from any further argument. They are the “hinges” on which enquiry turns.

Out of Wittgenstein’s ideas has developed a general notion of “entitlement”, which is a kind of rational warrant to hold certain propositions which does not come with the same requirements as “justification”. Entitlement provides epistemic rights to hold a proposition, without responsibilities to base the belief in it on an argument. Crispin Wright (2004) has argued that there are certain principles, including the Uniformity Principle, that we are entitled in this sense to hold.

Some philosophers have set themselves the task of determining a set or sets of postulates which form a plausible basis for inductive inferences. Bertrand Russell, for example, argued that five postulates lay at the root of inductive reasoning (Russell 1948). Arthur Burks, on the other hand, proposed that the set of postulates is not unique, but there may be multiple sets of postulates corresponding to different inductive methods (Burks 1953, 1955).

The main objection to all these views is that they do not really solve the problem of induction in a way that adequately secures the pillars on which inductive inference stands. As Salmon puts it, “admission of unjustified and unjustifiable postulates to deal with the problem is tantamount to making scientific method a matter of faith” (Salmon 1966: 48).

Rather than allowing undefended empirical postulates to give normative support to an inductive inference, one could instead argue for a completely different conception of what is involved in justification. Like Wittgenstein, later ordinary language philosophers, notably P.F. Strawson, also questioned what exactly it means to ask for a justification of inductive inferences (Strawson 1952). This has become known as the “Ordinary language dissolution” of the problem of induction.

Strawson points out that it could be meaningful to ask for a deductive justification of inductive inferences. But it is not clear that this is helpful since this is effectively “a demand that induction shall be shown to be really a kind of deduction” (Strawson 1952: 230). Rather, Strawson says, when we ask about whether a particular inductive inference is justified, we are typically judging whether it conforms to our usual inductive standards. Suppose, he says, someone has formed the belief by inductive inference that All f ’s are g . Strawson says that if that person is asked for their grounds or reasons for holding that belief,

I think it would be felt to be a satisfactory answer if he replied: “Well, in all my wide and varied experience I’ve come across innumerable cases of f and never a case of f which wasn’t a case of g ”. In saying this, he is clearly claiming to have inductive support, inductive evidence, of a certain kind, for his belief. (Strawson 1952)

That is just because inductive support, as it is usually understood, simply consists of having observed many positive instances in a wide variety of conditions.

In effect, this approach denies that producing a chain of reasoning is a necessary condition for justification. Rather, an inductive inference is justified if it conforms to the usual standards of inductive justification. But, is there more to it? Might we not ask what reason we have to rely on those inductive standards?

It surely makes sense to ask whether a particular inductive inference is justified. But the answer to that is fairly straightforward. Sometimes people have enough evidence for their conclusions and sometimes they do not. Does it also make sense to ask about whether inductive procedures generally are justified? Strawson draws the analogy between asking whether a particular act is legal. We may answer such a question, he says, by referring to the law of the land.

But it makes no sense to inquire in general whether the law of the land, the legal system as a whole, is or is not legal. For to what legal standards are we appealing? (Strawson 1952: 257)

According to Strawson,

It is an analytic proposition that it is reasonable to have a degree of belief in a statement which is proportional to the strength of the evidence in its favour; and it is an analytic proposition, though not a proposition of mathematics, that, other things being equal, the evidence for a generalisation is strong in proportion as the number of favourable instances, and the variety of circumstances in which they have been found, is great. So to ask whether it is reasonable to place reliance on inductive procedures is like asking whether it is reasonable to proportion the degree of one’s convictions to the strength of the evidence. Doing this is what “being reasonable” means in such a context. (Strawson 1952: 256–57)

Thus, according to this point of view, there is no further question to ask about whether it is reasonable to rely on inductive inferences.

The ordinary language philosophers do not explicitly argue against Hume’s premise P8 . But effectively what they are doing is offering a whole different story about what it would mean to be justified in believing the conclusion of inductive inferences. What is needed is just conformity to inductive standards, and there is no real meaning to asking for any further justification for those.

The main objection to this view is that conformity to the usual standards is insufficient to provide the needed justification. What we need to know is whether belief in the conclusion of an inductive inference is “epistemically reasonable or justified in the sense that …there is reason to think that it is likely to be true” (BonJour 1998: 198). The problem Hume has raised is whether, despite the fact that inductive inferences have tended to produce true conclusions in the past, we have reason to think the conclusion of an inductive inference we now make is likely to be true. Arguably, establishing that an inductive inference is rational in the sense that it follows inductive standards is not sufficient to establish that its conclusion is likely to be true. In fact Strawson allows that there is a question about whether “induction will continue to be successful”, which is distinct from the question of whether induction is rational. This question he does take to hinge on a “contingent, factual matter” (Strawson 1952: 262). But if it is this question that concerned Hume, it is no answer to establish that induction is rational, unless that claim is understood to involve or imply that an inductive inference carried out according to rational standards is likely to have a true conclusion.

Another solution based on an alternative criterion for justification is the “pragmatic” approach initiated by Reichenbach (1938 [2006]). Reichenbach did think Hume’s argument unassailable, but nonetheless he attempted to provide a weaker kind of justification for induction. In order to emphasize the difference from the kind of justification Hume sought, some have given it a different term and refer to Reichenbach’s solution as a “vindication”, rather than a justification of induction (Feigl 1950; Salmon 1963).

Reichenbach argued that it was not necessary for the justification of inductive inference to show that its conclusion is true. Rather “the proof of the truth of the conclusion is only a sufficient condition for the justification of induction, not a necessary condition” (Reichenbach 2006: 348). If it could be shown, he says, that inductive inference is a necessary condition of success, then even if we do not know that it will succeed, we still have some reason to follow it. Reichenbach makes a comparison to the situation where a man is suffering from a disease, and the physician says “I do not know whether an operation will save the man, but if there is any remedy, it is an operation” (Reichenbach 1938 [2006: 349]). This provides some kind of justification for operating on the man, even if one does not know that the operation will succeed.

In order to get a full account, of course, we need to say more about what is meant for a method to have “success”, or to “work”. Reichenbach thought that this should be defined in relation to the aim of induction. This aim, he thought, is “ to find series of events whose frequency of occurrence converges towards a limit ” (1938 [2006: 350]).

Reichenbach applied his strategy to a general form of “statistical induction” in which we observe the relative frequency \(f_n\) of a particular event in n observations and then form expectations about the frequency that will arise when more observations are made. The “inductive principle” then states that if after a certain number of instances, an observed frequency of \(m/n\) is observed, for any prolongation of the series of observations, the frequency will continue to fall within a small interval of \(m/n\). Hume’s examples are special cases of this principle, where the observed frequency is 1. For example, in Hume’s bread case, suppose bread was observed to nourish n times out of n (i.e. an observed frequency of 100%), then according to the principle of induction, we expect that as we observe more instances, the frequency of nourishing ones will continue to be within a very small interval of 100%. Following this inductive principle is also sometimes referred to as following the “straight rule”. The problem then is to justify the use of this rule.

Reichenbach argued that even if Hume is right to think that we cannot be justified in thinking for any particular application of the rule that the conclusion is likely to be true, for the purposes of practical action we do not need to establish this. We can instead regard the inductive rule as resulting in a “posit”, or statement that we deal with as if it is true. We posit a certain frequency f on the basis of our evidence, and this is like making a wager or bet that the frequency is in fact f . One strategy for positing frequencies is to follow the rule of induction.

Reichenbach proposes that we can show that the rule of induction meets his weaker justification condition. This does not require showing that following the inductive principle will always work. It is possible that the world is so disorderly that we cannot construct series with any limits. In that case, neither the inductive principle, nor any other method will succeed. But, he argues, if there is a limit, by following the inductive principle we will eventually find it. There is some element of a series of observations, beyond which the principle of induction will lead to the true value of the limit. Although the inductive rule may give quite wrong results early in the sequence, as it follows chance fluctuations in the sample frequency, it is guaranteed to eventually approximate the limiting frequency, if such a limit exists. Therefore, the rule of induction is justified as an instrument of positing because it is a method of which we know that if it is possible to achieve the aim of inductive inference we shall do so by means of this method (Reichenbach 1949: 475).

One might question whether Reichenbach has achieved his goal of showing that following the inductive rule is a necessary condition of success. In order to show that, one would also need to establish that no other methods can also achieve the aim. But, as Reichenbach himself recognises, many other rules of inference as well as the straight rule may also converge on the limit (Salmon 1966: 53). In fact, any method which converges asymptotically to the straight rule also does so. An easily specified class of such rules are those which add to the inductive rule a function \(c_n\) in which the \(c_n\) converge to zero with increasing n .

Reichenbach makes two suggestions aimed at avoiding this problem. On the one hand, he claims, since we have no real way to pick between methods, we might as well just use the inductive rule since it is “easier to handle, owing to its descriptive simplicity”. He also claims that the method which embodies the “smallest risk” is following the inductive rule (Reichenbach 1938 [2006: 355–356]).

There is also the concern that there could be a completely different kind of rule which converges on the limit. We can consider, for example, the possibility of a soothsayer or psychic who is able to predict future events reliably. Here Reichenbach argues that induction is still necessary in such a case, because it has to be used to check whether the other method works. It is only by using induction, Reichenbach says, that we could recognise the reliability of the alternative method, by examining its track record.

In assessing this argument, it is helpful to distinguish between levels at which the principle of induction can be applied. Following Skyrms (2000), we may distinguish between level 1, where candidate methods are applied to ordinary events or individuals, and level 2, where they are applied not to individuals or events, but to the arguments on level 1. Let us refer to “object-induction” when the inductive principle is applied at level 1, and “meta-induction” when it is applied at level 2. Reichenbach’s response does not rule out the possibility that another method might do better than object-induction at level 1. It only shows that the success of that other method may be recognised by a meta-induction at level 2 (Skyrms 2000). Nonetheless, Reichenbach’s thought was later picked up and developed into the suggestion that a meta-inductivist who applies induction not only at the object level to observations, but also to the success of others’ methods, might by those means be able to do as well predictively as the alternative method (Schurz 2008; see section 5.5 for more discussion of meta-induction).

Reichenbach’s justification is generally taken to be a pragmatic one, since though it does not supply knowledge of a future event, it supplies a sufficient reason for action (Reichenbach 1949: 481). One might question whether a pragmatic argument can really deliver an all-purpose, general justification for following the inductive rule. Surely a pragmatic solution should be sensitive to differences in pay-offs that depend on the circumstances. For example, Reichenbach offers the following analogue to his pragmatic justification:

We may compare our situation to that of a man who wants to fish in an unexplored part of the sea. There is no one to tell him whether or not there are fish in this place. Shall he cast his net? Well, if he wants to fish in that place, I should advise him to cast the net, to take the chance at least. It is preferable to try even in uncertainty than not to try and be certain of getting nothing. (Reichenbach 1938 [2006: 362–363])

As Lange points out, the argument here “presumes that there is no cost to trying”. In such a situation, “the fisherman has everything to gain and nothing to lose by casting his net” (Lange 2011: 77). But if there is some significant cost to making the attempt, it may not be so clear that the most rational course of action is to cast the net. Similarly, whether or not it would make sense to adopt the policy of making no predictions, rather than the policy of following the inductive rule, may depend on what the practical penalties are for being wrong. A pragmatic solution may not be capable of offering rationale for following the inductive rule which is applicable in all circumstances.

Another question is whether Reichenbach has specified the aim of induction too narrowly. Finding series of events whose frequency of occurrence converges to a limit ties the vindication to the long-run, while allowing essentially no constraint on what can be posited in the short-run. Yet it is in the short run that inductive practice actually occurs and where it really needs justification (BonJour 1998: 194; Salmon 1966: 53).

Formal learning theory can be regarded as a kind of extension of the Reichenbachian programme. It does not offer justifications for inductive inferences in the sense of giving reasons why they should be taken as likely to provide a true conclusion. Rather it offers a “means-ends” epistemology -- it provides reasons for following particular methods based on their optimality in achieving certain desirable epistemic ends, even if there is no guarantee that at any given stage of inquiry the results they produce are at all close to the truth (Schulte 1999).

Formal learning theory is particularly concerned with showing that methods are “logically reliable” in the sense that they arrive at the truth given any sequence of data consistent with our background knowledge (Kelly 1996). However, it goes further than this. As we have just seen, one of the problems for Reichenbach was that there are too many rules which converge in the limit to the true frequency. Which one should we then choose in the short-run? Formal learning theory broadens Reichenbach’s general strategy by considering what happens if we have other epistemic goals besides long-run convergence to the truth. In particular, formal learning theorists have considered the goal of getting to the truth as efficiently, or quickly, as possible, as well as the goal of minimising the number of mind-changes, or retractions along the way. It has then been argued that the usual inductive method, which is characterised by a preference for simpler hypotheses (Occam’s razor), can be justified since it is the unique method which meets the standards for getting to the truth in the long run as efficiently as possible, with a minimum number of retractions (Kelly 2007).

Steel (2010) has proposed that the Principle of Induction (understood as a rule which makes inductive generalisations along the lines of the Straight Rule) can be given a means-ends justification by showing that following it is both necessary and sufficient for logical reliability. The proof is an a priori mathematical one, thus it allegedly avoids the circularity of Hume’s second horn. However, Steel also does not see the approach as an attempt to grasp Hume’s first horn, since the proof is only relative to a certain choice of epistemic ends.

As with other results in formal learning theory, this solution is also only valid relative to a given hypothesis space and conception of possible sequences of data. For this reason, some have seen it as not addressing Hume’s problem of giving grounds for a particular inductive inference (Howson 2011). An alternative attitude is that it does solve a significant part of Hume’s problem (Steel 2010). There is a similar dispute over formal learning theory’s treatment of Goodman’s riddle (Chart 2000, Schulte 2017).

Another approach to pursuing a broadly Reichenbachian programme is Gerhard Schurz’s strategy based on meta-induction (Schurz 2008, 2017, 2019). Schurz draws a distinction between applying inductive methods at the level of events—so-called “object-level” induction (OI), and applying inductive methods at the level of competing prediction methods—so-called “meta-induction” (MI). Whereas object-level inductive methods make predictions based on the events which have been observed to occur, meta-inductive methods make predictions based on aggregating the predictions of different available prediction methods according to their success rates. Here, the success rate of a method is defined according to some precise way of scoring success in making predictions.

The starting point of the meta-inductive approach is that the aim of inductive inference is not just, as Reichenbach had it, finding long-run limiting frequencies, but also predicting successfully in both the long and short run. Even if Hume has precluded showing that the inductive method is reliable in achieving successful prediction, perhaps it can still be shown that it is “predictively optimal”. A method is “predictively optimal” if it succeeds best in making successful predictions out of all competing methods, no matter what data is received. Schurz brings to bear results from the regret-based learning framework in machine learning that show that there is a meta-inductive strategy that is predictively optimal among all predictive methods that are accessible to an epistemic agent (Cesa-Bianchi and Lugosi 2006, Schurz 2008, 2017, 2019). This meta-inductive strategy, which Schurz calls “wMI”, predicts a weighted average of the predictions of the accessible methods, where the weights are “attractivities”, which measure the difference between the method’s own success rate and the success rate of wMI.

The main result is that the wMI strategy is long-run optimal in the sense that it converges to the maximum success rate of the accessible prediction methods. Worst-case bounds for short-run performance can also be derived. The optimality result forms the basis for an a priori means-ends justification for the use of wMI. Namely, the thought is, it is reasonable to use wMI, since it achieves the best success rates possible in the long run out of the given methods.

Schurz also claims that this a priori justification of wMI, together with the contingent fact that inductive methods have so far been much more successful than non-inductive methods, gives rise to an a posteriori non-circular justification of induction. Since wMI will achieve in the long run the maximal success rate of the available prediction methods, it is reasonable to use it. But as a matter of fact, object-inductive prediction methods have been more successful than non-inductive methods so far. Therefore Schurz says “it is meta-inductively justified to favor object-inductivistic strategies in the future” (Schurz 2019: 85). This justification, he claims, is not circular because meta-induction has an a priori independent justification. The idea is that since it is a priori justified to use wMI, it is also a priori justified to use the maximally successful method at the object level. Since it turns out that that the maximally successful method is object-induction, then we have a non-circular a posteriori argument that it is reasonable to use object-induction.

Schurz’s original theorems on the optimality of wMI apply to the case where there are finitely many predictive methods. One point of discussion is whether this amounts to an important limitation on its claims to provide a full solution of the problem of induction. The question then is whether it is necessary that the optimality results be extended to an infinite, or perhaps an expanding pool of strategies (Eckhardt 2010, Sterkenburg 2019, Schurz 2021a).

Another important issue concerns what it means for object-induction to be “meta-inductively justified”. The meta-inductive strategy wMI and object-induction are clearly different strategies. They could result in different predictions tomorrow, if OI would stop working and another method would start to do better. In that case, wMI would begin to favour the other method, and wMI would start to come apart from OI. The optimality results provide a reason to follow wMI. How exactly does object-induction inherit that justification? At most, it seems that we get a justification for following OI on the next time-step, on the grounds that OI’s prediction approximately coincides with that of wMI (Sterkenburg 2020, Sterkenburg (forthcoming)). However, this requires a stronger empirical postulate than simply the observation that OI has been more successful than non-inductive methods. It also requires something like that “as a matter of empirical fact, the strategy OI has been so much more successful than its competitors, that the meta-inductivist attributes it such a large share of the total weight that its prediction (approximately) coincides with OI’s prediction” (Sterkenburg 2020: 538). Furthermore, even if we allow that the empirical evidence does back up such a strong claim, the issue remains that the meta-inductive justification is in support of following the strategy of meta-induction, not in support of the strategy of following OI (Sterkenburg (2020), sec. 3.3.2).

So far we have considered the various ways in which we might attempt to solve the problem of induction by resisting one or other premise of Hume’s argument. Some philosophers have however seen his argument as unassailable, and have thus accepted that it does lead to inductive skepticism, the conclusion that inductive inferences cannot be justified. The challenge then is to find a way of living with such a radical-seeming conclusion. We appear to rely on inductive inference ubiquitously in daily life, and it is also generally thought that it is at the very foundation of the scientific method. Can we go on with all this, whilst still seriously thinking none of it is justified by any rational argument?

One option here is to argue, as does Nicholas Maxwell, that the problem of induction is posed in an overly restrictive context. Maxwell argues that the problem does not arise if we adopt a different conception of science than the ‘standard empiricist’ one, which he denotes ‘aim-oriented empiricism’ (Maxwell 2017).

Another option here is to think that the significance of the problem of induction is somehow restricted to a skeptical context. Hume himself seems to have thought along these lines. For instance he says:

Nature will always maintain her rights, and prevail in the end over any abstract reasoning whatsoever. Though we should conclude, for instance, as in the foregoing section, that, in all reasonings from experience, there is a step taken by the mind, which is not supported by any argument or process of the understanding; there is no danger, that these reasonings, on which almost all knowledge depends, will ever be affected by such a discovery. (E. 5.1.2)

Hume’s purpose is clearly not to argue that we should not make inductive inferences in everyday life, and indeed his whole method and system of describing the mind in naturalistic terms depends on inductive inferences through and through. The problem of induction then must be seen as a problem that arises only at the level of philosophical reflection.

Another way to mitigate the force of inductive skepticism is to restrict its scope. Karl Popper, for instance, regarded the problem of induction as insurmountable, but he argued that science is not in fact based on inductive inferences at all (Popper 1935 [1959]). Rather he presented a deductivist view of science, according to which it proceeds by making bold conjectures, and then attempting to falsify those conjectures. In the simplest version of this account, when a hypothesis makes a prediction which is found to be false in an experiment, the hypothesis is rejected as falsified. The logic of this procedure is fully deductive. The hypothesis entails the prediction, and the falsity of the prediction refutes the hypothesis by modus tollens. Thus, Popper claimed that science was not based on the extrapolative inferences considered by Hume. The consequence then is that it is not so important, at least for science, if those inferences would lack a rational foundation.

Popper’s account appears to be incomplete in an important way. There are always many hypotheses which have not yet been refuted by the evidence, and these may contradict one another. According to the strictly deductive framework, since none are yet falsified, they are all on an equal footing. Yet, scientists will typically want to say that one is better supported by the evidence than the others. We seem to need more than just deductive reasoning to support practical decision-making (Salmon 1981). Popper did indeed appeal to a notion of one hypothesis being better or worse “corroborated” by the evidence. But arguably, this took him away from a strictly deductive view of science. It appears doubtful then that pure deductivism can give an adequate account of scientific method.

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• Vickers, John, “The Problem of Induction,” Stanford Encyclopedia of Philosophy (Spring 2018 Edition), Edward N. Zalta (ed.), URL = < https://plato.stanford.edu/archives/spr2018/entries/induction-problem/ >. [This was the previous entry on the problem of induction in the Stanford Encyclopedia of Philosophy — see the version history .]
• Teaching Theory of Knowledge: Probability and Induction , organization of topics and bibliography by Brad Armendt (Arizona State University) and Martin Curd (Purdue).
• Forecasting Principles , A brief survey of prediction markets.

Bayes’ Theorem | belief, formal representations of | confirmation | epistemology, formal | Feigl, Herbert | Goodman, Nelson | Hume, David | Kant, Immanuel: and Hume on causality | laws of nature | learning theory, formal | logic: inductive | Popper, Karl | probability, interpretations of | Reichenbach, Hans | simplicity | skepticism | statistics, philosophy of | Strawson, Peter Frederick

Acknowledgments

Particular thanks are due to Don Garrett and Tom Sterkenburg for helpful feedback on a draft of this entry. Thanks also to David Atkinson, Simon Friederich, Jeanne Peijnenburg, Theo Kuipers and Jan-Willem Romeijn for comments.

Copyright © 2022 by Leah Henderson < l . henderson @ rug . nl >

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8.2: Deductive Reasoning + Inductive Reasoning

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• Mehgan Andrade and Neil Walker
• College of the Canyons

Deductive Reasoning

Deductive reasoning is concerned with syllogisms in which the conclusion follows logically from the premises. The following example about Knut makes this process clear:

1. Premise: Knut knows: If it is warm, one needs shorts and T-Shirts.

2. Premise: He also knows that it is warm in Spain during summer.

Conclusion: Therefore, Knut reasons that he needs shorts and T-Shirts in Spain.

In the given example it is obvious that the premises are about rather general information and the resulting conclusion is about a more special case which can be inferred from the two premises. Hereafter it is differentiated between the two major kinds of syllogisms, namely categorical and conditional ones.

Categorical Syllogisms

In categorical syllogisms the statements of the premises begin typically with “all”, “none” or “some” and the conclusion starts with “therefore” or “hence”. These kinds of syllogisms fulfill the task of describing a relationship between two categories. In the example given above in the introduction of deductive reasoning these categories are Spain and the need for shorts and T- Shirts. Two different approaches serve the study of categorical syllogisms which are the normative approach and the descriptive approach.

The normative approach

The normative approach is based on logic and deals with the problem of categorizing conclusions as either valid or invalid. “Valid” means that the conclusion follows logically from the premises whereas “invalid” means the contrary. Two basic principles and a method called Euler Circles (Figure 1) have been developed to help judging about the validity. The first principle was created by Aristotle and says “If the two premises are true, the conclusion of a valid syllogism must be true” (cp. Goldstein, 2005). The second principle describes that “The validity of a syllogism is determined only by its form, not its content.” These two principles explain why the following syllogism is (surprisingly) valid:

All flowers are animals. All animals can jump. Therefore, all flowers can jump.

Even though it is quite obvious that the first premise is not true and further that the conclusion is not true, the whole syllogism is still valid. Applying formal logic to the syllogism in the example, the conclusion is valid.

Due to this precondition it is possible to display a syllogism formally with symbols or letters and explain its relationship graphically with the help of diagrams. There are various ways to demonstrate a premise graphically. Starting with a circle to represent the first premise and adding one or more circles for the second one (Figure 1), the crucial move is to compare the constructed diagrams with the conclusion. It should be clearly laid out whether the diagrams are contradictory or not. Agreeing with one another, the syllogism is valid. The displayed syllogism (Figure 1) is obviously valid. The conclusion shows that everything that can jump contains animals which again contains flowers. This agrees with the two premises which point out that flowers are animals and that these are able to jump. The method of Euler Circles is a good device to make syllogisms better conceivable.

The descriptive approach

The descriptive approach is concerned with estimating people´s ability of judging validity and explaining judging errors. This psychological approach uses two methods in order to determine people`s performance:

Method of evaluation : People are given two premises, a conclusion and the task to judge whether the syllogism is valid or not. (preferred one)

Method of production : Participants are supplied with two premises and asked to develop a logically valid conclusion. (if possible)

While using the method of evaluation researchers found typical misjudgments about syllogisms. Premises starting with “All”, “Some” or “No” imply a special atmosphere and influence a person in the process of decision making. One mistake often occurring is judging a syllogism incorrectly as valid, in which the two premises as well as the conclusion starts with “All”. The influence of the provided atmosphere leads to the right decision at most times, but is definitely not reliable and guides the person to a rash decision. This phenomenon is called the atmosphere effect .

In addition to the form of a syllogism, the content is likely to influence a person’s decision as well and causes the person to neglect his logical thinking. The belief bias states that people tend to judge syllogisms with believable conclusions as valid, while they tend to judge syllogisms with unbelievable conclusions as invalid. Given a conclusion as like “Some bananas are pink”, hardly any participants would judge the syllogism as valid, even though it might be valid according to its premises (e.g. Some bananas are fruits. All fruits are pink.)

Mental models of deductive reasoning

It is still not possible to consider what mental processes might occur when people are trying to determine whether a syllogism is valid. After researchers observed that Euler Circles can be used to determine the validity of a syllogism, Phillip Johnson–Laird (1999) wondered whether people would use such circles naturally without any instruction how to use them. At the same time he found out that they do not work for some more complex syllogisms and that a problem can be solved by applying logical rules, but most people solve them by imagining the situation. This is the basic idea of people using mental models – a specific situation that is represented in a person’s mind that can be used to help determine the validity of syllogisms – to solve deductive reasoning problems. The basic principle behind the Mental Model Theory is: A conclusion is valid only if it cannot be refuted by any mode of the premises. This theory is rather popular because it makes predictions that can be tested and because it can be applied without any knowledge about rules of logic. But there are still problems facing researchers when trying to determine how people reason about syllogisms. These problems include the fact that a variety of different strategies are used by people in reasoning and that some people are better in solving syllogisms than others.

Effects of culture on deductive reasoning

People can be influenced by the content of syllogisms rather than by focusing on logic when judging their validity. Psychologists have wondered whether people are influenced by their cultures when judging. Therefore, they have done cross–cultural experiments in which reasoning problems were presented to people of different cultures. They observed that people from different cultures judge differently to these problems. People use evidence from their own experience (empirical evidence) and ignore evidence presented in the syllogism (theoretical evidence).

Conditional syllogisms

Another type of syllogisms is called “conditional syllogism”. Just like the categorical one, it also has two premises and a conclusion. In difference the first premise has the form “If … then”.

Syllogisms like this one are common in everyday life. Consider the following example from the story about Knut:

1. Premise: If it is raining, Knut`s wife gets wet.

2. Premise: It is raining.

Conclusion: Therefore, Knut`s wife gets wet.

Conditional syllogisms are typically given in the abstract form: “If p then q”, where “p” is called the antecedent and “q” the consequent .

Forms of conditional syllogisms

There are four major forms of conditional syllogisms, namely Modus Ponens, Modus Tollens, Denying The Antecedent and Affirming The Consequent. Obviously, the validity of the syllogisms with valid conclusions is easier to judge in a correct manner than the validity of the ones with invalid conclusions. The conclusion in the instance of the modus ponens isapparently valid. In the example it is very clear that Knut`s wife gets wet, if it is raining.

The validity of the modus tollens is more difficult to recognize. Referring to the example, in the case that Knut`s wife does not get wet it can`t be raining. Because the first premise says that if it is raining, she gets wet. So the reason for Knut`s wife not getting wet is that it is not raining. Consequently, the conclusion is valid. The validity of the remaining two kinds of conditional syllogisms is judged correctly only by 40% of people. If the method of denying the antecedent is applied, the second premise says that it is not raining. But from this fact it follows not logically that Knut`s wife does not get wet – obviously rain is not the only reason for her to get wet. It could also be the case that the sun is shining and Knut tests his new water pistol and makes her wet. So, this kind of conditional syllogism does not lead to a valid conclusion. Affirming the consequent in the case of the given example means that the second premise says that Knut`s wife gets wet. But again the reason for this can be circumstances apart from rain. So, it follows not logically that it is raining. In consequence, the conclusion of this syllogism is invalid. The four kinds of syllogisms have shown that it is not always easy to make correct judgments concerning the validity of the conclusions. The following passages will deal with other errors people make during the process of conditional reasoning.

The Wason Selection Task

The Wason Selection Task [1] is a famous experiment which shows that people make more errors in the process of reasoning, if it is concerned with abstract items than if it involves real- world items (Wason, 1966). In the abstract version of the Wason Selection Task four cards are shown to the participants with each a letter on one side and a number on the other (Figure 3, yellow cards). The task is to indicate the minimum number of cards that have to be turned over to test whether the following rule is observed: “If there is a vowel on one side then there is an even number on the other side”. 53% of participants selected the ‘E’ card which is correct, because turning this card over is necessary for testing the truth of the rule. However still another card needs to be turned over. 64 % indicated that the ‘4’ card has to be turned over which is not right. Only 4% of participants answered correctly that the ‘7’ card needs to be turned over in addition to the ‘E’. The correctness of turning over these two cards becomes more obvious if the same task is stated in terms of real-world items instead of vowels and numbers. One of the experiments for determining this was the beer/drinking-age problem used by Richard Griggs and James Cox (1982). This experiment is identical to the Wason Selection Task except that instead of numbers and letters on the cards everyday terms (beer, soda and ages) were used (Figure 3, green cards). Griggs and Cox gave the following rule to the participants: “If a person is drinking beer then he or she must be older than 19 years.” In this case 73% of participants answered in a correct way, namely that the cards with “Beer” and “14 years” on it have to be turned over to test whether the rule is kept.

Why is the performance better in the case of real–world items?

There are two different approaches which explain why participants’ performance is significantly better in the case of the beer/drinking-age problem than in the abstract version of the Wason Selection Task, namely one approach concerning permission schemas and an evolutionary approach.

The regulation: “If one is 19 years or older then he/she is allowed to drink alcohol”, is known by everyone as an experience from everyday life (also called permission schema ). As this permission schema is already learned by the participants it can be applied to the Wason Selection Task for real–world items to improve participants` performance. On the contrary such a permission schema from everyday life does not exist for the abstract version of the Wason Selection Task.

The evolutionary approach concerns the important human ability of cheater-detection . This approach states that an important aspect of human behavior especially in the past was/is the ability for two persons to cooperate in a way that is beneficial for both of them. As long as each person receives a benefit for whatever he/she does in favor of the other one, everything works well in their social exchange. But if someone cheats and receives benefit from others without giving it back, some problem arises (see also chapter 3. Evolutionary Perspective on Social Cognitions [2]). It is assumed that the property to detect cheaters has become a part of human`s cognitive makeup during evolution. This cognitive ability improves the performance in the beer/drinking-age version of the Wason Selection Task as it allows people to detect a cheating person who does not behave according to the rule. Cheater-detection does not work in the case of the abstract version of the Wason Selection Task as vowels and numbers do not behave or even cheat at all as opposed to human beings.

Inductive reasoning

In the previous sections deductive reasoning was discussed, reaching conclusions based on logical rules applied to a set of premises. However, many problems cannot be represented in a way that would make it possible to use these rules to get a conclusion. This subchapter is about a way to be able to decide in terms of these problems as well: inductive reasoning. Figure 4, Deductive and inductive reasoning Inductive reasoning is the process of making simple observations of a certain kind and applying these observations via generalization to a different problem to make a decision. Hence one infers from a special case to the general principle which is just the opposite of the procedure of deductive reasoning (Figure 3).

A good example for inductive reasoning is the following:

Premise: All crows Knut and his wife have ever seen are black. Conclusion: Therefore, they reason that all crows on earth are black.

In this example it is obvious that Knut and his wife infer from the simple observation about the crows they have seen to the general principle about all crows. Considering figure 4 this means that they infer from the subset (yellow circle) to the whole (blue circle). As in this example it is typical in a process of inductive reasoning that the premises are believed to support the conclusion, but do not ensure it.

Forms of inductive reasoning

The two different forms of inductive reasoning are "strong" and "weak" induction. The former describes that the truth of the conclusion is very likely, if the assumed premises are true. An example for this form of reasoning is the one given in the previous section. In this case it is obvious that the premise ("All crows Knut and his wife have ever seen are black") gives good evidence for the conclusion ("All crows on earth are black") to be true. But nevertheless it is still possible, although very unlikely, that not all crows are black.

On the contrary, conclusions reached by "weak induction" are supported by the premises in a rather weak manner. In this approach the truth of the premises makes the truth of the conclusion possible, but not likely.

An example for this kind of reasoning is the following:

Premise: Knut always hears music with his IPod.

Conclusion: Therefore, he reasons that all music is only heard with IPods.

In this instance the conclusion is obviously false. The information the premise contains is not very representative and although it is true, it does not give decisive evidence for the truth of the conclusion. To sum it up, strong inductive reasoning gets to conclusions which are very probable whereas the conclusions reached through weak inductive reasoning on the base of the premises are unlikely to be true.

Reliability of conclusions

If the strength of the conclusion of an inductive argument has to be determined, three factors concerning the premises play a decisive role. The following example which refers to Knut and his wife and the observations they made about the crows (see previous sections) displays these factors: When Knut and his wife observe in addition to the black crows in Germany also the crows in Spain, the number of observations they make concerning the crows obviously increases. Furthermore, the representativeness of these observations is supported, if Knut and his wife observe the crows at all different day- and night times and see that they are black every time. Theoretically it may be that the crows change their color at night what would make the conclusion that all crows are black wrong. The quality of the evidence for all crows to be black increases, if Knut and his wife add scientific measurements which support the conclusion. For example they could find out that the crows' genes determine that the only color they can have is black. Conclusions reached through a process of inductive reasoning are never definitely true as no one has seen all crows on earth and as it is possible, although very unlikely, that there is a green or brown exemplar. The three mentioned factors contribute decisively to the strength of an inductive argument. So, the stronger these factors are, the more reliable are the conclusions reached through induction.

Processes and constraints

In a process of inductive reasoning people often make use of certain heuristics which lead in many cases quickly to adequate conclusions but sometimes may cause errors. In the following, two of these heuristics ( availability heuristic and representativeness heuristic ) are explained. Subsequently, the confirmation bias is introduced which sometimes influences peoples’ reasons according to their own opinion without them realising it.

The availability heuristic

Things that are more easily remembered are judged to be more prevalent. An example for this is an experiment done by Lichtenstein et al. (1978). The participants were asked tochoose from two different lists the causes of death which occur more often. Because of the availability heuristic people judged more “spectacular” causes like homicide or tornado to cause more deaths than others, like asthma. The reason for the subjects answering in such a way is that for example films and news in television are very often about spectacular and interesting causes of death. This is why these information are much more available to the subjects in the experiment. Another effect of the usage of the availability heuristic is called illusory correlations . People tend to judge according to stereotypes. It seems to them that there are correlations between certain events which in reality do not exist. This is what is known by the term “prejudice”. It means that a much oversimplified generalization about a group of people is made. Usually a correlation seems to exist between negative features and a certain class of people (often fringe groups). If, for example, one's neighbour is jobless and very lazy one tends to correlate these two attributes and to create the prejudice that all jobless people are lazy.

This illusory correlation occurs because one takes into account information which is available and judges this to be prevalent in many cases.

The representativeness heuristic

If people have to judge the probability of an event they try to find a comparable event and assume that the two events have a similar probability. Amos Tversky and Daniel Kahneman (1974) presented the following task to their participants in an experiment: “We randomly chose a man from the population of the U.S., Robert, who wears glasses, speaks quietly and reads a lot. Is it more likely that he is a librarian or a farmer?” More of the participants answered that Robert is a librarian which is an effect of the representativeness heuristic. The comparable event which the participants chose was the one of a typical librarian as Robert with his attributes of speaking quietly and wearing glasses resembles this event more than the event of a typical farmer. So, the event of a typical librarian is better comparable with Robert than the event of a typical farmer. Of course this effect may lead to errors as Robert is randomly chosen from the population and as it is perfectly possible that he is a farmer although he speaks quietly and wears glasses.

The representativeness heuristic also leads to errors in reasoning in cases where the conjunction rule is violated. This rule states that the conjunction of two events is never more likely to be the case than the single events alone. An example for this is the case of the feminist bank teller (Tversky & Kahneman, 1983). If we are introduced to a woman of whom we know that she is very interested in women’s rights and has participated in many political activities in college and we are to decide whether it is more likely that she is a bank teller or a feminist bank teller, we are drawn to conclude the latter as the facts we have learnt about her resemble the event of a feminist bank teller more than the event of only being a bank teller.

But it is in fact much more likely that somebody is just a bank teller than it is that someone is a feminist in addition to being a bank teller. This effect is illustrated in figure 6 where the green square, which stands for just being a bank teller, is much larger and thus more probable than the smaller violet square, which displays the conjunction of bank tellers and feminists, which is a subset of bank tellers.

The confirmation bias

This phenomenon describes the fact that people tend to decide in terms of what they themselves believe to be true or good. If, for example, someone believes that one has bad luck on Friday the thirteenth, he will especially look for every negative happening at this particular date but will be inattentive to negative happenings on other days. This behaviour strengthens the belief that there exists a relationship between Friday the thirteenth and having bad luck.

This example shows that the actual information is not taken into account to come to a conclusion but only the information which supports one's own belief. This effect leads to errors as people tend to reason in a subjective manner, if personal interests and beliefs are involved. All the mentioned factors influence the subjective probability of an event so that it differs from the actual probability ( probability heuristic ). Of course all of these factors do not always appear alone, but they influence one another and can occur in combination during the process of reasoning.

Why inductive reasoning at all?

All the described constraints show how prone to errors inductive reasoning is and so the question arises, why we use it at all? But inductive reasons are important nevertheless because they act as shortcuts for our reasoning. It is much easier and faster to apply the availability heuristic or the representativeness heuristic to a problem than to take into account all information concerning the current topic and draw a conclusion by using logical rules. In the following excerpt of very usual actions there is a lot of inductive reasoning involved although one does not realize it on the first view. It points out the importance of this cognitive ability: The sunrise every morning and the sunset in the evening, the change of seasons, the TV program, the fact that a chair does not collapse when we sit on it or the light bulb that flashes after we have pushed a button.

All of these cases are conclusions derived from processes of inductive reasoning. Accordingly, one assumes that the chair one is sitting on does not collapse as the chairs on which one sat before did not collapse. This does not ensure that the chair does not break into pieces but nevertheless it is a rather helpful conclusion to assume that the chair remains stable as this is very probable. To sum it up, inductive reasoning is rather advantageous in situations where deductive reasoning is just not applicable because only evidence but no proved facts are available. As these situations occur rather often in everyday life, living without the use of inductive reasoning is inconceivable.

Induction vs. deduction

The table below (Figure 6) summarizes the most prevalent properties and differences between deductive and inductive reasoning which are important to keep in mind.

Decision making

According to the different levels of consequences, each process of making a decision requires appropriate effort and various aspects to be considered. The following excerpt from the story about Knut makes this obvious: “After considering facts like the warm weather in Spain and shirts and shorts being much more comfortable in this case (information gathering and likelihood estimation) Knut reasons that he needs them for his vacation. In consequence, he finally makes the decision to pack mainly shirts and shorts in his bag (final act of choosing).” Now it seems like there cannot be any decision making without previous reasoning, but that is not true. Of course there are situations in which someone decides to do something spontaneously, with no time to reason about it. We will not go into detail here but you might think about questions like "Why do we choose one or another option in that case?"

Choosing among alternatives

The psychological process of decision making constantly goes along with situations in daily life. Thinking about Knut again we can imagine him to decide between packing more blue or more green shirts for his vacation (which would only have minor consequences) but also about applying a specific job or having children with his wife (which would have relevant influence on important circumstances of his future life). The mentioned examples are both characterized by personal decisions, whereas professional decisions, dealing for example with economic or political issues, are just as important.

The utility approach

There are three different ways to analyze decision making. The normative approach assumes a rational decision-maker with well-defined preferences. While the rational choice theory is based on a priori considerations, the descriptive approach is based on empirical observations and on experimental studies of choice behavior. The prescriptive enterprise develops methods in order to improve decision making. According to Manktelow and Reber´s definition, “utility" refers to outcomes that are desirable because they are in the person’s best interest” (Reber, A. S., 1995; Manktelow, K., 1999). This normative/descriptive approach characterizes optimal decision making by the maximum expected utility in terms of monetary value. This approach can be helpful in gambling theories, but simultaneously includes several disadvantages. People do not necessarily focus on the monetary payoff, since they find value in things other than money, such as fun, free time, family, health and others. But that is not a big problem, because it is possible to apply the graph (Figure 7), which shows the relation between (monetary) gains/losses and their subjective value / utility, which is equal to all the valuable things mentioned above. Therefore, not choosing the maximal monetary value does not automatically describe an irrational decision process.

Misleading effects

But even respecting the considerations above there might still be problems to make the “right” decision because of different misleading effects, which mainly arise because of the constraints of inductive reasoning. In general this means that our model of a situation/problem might not be ideal to solve it in an optimal way. The following three points are typical examples for such effects.

Subjective models

This effect is rather equal to the illusory correlations mentioned before in the part about the constraints of inductive reasoning. It is about the problem that models which people create might be misleading, since they rely on subjective speculations. An example could be deciding where to move by considering typical prejudices of the countries (e.g. always good pizza, nice weather and a relaxed life-style in Italy in contrast to some kind of boring food and steady rain in Great Britain). The predicted events are not equal to the events occurring indeed. (Kahneman & Tversky, 1982; Dunning & Parpal, 1989)

Focusing illusion

Another misleading effect is the so-called focusing illusion . By considering only the most obvious aspects in order to make a certain decision (e.g. the weather) people often neglect various really important outcomes (e.g. circumstances at work). This effect occurs more often, if people judge about others compared with judgments about their own living.

Framing effect

A problem can be described in different ways and therefore evoke different decision strategies. If a problem is specified in terms of gains, people tend to use a risk-aversion strategy, while a problem description in terms of losses leads to apply a risk-taking strategy. An example of the same problem and predictably different choices is the following experiment: A group of people is asked to imagine themselves $300 richer than they are, is confronted with the choice of a sure gain of $100 or an equal chance to gain $200 or nothing. Most people avoid the risk and take the sure gain, which means they take the risk-aversion strategy. Alternatively if people are asked to assume themselves to be $500 richer than in reality, given the options of a sure loss of $100 or an equal chance to lose $200 or nothing, the majority opts for the risk of losing $200 by taking the risk seeking or risk-taking strategy. This phenomenon is known as framing effect and can also be illustrated by figure 8 above, which is a concave function for gains and a convex one for losses. (Foundations of Cognitive Psychology, Levitin, D. J., 2002)

Justification in decision making

Decision making often includes the need to assign a reason for the decision and therefore justify it. This factor is illustrated by an experiment by A. Tversky and E. Shafir (1992): A very attractive vacation package has been offered to a group of students who have just passed an exam and to another group of students who have just failed the exam and have the chance to rewrite it after the holidays coming up. All students have the options to buy the ticket straight away, to stay at home, or to pay $5 for keeping the option open to buy it later. At this point, there is no difference between the two groups, since the number of students who passed the exam and decided to book the flight (with the justification of a deserving a reward), is the same as the number of students who failed and booked the flight (justified as consolation and having time for reoccupation). A third group of students who were informed to receive their results in two more days was confronted with the same problem. The majority decided to pay $5 and keep the option open until they would get their results. The conclusion now is that even though the actual exam result does not influence the decision, it is required in order to provide a rationale.

Executive functions

Subsequently, the question arises how this cognitive ability of making decisions is realized in the human brain. As we already know that there are a couple of different tasks involved in the whole process, there has to be something that coordinates and controls those brain activities – namely the executive functions. They are the brain's conductor, instructing other brain regions to perform, or be silenced, and generally coordinating their synchronized activity (Goldberg, 2001). Thus, they are responsible for optimizing the performance of all “multi-threaded” cognitive tasks.

Locating those executive functions is rather difficult, as they cannot be appointed to a single brain region. Traditionally, they have been equated with the frontal lobes, or rather the prefrontal regions of the frontal lobes; but it is still an open question whether all of their aspects can be associated with these regions.

Nevertheless, we will concentrate on the prefrontal regions of the frontal lobes, to get an impression of the important role of the executive functions within cognition. Moreover, it is possible to subdivide these regions into functional parts. But it is to be noted that not all researchers regard the prefrontal cortex as containing functionally different regions.

Executive functions in practice

According to Norman and Shallice, there are five types of situations in which executive functions may be needed in order to optimize performance, as the automatic activation of behavior would be insufficient. These are situations involving...

1. planning or decision making.

2. error correction or trouble shooting.

3. responses containing novel sequences of actions.

4. technical difficulties or dangerous circumstances.

5. the control of action or the overcoming of strong habitual responses.

The following parts will have a closer look to each of these points, mainly referring to brain- damaged individuals. Surprisingly, intelligence in general is not affected in cases of frontal lobe injuries (Warrington, James & Maciejewski, 1986). However, dividing intelligence into crystallised intelligence (based on previously acquired knowledge) and fluid intelligence (meant to rely on the current ability of solving problems), emphasizes the executive power of the frontal lobes, as patients with lesions in these regions performed significantly worse in tests of fluid intelligence (Duncan, Burgess & Emslie, 1995).

1. Planning or decision making: Impairments in abstract and conceptual thinking

To solve many tasks it is important that one is able to use given information. In many cases, this means that material has to be processed in an abstract rather than in a concrete manner.

Patients with executive dysfunction have abstraction difficulties. This is proven by a card sorting experiment (Delis et al., 1992): The cards show names of animals and black or white triangles placed above or below the word. Again, the cards can be sorted with attention to different attributes of the animals (living on land or in water, domestic or dangerous, large or small) or the triangles (black or white, above or below word). People with frontal lobe damage fail to solve the task because they cannot even conceptualize the properties of the animals or the triangles, thus are not able to deduce a sorting-rule for the cards (in contrast, there are some individuals only perseverating; they find a sorting-criterion but are unable to switch to a new one). These problems might be due to a general difficulty in strategy formation.

Goal directed behavior

Let us again take Knut into account to get an insight into the field of goal directed behavior – in principle, this is nothing but problem solving since it is about organizing behavior towards a goal. Thus, when Knut is packing his bag for his holiday, he obviously has a goal in mind (in other words: He wants to solve a problem) – namely get ready before the plane starts. There are several steps necessary during the process of reaching a certain goal:

Goal must be kept in mind:

Knut should never forget that he has to pack his bag in time. Dividing into subtasks and sequencing:

Knut packs his bag in a structured way. He starts packing the crucial things and then goes on

Completed portions must be kept in mind:

If Knut already packed enough underwear into his bag, he would not need to search for more. Flexibility and adaptability:

Imagine that Knut wants to pack his favourite T-Shirt, but he realizes that it is dirty. In this case,

Knut has to adapt to this situation and has to pick another T-Shirt that was not in his plan originally.

Evaluation of actions:

Along the way of reaching his ultimate goal Knut constantly has to evaluate his performance in terms of ‘How am I doing considering that I have the goal of packing my bag?’.

Executive dysfunction and goal directed behavior

The breakdown of executive functions impairs goal directed behavior to a large extend. In which way cannot be stated in general, it depends on the specific brain regions that are damaged. So it is quite possible that an individual with a particular lesion has problems with two or three of the five points described above and performs within average regions when the other abilities are tested. However, if only one link is missing from the chain, the whole plan might get very hard or even impossible to master. Furthermore, the particular hemisphere affected plays a role as well.

Another interesting result was the fact that lesions in the frontal lobes of left and right hemisphere impaired different abilities. While a lesion in the right hemisphere caused trouble in making regency judgements, a lesion in the left hemisphere impaired the patient’s performance only when the presented material was verbal or in a variation of the experiment that required self-ordered sequencing. Because of that we know that the ability to sequence behavior is not only located in the frontal lobe but in the left hemisphere particularly when it comes to motor action.

Problems in sequencing

In an experiment by Milner (1982), people were shown a sequence of cards with pictures. The experiment included two different tasks: recognition trials and recency trials. In the former the patients were shown two different pictures, one of them has appeared in the sequence before, and the participants had to decide which one it was. In the latter they were shown two different pictures, both of them have appeared before, they had to name the picture that was shown more recently than the other one.

The results of this experiment showed that people with lesions in temporal regions have more trouble with the recognition trial and patients with frontal lesions have difficulties with the recency trial since anterior regions are important for sequencing. This is due to the fact that the recognition trial demanded a properly functioning recognition memory [3], the recency trial a properly functioning memory for item order [3]. These two are dissociable and seem to be processed in different areas of the brain. The frontal lobe is not only important for sequencing but also thought to play a major role for working memory [3] . This idea is supported by the fact that lesions in the lateral regions of the frontal lobe are much more likely to impair the ability of 'keeping things in mind' than damage to other areas of the frontal cortex do. But this is not the only thing there is to sequencing. For reaching a goal in the best possible way it is important that a person is able to figure out which sequence of actions, which strategy, best suits the purpose, in addition to just being able to develop a correct sequence.

This is proven by an experiment called 'Tower of London' (Shallice, 1982) which is similar to the famous 'Tower of Hanoi' [4] task with the difference that this task required three balls to be put onto three poles of different length so that one pole could hold three balls, the second one two and the third one only one ball, in a way that a changeable goal position is attained out of a fixed initial position in as few moves as possible. Especially patients with damage to the left frontal lobe proved to work inefficiently and ineffectively on this task. They needed many moves and engaged in actions that did not lead toward the goal.

Problems with the interpretation of available information

Quite often, if we want to reach a goal, we get hints on how to do it best. This means we have to be able to interpret the available information in terms of what the appropriate strategy would be. For many patients of executive dysfunction this is not an easy thing to do either.

They have trouble to use this information and engage in inefficient actions. Thus, it will take them much longer to solve a task than healthy people who use the extra information and develop an effective strategy.

Problems with self-criticism and -monitoring

The last problem for people with frontal lobe damage we want to present here is the last point in the above list of properties important for proper goal directed behavior. It is the ability to evaluate one's actions, an ability that is missing in most patients. These people are therefore very likely to 'wander off task' and engage in behavior that does not help them to attain their goal. In addition to that, they are also not able to determine whether their task is already completed at all. Reasons for this are thought to be a lack of motivation or lack of concern about one's performance (frontal lobe damage is usually accompanied by changes in emotional processing) but these are probably not the only explanations for these problems. Another important brain region in this context – the medial portion of the frontal lobe – is responsible for detecting behavioral errors made while working towards a goal. This has been shown by ERP experiments [5] where there was an error-related negativity 100ms after an error has been made. If this area is damaged, this mechanism cannot work properly anymore and the patient loses the ability to detect errors and thus monitor his own behavior. However, in the end we must add that although executive dysfunction causes an enormous number of problems in behaving correctly towards a goal, most patients when assigned with a task are indeed anxious to solve it but are just unable to do so.

2. Error correction and trouble shooting

The most famous experiment to investigate error correction and trouble shooting is the Wisconsin Card Sorting Test (WCST). A participant is presented with cards that show certain objects. These cards are defined by shape, color and number of the objects on the cards. These cards now have to be sorted according to a rule based on one of these three criteria. The participant does not know which rule is the right one but has to reach the conclusion after positive or negative feedback of the experimenter. Then at some point, after the participant has found the correct rule to sort the cards, the experimenter changes the rule and the previous correct sorting will lead to negative feedback. The participant has to realize the change and adapt to it by sorting the cards according to the new rule.

Patients with executive dysfunction have problems identifying the rule in the first place. It takes them noticeably longer because they have trouble using already given information to make a conclusion. But once they got to sorting correctly and the rule changes, they keep sorting the cards according to the old rule although many of them notice the negative feedback. They are just not able to switch to another sorting-principle, or at least they need many tries to learn the new one. They perseverate .

Problems in shifting and modifying strategies

Intact neuronal tissue in the frontal lobe is also crucial for another executive function connected with goal directed behavior that we described above: Flexibility and adaptability. This means that persons with frontal lobe damage will have difficulties in shifting their way of thinking – meaning creating a new plan after recognizing that the original one cannot becarried out for some reason. Thus, they are not able to modify their strategy according to this new problem. Even when it is clear that one hypothesis cannot be the right one to solve a task, patients will stick to it nevertheless and are unable to abandon it (called 'tunnelvision').

Moreover, such persons do not use as many appropriate hypotheses for creating a strategy as people with damage to other brain regions do. In what particular way this can be observed in patients can again not be stated in general but depends on the nature of the shift that has to be made.

These earlier described problems of 'redirecting' of one's strategies stand in contrast to the atcual 'act of switching' between tasks. This is yet another problem for patients with frontal lobe damage. Since the control system that leads task switching as such is independent from the parts that actually perform these tasks, the task switching is particularly impaired in patients with lesions to the dorsolateral prefrontal cortex while at the same time they have no trouble with performing the single tasks alone. This of course, causes a lot of problems in goal directed behavior because as it was said before: Most tasks consist of smaller subtasks that have to be completed.

3. Responses containing novel sequences of actions

Many clinical tests have been done, requiring patients to develop strategies for dealing with novel situations. In the Cognitive Estimation Task (Shallice & Evans, 1978) patients are presented with questions whose answers are unlikely to be known. People with damage to the prefrontal cortex have major difficulties to produce estimates for questions like: “How many camels are in Holland?”. In the FAS Test (Miller, 1984) subjects have to generate sequences of words (not proper names) beginning with a certain letter (“F” , “A” or “S”) in a one-minute period. This test involves developing new strategies, selecting between alternatives and avoiding repeating previous given answers. Patients with left lateral prefrontal lesions are often impaired (Stuss et al., 1998).

4. Technical difficulties or dangerous circumstances

One single mistake in a dangerous situation may easily lead to serious injuries while a mistake in a technical difficult situation (e.g. building a house of cards) would obviously lead to failure. Thus, in such situations, automatic activation of responses clearly would be insufficient and executive functions seem to be the only solution for such problems. Wilkins, Shallice and McCarthy (1987) were able to prove a connection between dangerous or difficult situations and the prefrontal cortex, as patients with lesions to this area were impaired during experiments concerning dangerous or difficult situations. The ventromedial and orbitofrontal cortex may be particularly important for these aspects of executivefunctions.

5. Control of action or the overcoming of strong habitual responses

Deficits in initiation, cessation and control of action

We start by describing the effects of the loss of the ability to start something, to initiate an action. A person with executive dysfunction is likely to have trouble beginning to work on a task without strong help from the outside, while people with left frontal lobe damage often show impaired spontaneous speech and people with right frontal lobe damage rather show poor nonverbal fluency. Of course, one reason is the fact that this person will not have any intention, desire or concern on his or her own of solving the task since this is yet another characteristic of executive dysfunction. But it is also due to a psychological effect often connected with the loss of properly executive functioning: Psychological inertia. Like in physics, inertia in this case means that an action is very hard to initiate, but once started, it is again very hard to shift or stop. This phenomenon is characterized by engagement in repetitive behavior, is called perseveration (cp. WCST [6]).

Another problem caused by executive dysfunction can be observed in patients suffering from the so called environmental dependency syndrome . Their actions are impelled or obligated by their physical or social environment. This manifests itself in many different ways and depends to a large extent on the individual’s personal history. Examples are patients who begin to type when they see a computer key board, who start washing the dishes upon seeing a dirty kitchen or who hang up pictures on the walls when finding hammer, nails and pictures on the floor. This makes these people appear as if they were acting impulsively or as if they have lost their ‘free will’. It shows a lack of control for their actions. This is due to the fact that an impairment in their executive functions causes a disconnection between thought and action. These patients know that their actions are inappropriate but like in the WCST, they cannot control what they are doing. Even if they are told by which attribute to sort the cards, they will still keep sorting them sticking to the old rule due to major difficulties in the translation of these directions into action.

What is needed to avoid problems like these are the abilities to start, stop or change an action but very likely also the ability to use information to direct behavior.

Deficits in cognitive estimation

Next to the difficulties to produce estimates to questions whose answers are unlikely known, patients with lesions to the frontal lobes have problems with cognitive estimation in general. Cognitive estimation is the ability to use known information to make reasonable judgments or deductions about the world. Now the inability for cognitive estimation is the third type of deficits often observed in individuals with executive dysfunction. It is already known that people with executive dysfunction have a relatively unaffected knowledge base. This means they cannot retain knowledge about information or at least they are unable to make inferences based on it. There are various effects which are shown on such individuals. Now for example patients with frontal lobe damage have difficulty estimating the length of the spine of an average woman.

Making such realistic estimations requires inferencing based on other knowledge which is in this case, knowing that the height of the average woman is about 5ft 6 in (168cm) and considering that the spine runs about one third to one half the length of the body and so on. Patients with such a dysfunction do not only have difficulties in their estimates of cognitive information but also in their estimates of their own capacities (such as their ability to direct activity in goal – oriented manner or in controlling their emotions). Prigatuno, Altman and O’Brien (1990) reported that when patients with anterior lesions associated with diffuse axonal injury to other brain areas are asked how capable they are of performing tasks such as scheduling their daily activities or preventing their emotions from affecting daily activities, they grossly overestimate their abilities. From several experiments Smith and Miler (1988) found out that individuals with frontal lobe damages have no difficulties in determining whether an item was in a specific inspection series they find it difficult to estimate how frequently an item did occur. This may not only reflect difficulties in cognitive estimation but also in memory task that place a premium on remembering temporal information. Thus both difficulties (in cognitive estimation and in temporal sequencing) may contribute to a reduced ability to estimate frequency of occurrence.

Despite these impairments in some domains the abilities of estimation are preserved in patients with frontal lobe damage. Such patients also do have problems in estimating how well they can prevent their emotions for affecting their daily activities. They are also as good at judging how many dues they will need to solve a puzzle as patients with temporal lobe damage or neurologically intact people.

Theories of frontal lobe function in executive control

In order to explain that patients with frontal lobe damage have difficulties in performing executive functions, four major approaches have developed. Each of them leads to an improved understanding of the role of frontal regions in executive functions, but none of these theories covers all the deficits occurred.

Role of working memory

The most anatomically specific approach assumes the dorsolateral prefrontal area of the frontal lobe to be critical for working memory. The working memory which has to be clearly distinguished from the long term memory keeps information on-line for use in performing a task. Not being generated for accounting for the broad array of dysfunctions it focuses on the three following deficits:

1. Sequencing information and directing behavior toward a goal

2. Understanding of temporal relations between items and events

3. Some aspects of environmental dependency and perseveration

Research on monkeys has been helpful to develop this approach (the delayed-response paradigm, Goldman-Rakic, 1987, serves as a classical example).

Role of Controlled Versus Automatic Processes

There are two theories based on the underlying assumption that the frontal lobes are especially important for controlling behavior in non-experienced situations and for overriding stimulus- response associations, but contribute little to automatic and effortless behavior (Banich, 1997). Stuss and Benson (1986) consider control over behavior to occur in a hierarchical manner. They distinguish between three different levels, of which each is associated with a particular brain region. In the first level sensory information is processed automatically by posterior regions, in the next level (associated with the executive functions of the frontal lobe) conscious control is needed to direct behavior toward a goal and at the highest level controlled self-reflection takes place in the prefrontal cortex. This model is appropriate for explaining deficits in goal-oriented behavior, in dealing with novelty, the lack of cognitive flexibility and the environmental dependency syndrome. Furthermore it can explain the inability to control action consciously and to criticise oneself. The second model developed by Shalice (1982) proposes a system consisting of two parts that influence the choice of behavior. The first part, a cognitive system called contention scheduling, is in charge of more automatic processing. Various links and processing schemes cause a single stimulus to result in an automatic string of actions. Once an action is initiated, it remains active until inhibited. The second cognitive system is the supervisory attentional system which directs attention and guides action through decision processes and is only active “when no processing schemes are available, when the task is technically difficult, when problem solving is required and when certain response tendencies must be overcome” (Banich , 1997). This theory supports the observations of few deficits in routine situations, but relevant problems in dealing with novel tasks (e.g. the Tower of London task, Shallice, 1982), since no schemes in contention scheduling exist for dealing with it.

Impulsive action is another characteristic of patients with frontal lobe damages which can be explained by this theory. Even if asked not to do certain things, such patients stick to their routines and cannot control their automatic behavior.

Use of Scripts

The approach based on scripts, which are sets of events, actions and ideas that are linked to form a unit of knowledge was developed by Schank (1982) amongst others. Containing information about the setting in which an event occurs, the set of events needed to achieve the goal and the end event terminating the action. Such managerial knowledge units (MKUs) are supposed to be stored in the prefrontal cortex. They are organized in a hierarchical manner being abstract at the top and getting more specific at the bottom. Damage of the scripts leads to the inability to behave goal-directed, finding it easier to cope with usual situations (due to the difficulty of retrieving a MKU of a novel event) and deficits in the initiation and cessation of action (because of MKUs specifying the beginning and ending of an action.)

Role of a goal list

The perspective of artificial intelligence and machine learning introduced an approach which assumes that each person has a goal list, which contains the tasks requirements or goals. This list is fundamental to guiding behavior and since frontal lobe damages disrupt the ability to form a goal list, the theory helps to explain difficulties in abstract thinking, perceptual analysis, verbal output and staying on task. It can also account for the strong environmental influence on patients with frontal lobe damages, due to the lack of internal goals and the difficulty of organizing actions toward a goal.

It is important to keep in mind that reasoning and decision making are closely connected to each other: Decision making in many cases happens with a previous process of reasoning. People's everyday life is decisively coined by the synchronized appearance of these two human cognitive features. This synchronization, in turn, is realized by the executive functions which seem to be mainly located in the frontal lobes of the brain.

Deductive Reasoning + Inductive Reasoning

There is more than one way to start with information and arrive at an inference; thus, there is more than one way to reason. Each has its own strengths, weaknesses, and applicability to the real world.

In this form of reasoning a person starts with a known claim or general belief, and from there determines what follows. Essentially, deduction starts with a hypothesis and examines the possibilities within that hypothesis to reach a conclusion. Deductive reasoning has the advantage that, if your original premises are true in all situations and your reasoning is correct, your conclusion is guaranteed to be true. However, deductive reasoning has limited applicability in the real world because there are very few premises which are guaranteed to be true all of the time.

A syllogism is a form of deductive reasoning in which two statements reach a logical conclusion. An example of a syllogism is, “All dogs are mammals; Kirra is a dog; therefore, Kirra is a mammal.”

Inductive reasoning makes broad inferences from specific cases or observations. In this process of reasoning, general assertions are made based on specific pieces of evidence. Scientists use inductive reasoning to create theories and hypotheses. An example of inductive reasoning is, “The sun has risen every morning so far; therefore, the sun rises every morning.” Inductive reasoning is more practical to the real world because it does not rely on a known claim; however, for this same reason, inductive reasoning can lead to faulty conclusions. A faulty example of inductive reasoning is, “I saw two brown cats; therefore, the cats in this neighborhood are brown.”

Interactive Element

Sherlock Holmes, master of reasoning : In this video, we see the famous literary character Sherlock Holmes use both inductive and deductive reasoning to form inferences about his friends. As you can see, inductive reasoning can lead to erroneous conclusions. Can you distinguish between his deductive (general to specific) and inductive (specific to general) reasoning?

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9.7: Inductive and Deductive Reasoning

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Learning Objectives

• Differentiate between deductive and inductive reasoning

Deductive and Inductive Arguments: Two Ways of Understanding

We have two basic approaches for how we come to believe something is true.

The first way is that we are exposed to several different examples of a situation, and from those examples, we conclude a general truth. For instance, you visit your local grocery store daily to pick up necessary items. You notice that on Friday, two weeks ago, all the clerks in the store were wearing football jerseys. Again, last Friday, the clerks wore their football jerseys. Today, also a Friday, they’re wearing them again. From just these observations, you can conclude that on all Fridays, these supermarket employees will wear football jerseys to support their local team.

This type of pattern recognition, leading to a conclusion, is known as inductive reasoning .

Knowledge can also move the opposite direction. Say that you read in the news about a tradition in a local grocery store, where employees wore football jerseys on Fridays to support the home team. This time, you’re starting from the overall rule, and you would expect individual evidence to support this rule. Each time you visited the store on a Friday, you would expect the employees to wear jerseys.

Such a case, of starting with the overall statement and then identifying examples that support it, is known as deductive reasoning .

In the process of deduction, you begin with some statements, called “premises,” that are assumed to be true, you then determine what else would have to be true if the premises are true.

For example, you could begin by assuming that God exists, and is good, and then determine what would logically follow from such an assumption. With this premise, you would look for evidence supporting a belief in God.

With deduction, you can provide absolute proof of your conclusions, given that your premises are correct. The premises themselves, however, remain unproven and unprovable.

Examples of deductive logic:

• All men are mortal. Joe is a man. Therefore Joe is mortal. If the first two statements are true, then the conclusion must be true.
• Bachelors are unmarried men. Bill is unmarried. Therefore, Bill is a bachelor.
• To get a Bachelor’s degree at a college, a student must have 120 credits. Sally has more than 130 credits. Therefore, Sally has a bachelor’s degree.

In the process of induction, you begin with some data, and then determine what general conclusion(s) can logically be derived from those data. In other words, you determine what theory or theories could explain the data.

For example, you note that the probability of becoming schizophrenic is greatly increased if at least one parent is schizophrenic, and from that you conclude that schizophrenia may be inherited. That is certainly a reasonable hypothesis given the data.

However, induction does not prove that the theory is correct. There are often alternative theories that are also supported by the data. For example, the behavior of the schizophrenic parent may cause the child to be schizophrenic, not the genes.

What is important in induction is that the theory does indeed offer a logical explanation of the data. To conclude that the parents have no effect on the schizophrenia of the children is not supportable given the data, and would not be a logical conclusion.

Examples of inductive logic:

• This cat is black. That cat is black. A third cat is black. Therefore all cats are black.
• This marble from the bag is black. That marble from the bag is black. A third marble from the bag is black. Therefore all the marbles in the bag black.
• Most universities and colleges in Utah ban alcohol from campus. Therefore most universities and colleges in the U.S. ban alcohol from campus.

Deduction and induction by themselves are inadequate to make a compelling argument. While deduction gives absolute proof, it never makes contact with the real world, there is no place for observation or experimentation, and no way to test the validity of the premises. And, while induction is driven by observation, it never approaches actual proof of a theory. Therefore an effective paper will include both types of logic.

This video reviews some of the distinctions between inductive and deductive reasoning.

You can view the transcript for “Inductive VS Deductive Reasoning by Shmoop” here (opens in new window) .

https://assessments.lumenlearning.co...essments/20280

https://assessments.lumenlearning.co...essments/20281

deductive reasoning : top-down reasoning; a method of reasoning in which a certain conclusion follows general premises.

inductive reasoning : bottom-up reasoning; a method of reasoning in which several premises provide evidence of a probable conclusion.

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• Image of inductive and deductive reasoning. Provided by : Lumen Learning. License : CC BY: Attribution
• Argument Terminology. Authored by : Farcaster. Located at : https://en.Wikipedia.org/wiki/Argument#/media/File:Argument_terminology_used_in_logic.png . License : CC BY-SA: Attribution-ShareAlike
• Inductive VS Deductive Reasoning by Shmoop. Authored by : Shmoop. Located at : https://www.youtube.com/watch?v=VXW5mLE5Y2g&feature=youtu.be . License : Other . License Terms : Standard YouTube License
• Inductive and Deductive Reasoning. Provided by : Utah State University. Located at : ocw.usu.edu/English/introduction-to-writing-academic-prose/inductive-and-deductive-reasoning.html. Project : English 1010 Handbook. License : Public Domain: No Known Copyright
• The Logical Structure of Arguments. Authored by : Radford University. Located at : lcubbison.pressbooks.com/chapter/core-201-analyzing-arguments/. Project : Core Curriculum Handbook. License : Public Domain: No Known Copyright

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Methodology

• Inductive vs. Deductive Research Approach | Steps & Examples

Inductive vs. Deductive Research Approach | Steps & Examples

Published on April 18, 2019 by Raimo Streefkerk . Revised on June 22, 2023.

The main difference between inductive and deductive reasoning is that inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory .

In other words, inductive reasoning moves from specific observations to broad generalizations . Deductive reasoning works the other way around.

Both approaches are used in various types of research , and it’s not uncommon to combine them in your work.

Table of contents

Inductive research approach, deductive research approach, combining inductive and deductive research, other interesting articles, frequently asked questions about inductive vs deductive reasoning.

When there is little to no existing literature on a topic, it is common to perform inductive research , because there is no theory to test. The inductive approach consists of three stages:

• A low-cost airline flight is delayed
• Dogs A and B have fleas
• Elephants depend on water to exist
• Another 20 flights from low-cost airlines are delayed
• All observed dogs have fleas
• All observed animals depend on water to exist
• Low cost airlines always have delays
• All dogs have fleas
• All biological life depends on water to exist

Limitations of an inductive approach

A conclusion drawn on the basis of an inductive method can never be fully proven. However, it can be invalidated.

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When conducting deductive research , you always start with a theory. This is usually the result of inductive research. Reasoning deductively means testing these theories. Remember that if there is no theory yet, you cannot conduct deductive research.

The deductive research approach consists of four stages:

• If passengers fly with a low cost airline, then they will always experience delays
• All pet dogs in my apartment building have fleas
• All land mammals depend on water to exist
• Collect flight data of low-cost airlines
• Test all dogs in the building for fleas
• Study all land mammal species to see if they depend on water
• 5 out of 100 flights of low-cost airlines are not delayed
• 10 out of 20 dogs didn’t have fleas
• All land mammal species depend on water
• 5 out of 100 flights of low-cost airlines are not delayed = reject hypothesis
• 10 out of 20 dogs didn’t have fleas = reject hypothesis
• All land mammal species depend on water = support hypothesis

Limitations of a deductive approach

The conclusions of deductive reasoning can only be true if all the premises set in the inductive study are true and the terms are clear.

• All dogs have fleas (premise)
• Benno is a dog (premise)
• Benno has fleas (conclusion)

Many scientists conducting a larger research project begin with an inductive study. This helps them develop a relevant research topic and construct a strong working theory. The inductive study is followed up with deductive research to confirm or invalidate the conclusion. This can help you formulate a more structured project, and better mitigate the risk of research bias creeping into your work.

Remember that both inductive and deductive approaches are at risk for research biases, particularly confirmation bias and cognitive bias , so it’s important to be aware while you conduct your research.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square goodness of fit test
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Inclusion and exclusion criteria

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

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Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.

Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.

Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.

You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.

A research project is an academic, scientific, or professional undertaking to answer a research question . Research projects can take many forms, such as qualitative or quantitative , descriptive , longitudinal , experimental , or correlational . What kind of research approach you choose will depend on your topic.

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7 Module 7: Thinking, Reasoning, and Problem-Solving

This module is about how a solid working knowledge of psychological principles can help you to think more effectively, so you can succeed in school and life. You might be inclined to believe that—because you have been thinking for as long as you can remember, because you are able to figure out the solution to many problems, because you feel capable of using logic to argue a point, because you can evaluate whether the things you read and hear make sense—you do not need any special training in thinking. But this, of course, is one of the key barriers to helping people think better. If you do not believe that there is anything wrong, why try to fix it?

The human brain is indeed a remarkable thinking machine, capable of amazing, complex, creative, logical thoughts. Why, then, are we telling you that you need to learn how to think? Mainly because one major lesson from cognitive psychology is that these capabilities of the human brain are relatively infrequently realized. Many psychologists believe that people are essentially “cognitive misers.” It is not that we are lazy, but that we have a tendency to expend the least amount of mental effort necessary. Although you may not realize it, it actually takes a great deal of energy to think. Careful, deliberative reasoning and critical thinking are very difficult. Because we seem to be successful without going to the trouble of using these skills well, it feels unnecessary to develop them. As you shall see, however, there are many pitfalls in the cognitive processes described in this module. When people do not devote extra effort to learning and improving reasoning, problem solving, and critical thinking skills, they make many errors.

As is true for memory, if you develop the cognitive skills presented in this module, you will be more successful in school. It is important that you realize, however, that these skills will help you far beyond school, even more so than a good memory will. Although it is somewhat useful to have a good memory, ten years from now no potential employer will care how many questions you got right on multiple choice exams during college. All of them will, however, recognize whether you are a logical, analytical, critical thinker. With these thinking skills, you will be an effective, persuasive communicator and an excellent problem solver.

The module begins by describing different kinds of thought and knowledge, especially conceptual knowledge and critical thinking. An understanding of these differences will be valuable as you progress through school and encounter different assignments that require you to tap into different kinds of knowledge. The second section covers deductive and inductive reasoning, which are processes we use to construct and evaluate strong arguments. They are essential skills to have whenever you are trying to persuade someone (including yourself) of some point, or to respond to someone’s efforts to persuade you. The module ends with a section about problem solving. A solid understanding of the key processes involved in problem solving will help you to handle many daily challenges.

7.1. Different kinds of thought

7.2. Reasoning and Judgment

7.3. Problem Solving

READING WITH PURPOSE

Remember and understand.

By reading and studying Module 7, you should be able to remember and describe:

• Concepts and inferences (7.1)
• Procedural knowledge (7.1)
• Metacognition (7.1)
• Characteristics of critical thinking:  skepticism; identify biases, distortions, omissions, and assumptions; reasoning and problem solving skills  (7.1)
• Reasoning:  deductive reasoning, deductively valid argument, inductive reasoning, inductively strong argument, availability heuristic, representativeness heuristic  (7.2)
• Fixation:  functional fixedness, mental set  (7.3)
• Algorithms, heuristics, and the role of confirmation bias (7.3)
• Effective problem solving sequence (7.3)

By reading and thinking about how the concepts in Module 6 apply to real life, you should be able to:

• Identify which type of knowledge a piece of information is (7.1)
• Recognize examples of deductive and inductive reasoning (7.2)
• Recognize judgments that have probably been influenced by the availability heuristic (7.2)
• Recognize examples of problem solving heuristics and algorithms (7.3)

Analyze, Evaluate, and Create

By reading and thinking about Module 6, participating in classroom activities, and completing out-of-class assignments, you should be able to:

• Use the principles of critical thinking to evaluate information (7.1)
• Explain whether examples of reasoning arguments are deductively valid or inductively strong (7.2)
• Outline how you could try to solve a problem from your life using the effective problem solving sequence (7.3)

7.1. Different kinds of thought and knowledge

• Take a few minutes to write down everything that you know about dogs.
• Do you believe that:
• Psychic ability exists?
• Hypnosis is an altered state of consciousness?
• Magnet therapy is effective for relieving pain?
• Aerobic exercise is an effective treatment for depression?
• UFO’s from outer space have visited earth?

On what do you base your belief or disbelief for the questions above?

Of course, we all know what is meant by the words  think  and  knowledge . You probably also realize that they are not unitary concepts; there are different kinds of thought and knowledge. In this section, let us look at some of these differences. If you are familiar with these different kinds of thought and pay attention to them in your classes, it will help you to focus on the right goals, learn more effectively, and succeed in school. Different assignments and requirements in school call on you to use different kinds of knowledge or thought, so it will be very helpful for you to learn to recognize them (Anderson, et al. 2001).

Factual and conceptual knowledge

Module 5 introduced the idea of declarative memory, which is composed of facts and episodes. If you have ever played a trivia game or watched Jeopardy on TV, you realize that the human brain is able to hold an extraordinary number of facts. Likewise, you realize that each of us has an enormous store of episodes, essentially facts about events that happened in our own lives. It may be difficult to keep that in mind when we are struggling to retrieve one of those facts while taking an exam, however. Part of the problem is that, in contradiction to the advice from Module 5, many students continue to try to memorize course material as a series of unrelated facts (picture a history student simply trying to memorize history as a set of unrelated dates without any coherent story tying them together). Facts in the real world are not random and unorganized, however. It is the way that they are organized that constitutes a second key kind of knowledge, conceptual.

Concepts are nothing more than our mental representations of categories of things in the world. For example, think about dogs. When you do this, you might remember specific facts about dogs, such as they have fur and they bark. You may also recall dogs that you have encountered and picture them in your mind. All of this information (and more) makes up your concept of dog. You can have concepts of simple categories (e.g., triangle), complex categories (e.g., small dogs that sleep all day, eat out of the garbage, and bark at leaves), kinds of people (e.g., psychology professors), events (e.g., birthday parties), and abstract ideas (e.g., justice). Gregory Murphy (2002) refers to concepts as the “glue that holds our mental life together” (p. 1). Very simply, summarizing the world by using concepts is one of the most important cognitive tasks that we do. Our conceptual knowledge  is  our knowledge about the world. Individual concepts are related to each other to form a rich interconnected network of knowledge. For example, think about how the following concepts might be related to each other: dog, pet, play, Frisbee, chew toy, shoe. Or, of more obvious use to you now, how these concepts are related: working memory, long-term memory, declarative memory, procedural memory, and rehearsal? Because our minds have a natural tendency to organize information conceptually, when students try to remember course material as isolated facts, they are working against their strengths.

One last important point about concepts is that they allow you to instantly know a great deal of information about something. For example, if someone hands you a small red object and says, “here is an apple,” they do not have to tell you, “it is something you can eat.” You already know that you can eat it because it is true by virtue of the fact that the object is an apple; this is called drawing an  inference , assuming that something is true on the basis of your previous knowledge (for example, of category membership or of how the world works) or logical reasoning.

Procedural knowledge

Physical skills, such as tying your shoes, doing a cartwheel, and driving a car (or doing all three at the same time, but don’t try this at home) are certainly a kind of knowledge. They are procedural knowledge, the same idea as procedural memory that you saw in Module 5. Mental skills, such as reading, debating, and planning a psychology experiment, are procedural knowledge, as well. In short, procedural knowledge is the knowledge how to do something (Cohen & Eichenbaum, 1993).

Metacognitive knowledge

Floyd used to think that he had a great memory. Now, he has a better memory. Why? Because he finally realized that his memory was not as great as he once thought it was. Because Floyd eventually learned that he often forgets where he put things, he finally developed the habit of putting things in the same place. (Unfortunately, he did not learn this lesson before losing at least 5 watches and a wedding ring.) Because he finally realized that he often forgets to do things, he finally started using the To Do list app on his phone. And so on. Floyd’s insights about the real limitations of his memory have allowed him to remember things that he used to forget.

All of us have knowledge about the way our own minds work. You may know that you have a good memory for people’s names and a poor memory for math formulas. Someone else might realize that they have difficulty remembering to do things, like stopping at the store on the way home. Others still know that they tend to overlook details. This knowledge about our own thinking is actually quite important; it is called metacognitive knowledge, or  metacognition . Like other kinds of thinking skills, it is subject to error. For example, in unpublished research, one of the authors surveyed about 120 General Psychology students on the first day of the term. Among other questions, the students were asked them to predict their grade in the class and report their current Grade Point Average. Two-thirds of the students predicted that their grade in the course would be higher than their GPA. (The reality is that at our college, students tend to earn lower grades in psychology than their overall GPA.) Another example: Students routinely report that they thought they had done well on an exam, only to discover, to their dismay, that they were wrong (more on that important problem in a moment). Both errors reveal a breakdown in metacognition.

The Dunning-Kruger Effect

In general, most college students probably do not study enough. For example, using data from the National Survey of Student Engagement, Fosnacht, McCormack, and Lerma (2018) reported that first-year students at 4-year colleges in the U.S. averaged less than 14 hours per week preparing for classes. The typical suggestion is that you should spend two hours outside of class for every hour in class, or 24 – 30 hours per week for a full-time student. Clearly, students in general are nowhere near that recommended mark. Many observers, including some faculty, believe that this shortfall is a result of students being too busy or lazy. Now, it may be true that many students are too busy, with work and family obligations, for example. Others, are not particularly motivated in school, and therefore might correctly be labeled lazy. A third possible explanation, however, is that some students might not think they need to spend this much time. And this is a matter of metacognition. Consider the scenario that we mentioned above, students thinking they had done well on an exam only to discover that they did not. Justin Kruger and David Dunning examined scenarios very much like this in 1999. Kruger and Dunning gave research participants tests measuring humor, logic, and grammar. Then, they asked the participants to assess their own abilities and test performance in these areas. They found that participants in general tended to overestimate their abilities, already a problem with metacognition. Importantly, the participants who scored the lowest overestimated their abilities the most. Specifically, students who scored in the bottom quarter (averaging in the 12th percentile) thought they had scored in the 62nd percentile. This has become known as the  Dunning-Kruger effect . Many individual faculty members have replicated these results with their own student on their course exams, including the authors of this book. Think about it. Some students who just took an exam and performed poorly believe that they did well before seeing their score. It seems very likely that these are the very same students who stopped studying the night before because they thought they were “done.” Quite simply, it is not just that they did not know the material. They did not know that they did not know the material. That is poor metacognition.

In order to develop good metacognitive skills, you should continually monitor your thinking and seek frequent feedback on the accuracy of your thinking (Medina, Castleberry, & Persky 2017). For example, in classes get in the habit of predicting your exam grades. As soon as possible after taking an exam, try to find out which questions you missed and try to figure out why. If you do this soon enough, you may be able to recall the way it felt when you originally answered the question. Did you feel confident that you had answered the question correctly? Then you have just discovered an opportunity to improve your metacognition. Be on the lookout for that feeling and respond with caution.

concept :  a mental representation of a category of things in the world

Dunning-Kruger effect : individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

inference : an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

metacognition :  knowledge about one’s own cognitive processes; thinking about your thinking

Critical thinking

One particular kind of knowledge or thinking skill that is related to metacognition is  critical thinking (Chew, 2020). You may have noticed that critical thinking is an objective in many college courses, and thus it could be a legitimate topic to cover in nearly any college course. It is particularly appropriate in psychology, however. As the science of (behavior and) mental processes, psychology is obviously well suited to be the discipline through which you should be introduced to this important way of thinking.

More importantly, there is a particular need to use critical thinking in psychology. We are all, in a way, experts in human behavior and mental processes, having engaged in them literally since birth. Thus, perhaps more than in any other class, students typically approach psychology with very clear ideas and opinions about its subject matter. That is, students already “know” a lot about psychology. The problem is, “it ain’t so much the things we don’t know that get us into trouble. It’s the things we know that just ain’t so” (Ward, quoted in Gilovich 1991). Indeed, many of students’ preconceptions about psychology are just plain wrong. Randolph Smith (2002) wrote a book about critical thinking in psychology called  Challenging Your Preconceptions,  highlighting this fact. On the other hand, many of students’ preconceptions about psychology are just plain right! But wait, how do you know which of your preconceptions are right and which are wrong? And when you come across a research finding or theory in this class that contradicts your preconceptions, what will you do? Will you stick to your original idea, discounting the information from the class? Will you immediately change your mind? Critical thinking can help us sort through this confusing mess.

But what is critical thinking? The goal of critical thinking is simple to state (but extraordinarily difficult to achieve): it is to be right, to draw the correct conclusions, to believe in things that are true and to disbelieve things that are false. We will provide two definitions of critical thinking (or, if you like, one large definition with two distinct parts). First, a more conceptual one: Critical thinking is thinking like a scientist in your everyday life (Schmaltz, Jansen, & Wenckowski, 2017).  Our second definition is more operational; it is simply a list of skills that are essential to be a critical thinker. Critical thinking entails solid reasoning and problem solving skills; skepticism; and an ability to identify biases, distortions, omissions, and assumptions. Excellent deductive and inductive reasoning, and problem solving skills contribute to critical thinking. So, you can consider the subject matter of sections 7.2 and 7.3 to be part of critical thinking. Because we will be devoting considerable time to these concepts in the rest of the module, let us begin with a discussion about the other aspects of critical thinking.

Let’s address that first part of the definition. Scientists form hypotheses, or predictions about some possible future observations. Then, they collect data, or information (think of this as making those future observations). They do their best to make unbiased observations using reliable techniques that have been verified by others. Then, and only then, they draw a conclusion about what those observations mean. Oh, and do not forget the most important part. “Conclusion” is probably not the most appropriate word because this conclusion is only tentative. A scientist is always prepared that someone else might come along and produce new observations that would require a new conclusion be drawn. Wow! If you like to be right, you could do a lot worse than using a process like this.

A Critical Thinker’s Toolkit 

Now for the second part of the definition. Good critical thinkers (and scientists) rely on a variety of tools to evaluate information. Perhaps the most recognizable tool for critical thinking is  skepticism (and this term provides the clearest link to the thinking like a scientist definition, as you are about to see). Some people intend it as an insult when they call someone a skeptic. But if someone calls you a skeptic, if they are using the term correctly, you should consider it a great compliment. Simply put, skepticism is a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided. People from Missouri should recognize this principle, as Missouri is known as the Show-Me State. As a skeptic, you are not inclined to believe something just because someone said so, because someone else believes it, or because it sounds reasonable. You must be persuaded by high quality evidence.

Of course, if that evidence is produced, you have a responsibility as a skeptic to change your belief. Failure to change a belief in the face of good evidence is not skepticism; skepticism has open mindedness at its core. M. Neil Browne and Stuart Keeley (2018) use the term weak sense critical thinking to describe critical thinking behaviors that are used only to strengthen a prior belief. Strong sense critical thinking, on the other hand, has as its goal reaching the best conclusion. Sometimes that means strengthening your prior belief, but sometimes it means changing your belief to accommodate the better evidence.

Many times, a failure to think critically or weak sense critical thinking is related to a  bias , an inclination, tendency, leaning, or prejudice. Everybody has biases, but many people are unaware of them. Awareness of your own biases gives you the opportunity to control or counteract them. Unfortunately, however, many people are happy to let their biases creep into their attempts to persuade others; indeed, it is a key part of their persuasive strategy. To see how these biases influence messages, just look at the different descriptions and explanations of the same events given by people of different ages or income brackets, or conservative versus liberal commentators, or by commentators from different parts of the world. Of course, to be successful, these people who are consciously using their biases must disguise them. Even undisguised biases can be difficult to identify, so disguised ones can be nearly impossible.

Here are some common sources of biases:

• Personal values and beliefs.  Some people believe that human beings are basically driven to seek power and that they are typically in competition with one another over scarce resources. These beliefs are similar to the world-view that political scientists call “realism.” Other people believe that human beings prefer to cooperate and that, given the chance, they will do so. These beliefs are similar to the world-view known as “idealism.” For many people, these deeply held beliefs can influence, or bias, their interpretations of such wide ranging situations as the behavior of nations and their leaders or the behavior of the driver in the car ahead of you. For example, if your worldview is that people are typically in competition and someone cuts you off on the highway, you may assume that the driver did it purposely to get ahead of you. Other types of beliefs about the way the world is or the way the world should be, for example, political beliefs, can similarly become a significant source of bias.
• Racism, sexism, ageism and other forms of prejudice and bigotry.  These are, sadly, a common source of bias in many people. They are essentially a special kind of “belief about the way the world is.” These beliefs—for example, that women do not make effective leaders—lead people to ignore contradictory evidence (examples of effective women leaders, or research that disputes the belief) and to interpret ambiguous evidence in a way consistent with the belief.
• Self-interest.  When particular people benefit from things turning out a certain way, they can sometimes be very susceptible to letting that interest bias them. For example, a company that will earn a profit if they sell their product may have a bias in the way that they give information about their product. A union that will benefit if its members get a generous contract might have a bias in the way it presents information about salaries at competing organizations. (Note that our inclusion of examples describing both companies and unions is an explicit attempt to control for our own personal biases). Home buyers are often dismayed to discover that they purchased their dream house from someone whose self-interest led them to lie about flooding problems in the basement or back yard. This principle, the biasing power of self-interest, is likely what led to the famous phrase  Caveat Emptor  (let the buyer beware) .  

Knowing that these types of biases exist will help you evaluate evidence more critically. Do not forget, though, that people are not always keen to let you discover the sources of biases in their arguments. For example, companies or political organizations can sometimes disguise their support of a research study by contracting with a university professor, who comes complete with a seemingly unbiased institutional affiliation, to conduct the study.

People’s biases, conscious or unconscious, can lead them to make omissions, distortions, and assumptions that undermine our ability to correctly evaluate evidence. It is essential that you look for these elements. Always ask, what is missing, what is not as it appears, and what is being assumed here? For example, consider this (fictional) chart from an ad reporting customer satisfaction at 4 local health clubs.

Clearly, from the results of the chart, one would be tempted to give Club C a try, as customer satisfaction is much higher than for the other 3 clubs.

There are so many distortions and omissions in this chart, however, that it is actually quite meaningless. First, how was satisfaction measured? Do the bars represent responses to a survey? If so, how were the questions asked? Most importantly, where is the missing scale for the chart? Although the differences look quite large, are they really?

Well, here is the same chart, with a different scale, this time labeled:

Club C is not so impressive any more, is it? In fact, all of the health clubs have customer satisfaction ratings (whatever that means) between 85% and 88%. In the first chart, the entire scale of the graph included only the percentages between 83 and 89. This “judicious” choice of scale—some would call it a distortion—and omission of that scale from the chart make the tiny differences among the clubs seem important, however.

Also, in order to be a critical thinker, you need to learn to pay attention to the assumptions that underlie a message. Let us briefly illustrate the role of assumptions by touching on some people’s beliefs about the criminal justice system in the US. Some believe that a major problem with our judicial system is that many criminals go free because of legal technicalities. Others believe that a major problem is that many innocent people are convicted of crimes. The simple fact is, both types of errors occur. A person’s conclusion about which flaw in our judicial system is the greater tragedy is based on an assumption about which of these is the more serious error (letting the guilty go free or convicting the innocent). This type of assumption is called a value assumption (Browne and Keeley, 2018). It reflects the differences in values that people develop, differences that may lead us to disregard valid evidence that does not fit in with our particular values.

Oh, by the way, some students probably noticed this, but the seven tips for evaluating information that we shared in Module 1 are related to this. Actually, they are part of this section. The tips are, to a very large degree, set of ideas you can use to help you identify biases, distortions, omissions, and assumptions. If you do not remember this section, we strongly recommend you take a few minutes to review it.

skepticism :  a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

bias : an inclination, tendency, leaning, or prejudice

• Which of your beliefs (or disbeliefs) from the Activate exercise for this section were derived from a process of critical thinking? If some of your beliefs were not based on critical thinking, are you willing to reassess these beliefs? If the answer is no, why do you think that is? If the answer is yes, what concrete steps will you take?

7.2 Reasoning and Judgment

• What percentage of kidnappings are committed by strangers?
• Which area of the house is riskiest: kitchen, bathroom, or stairs?
• What is the most common cancer in the US?
• What percentage of workplace homicides are committed by co-workers?

An essential set of procedural thinking skills is  reasoning , the ability to generate and evaluate solid conclusions from a set of statements or evidence. You should note that these conclusions (when they are generated instead of being evaluated) are one key type of inference that we described in Section 7.1. There are two main types of reasoning, deductive and inductive.

Deductive reasoning

Suppose your teacher tells you that if you get an A on the final exam in a course, you will get an A for the whole course. Then, you get an A on the final exam. What will your final course grade be? Most people can see instantly that you can conclude with certainty that you will get an A for the course. This is a type of reasoning called  deductive reasoning , which is defined as reasoning in which a conclusion is guaranteed to be true as long as the statements leading to it are true. The three statements can be listed as an  argument , with two beginning statements and a conclusion:

Statement 1: If you get an A on the final exam, you will get an A for the course

Statement 2: You get an A on the final exam

Conclusion: You will get an A for the course

This particular arrangement, in which true beginning statements lead to a guaranteed true conclusion, is known as a  deductively valid argument . Although deductive reasoning is often the subject of abstract, brain-teasing, puzzle-like word problems, it is actually an extremely important type of everyday reasoning. It is just hard to recognize sometimes. For example, imagine that you are looking for your car keys and you realize that they are either in the kitchen drawer or in your book bag. After looking in the kitchen drawer, you instantly know that they must be in your book bag. That conclusion results from a simple deductive reasoning argument. In addition, solid deductive reasoning skills are necessary for you to succeed in the sciences, philosophy, math, computer programming, and any endeavor involving the use of logic to persuade others to your point of view or to evaluate others’ arguments.

Cognitive psychologists, and before them philosophers, have been quite interested in deductive reasoning, not so much for its practical applications, but for the insights it can offer them about the ways that human beings think. One of the early ideas to emerge from the examination of deductive reasoning is that people learn (or develop) mental versions of rules that allow them to solve these types of reasoning problems (Braine, 1978; Braine, Reiser, & Rumain, 1984). The best way to see this point of view is to realize that there are different possible rules, and some of them are very simple. For example, consider this rule of logic:

therefore q

Logical rules are often presented abstractly, as letters, in order to imply that they can be used in very many specific situations. Here is a concrete version of the of the same rule:

I’ll either have pizza or a hamburger for dinner tonight (p or q)

I won’t have pizza (not p)

Therefore, I’ll have a hamburger (therefore q)

This kind of reasoning seems so natural, so easy, that it is quite plausible that we would use a version of this rule in our daily lives. At least, it seems more plausible than some of the alternative possibilities—for example, that we need to have experience with the specific situation (pizza or hamburger, in this case) in order to solve this type of problem easily. So perhaps there is a form of natural logic (Rips, 1990) that contains very simple versions of logical rules. When we are faced with a reasoning problem that maps onto one of these rules, we use the rule.

But be very careful; things are not always as easy as they seem. Even these simple rules are not so simple. For example, consider the following rule. Many people fail to realize that this rule is just as valid as the pizza or hamburger rule above.

if p, then q

therefore, not p

Concrete version:

If I eat dinner, then I will have dessert

I did not have dessert

Therefore, I did not eat dinner

The simple fact is, it can be very difficult for people to apply rules of deductive logic correctly; as a result, they make many errors when trying to do so. Is this a deductively valid argument or not?

Students who like school study a lot

Students who study a lot get good grades

Jane does not like school

Therefore, Jane does not get good grades

Many people are surprised to discover that this is not a logically valid argument; the conclusion is not guaranteed to be true from the beginning statements. Although the first statement says that students who like school study a lot, it does NOT say that students who do not like school do not study a lot. In other words, it may very well be possible to study a lot without liking school. Even people who sometimes get problems like this right might not be using the rules of deductive reasoning. Instead, they might just be making judgments for examples they know, in this case, remembering instances of people who get good grades despite not liking school.

Making deductive reasoning even more difficult is the fact that there are two important properties that an argument may have. One, it can be valid or invalid (meaning that the conclusion does or does not follow logically from the statements leading up to it). Two, an argument (or more correctly, its conclusion) can be true or false. Here is an example of an argument that is logically valid, but has a false conclusion (at least we think it is false).

Either you are eleven feet tall or the Grand Canyon was created by a spaceship crashing into the earth.

You are not eleven feet tall

Therefore the Grand Canyon was created by a spaceship crashing into the earth

This argument has the exact same form as the pizza or hamburger argument above, making it is deductively valid. The conclusion is so false, however, that it is absurd (of course, the reason the conclusion is false is that the first statement is false). When people are judging arguments, they tend to not observe the difference between deductive validity and the empirical truth of statements or conclusions. If the elements of an argument happen to be true, people are likely to judge the argument logically valid; if the elements are false, they will very likely judge it invalid (Markovits & Bouffard-Bouchard, 1992; Moshman & Franks, 1986). Thus, it seems a stretch to say that people are using these logical rules to judge the validity of arguments. Many psychologists believe that most people actually have very limited deductive reasoning skills (Johnson-Laird, 1999). They argue that when faced with a problem for which deductive logic is required, people resort to some simpler technique, such as matching terms that appear in the statements and the conclusion (Evans, 1982). This might not seem like a problem, but what if reasoners believe that the elements are true and they happen to be wrong; they will would believe that they are using a form of reasoning that guarantees they are correct and yet be wrong.

deductive reasoning :  a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

argument :  a set of statements in which the beginning statements lead to a conclusion

deductively valid argument :  an argument for which true beginning statements guarantee that the conclusion is true

Inductive reasoning and judgment

Every day, you make many judgments about the likelihood of one thing or another. Whether you realize it or not, you are practicing  inductive reasoning   on a daily basis. In inductive reasoning arguments, a conclusion is likely whenever the statements preceding it are true. The first thing to notice about inductive reasoning is that, by definition, you can never be sure about your conclusion; you can only estimate how likely the conclusion is. Inductive reasoning may lead you to focus on Memory Encoding and Recoding when you study for the exam, but it is possible the instructor will ask more questions about Memory Retrieval instead. Unlike deductive reasoning, the conclusions you reach through inductive reasoning are only probable, not certain. That is why scientists consider inductive reasoning weaker than deductive reasoning. But imagine how hard it would be for us to function if we could not act unless we were certain about the outcome.

Inductive reasoning can be represented as logical arguments consisting of statements and a conclusion, just as deductive reasoning can be. In an inductive argument, you are given some statements and a conclusion (or you are given some statements and must draw a conclusion). An argument is  inductively strong   if the conclusion would be very probable whenever the statements are true. So, for example, here is an inductively strong argument:

• Statement #1: The forecaster on Channel 2 said it is going to rain today.
• Statement #2: The forecaster on Channel 5 said it is going to rain today.
• Statement #3: It is very cloudy and humid.
• Statement #4: You just heard thunder.
• Conclusion (or judgment): It is going to rain today.

Think of the statements as evidence, on the basis of which you will draw a conclusion. So, based on the evidence presented in the four statements, it is very likely that it will rain today. Will it definitely rain today? Certainly not. We can all think of times that the weather forecaster was wrong.

A true story: Some years ago psychology student was watching a baseball playoff game between the St. Louis Cardinals and the Los Angeles Dodgers. A graphic on the screen had just informed the audience that the Cardinal at bat, (Hall of Fame shortstop) Ozzie Smith, a switch hitter batting left-handed for this plate appearance, had never, in nearly 3000 career at-bats, hit a home run left-handed. The student, who had just learned about inductive reasoning in his psychology class, turned to his companion (a Cardinals fan) and smugly said, “It is an inductively strong argument that Ozzie Smith will not hit a home run.” He turned back to face the television just in time to watch the ball sail over the right field fence for a home run. Although the student felt foolish at the time, he was not wrong. It was an inductively strong argument; 3000 at-bats is an awful lot of evidence suggesting that the Wizard of Ozz (as he was known) would not be hitting one out of the park (think of each at-bat without a home run as a statement in an inductive argument). Sadly (for the die-hard Cubs fan and Cardinals-hating student), despite the strength of the argument, the conclusion was wrong.

Given the possibility that we might draw an incorrect conclusion even with an inductively strong argument, we really want to be sure that we do, in fact, make inductively strong arguments. If we judge something probable, it had better be probable. If we judge something nearly impossible, it had better not happen. Think of inductive reasoning, then, as making reasonably accurate judgments of the probability of some conclusion given a set of evidence.

We base many decisions in our lives on inductive reasoning. For example:

Statement #1: Psychology is not my best subject

Statement #2: My psychology instructor has a reputation for giving difficult exams

Statement #3: My first psychology exam was much harder than I expected

Judgment: The next exam will probably be very difficult.

Decision: I will study tonight instead of watching Netflix.

Some other examples of judgments that people commonly make in a school context include judgments of the likelihood that:

• A particular class will be interesting/useful/difficult
• You will be able to finish writing a paper by next week if you go out tonight
• Your laptop’s battery will last through the next trip to the library
• You will not miss anything important if you skip class tomorrow
• Your instructor will not notice if you skip class tomorrow
• You will be able to find a book that you will need for a paper
• There will be an essay question about Memory Encoding on the next exam

Tversky and Kahneman (1983) recognized that there are two general ways that we might make these judgments; they termed them extensional (i.e., following the laws of probability) and intuitive (i.e., using shortcuts or heuristics, see below). We will use a similar distinction between Type 1 and Type 2 thinking, as described by Keith Stanovich and his colleagues (Evans and Stanovich, 2013; Stanovich and West, 2000). Type 1 thinking is fast, automatic, effortful, and emotional. In fact, it is hardly fair to call it reasoning at all, as judgments just seem to pop into one’s head. Type 2 thinking , on the other hand, is slow, effortful, and logical. So obviously, it is more likely to lead to a correct judgment, or an optimal decision. The problem is, we tend to over-rely on Type 1. Now, we are not saying that Type 2 is the right way to go for every decision or judgment we make. It seems a bit much, for example, to engage in a step-by-step logical reasoning procedure to decide whether we will have chicken or fish for dinner tonight.

Many bad decisions in some very important contexts, however, can be traced back to poor judgments of the likelihood of certain risks or outcomes that result from the use of Type 1 when a more logical reasoning process would have been more appropriate. For example:

Statement #1: It is late at night.

Statement #2: Albert has been drinking beer for the past five hours at a party.

Statement #3: Albert is not exactly sure where he is or how far away home is.

Judgment: Albert will have no difficulty walking home.

Decision: He walks home alone.

As you can see in this example, the three statements backing up the judgment do not really support it. In other words, this argument is not inductively strong because it is based on judgments that ignore the laws of probability. What are the chances that someone facing these conditions will be able to walk home alone easily? And one need not be drunk to make poor decisions based on judgments that just pop into our heads.

The truth is that many of our probability judgments do not come very close to what the laws of probability say they should be. Think about it. In order for us to reason in accordance with these laws, we would need to know the laws of probability, which would allow us to calculate the relationship between particular pieces of evidence and the probability of some outcome (i.e., how much likelihood should change given a piece of evidence), and we would have to do these heavy math calculations in our heads. After all, that is what Type 2 requires. Needless to say, even if we were motivated, we often do not even know how to apply Type 2 reasoning in many cases.

So what do we do when we don’t have the knowledge, skills, or time required to make the correct mathematical judgment? Do we hold off and wait until we can get better evidence? Do we read up on probability and fire up our calculator app so we can compute the correct probability? Of course not. We rely on Type 1 thinking. We “wing it.” That is, we come up with a likelihood estimate using some means at our disposal. Psychologists use the term heuristic to describe the type of “winging it” we are talking about. A  heuristic   is a shortcut strategy that we use to make some judgment or solve some problem (see Section 7.3). Heuristics are easy and quick, think of them as the basic procedures that are characteristic of Type 1.  They can absolutely lead to reasonably good judgments and decisions in some situations (like choosing between chicken and fish for dinner). They are, however, far from foolproof. There are, in fact, quite a lot of situations in which heuristics can lead us to make incorrect judgments, and in many cases the decisions based on those judgments can have serious consequences.

Let us return to the activity that begins this section. You were asked to judge the likelihood (or frequency) of certain events and risks. You were free to come up with your own evidence (or statements) to make these judgments. This is where a heuristic crops up. As a judgment shortcut, we tend to generate specific examples of those very events to help us decide their likelihood or frequency. For example, if we are asked to judge how common, frequent, or likely a particular type of cancer is, many of our statements would be examples of specific cancer cases:

Statement #1: Andy Kaufman (comedian) had lung cancer.

Statement #2: Colin Powell (US Secretary of State) had prostate cancer.

Statement #3: Bob Marley (musician) had skin and brain cancer

Statement #4: Sandra Day O’Connor (Supreme Court Justice) had breast cancer.

Statement #5: Fred Rogers (children’s entertainer) had stomach cancer.

Statement #6: Robin Roberts (news anchor) had breast cancer.

Statement #7: Bette Davis (actress) had breast cancer.

Judgment: Breast cancer is the most common type.

Your own experience or memory may also tell you that breast cancer is the most common type. But it is not (although it is common). Actually, skin cancer is the most common type in the US. We make the same types of misjudgments all the time because we do not generate the examples or evidence according to their actual frequencies or probabilities. Instead, we have a tendency (or bias) to search for the examples in memory; if they are easy to retrieve, we assume that they are common. To rephrase this in the language of the heuristic, events seem more likely to the extent that they are available to memory. This bias has been termed the  availability heuristic   (Kahneman and Tversky, 1974).

The fact that we use the availability heuristic does not automatically mean that our judgment is wrong. The reason we use heuristics in the first place is that they work fairly well in many cases (and, of course that they are easy to use). So, the easiest examples to think of sometimes are the most common ones. Is it more likely that a member of the U.S. Senate is a man or a woman? Most people have a much easier time generating examples of male senators. And as it turns out, the U.S. Senate has many more men than women (74 to 26 in 2020). In this case, then, the availability heuristic would lead you to make the correct judgment; it is far more likely that a senator would be a man.

In many other cases, however, the availability heuristic will lead us astray. This is because events can be memorable for many reasons other than their frequency. Section 5.2, Encoding Meaning, suggested that one good way to encode the meaning of some information is to form a mental image of it. Thus, information that has been pictured mentally will be more available to memory. Indeed, an event that is vivid and easily pictured will trick many people into supposing that type of event is more common than it actually is. Repetition of information will also make it more memorable. So, if the same event is described to you in a magazine, on the evening news, on a podcast that you listen to, and in your Facebook feed; it will be very available to memory. Again, the availability heuristic will cause you to misperceive the frequency of these types of events.

Most interestingly, information that is unusual is more memorable. Suppose we give you the following list of words to remember: box, flower, letter, platypus, oven, boat, newspaper, purse, drum, car. Very likely, the easiest word to remember would be platypus, the unusual one. The same thing occurs with memories of events. An event may be available to memory because it is unusual, yet the availability heuristic leads us to judge that the event is common. Did you catch that? In these cases, the availability heuristic makes us think the exact opposite of the true frequency. We end up thinking something is common because it is unusual (and therefore memorable). Yikes.

The misapplication of the availability heuristic sometimes has unfortunate results. For example, if you went to K-12 school in the US over the past 10 years, it is extremely likely that you have participated in lockdown and active shooter drills. Of course, everyone is trying to prevent the tragedy of another school shooting. And believe us, we are not trying to minimize how terrible the tragedy is. But the truth of the matter is, school shootings are extremely rare. Because the federal government does not keep a database of school shootings, the Washington Post has maintained their own running tally. Between 1999 and January 2020 (the date of the most recent school shooting with a death in the US at of the time this paragraph was written), the Post reported a total of 254 people died in school shootings in the US. Not 254 per year, 254 total. That is an average of 12 per year. Of course, that is 254 people who should not have died (particularly because many were children), but in a country with approximately 60,000,000 students and teachers, this is a very small risk.

But many students and teachers are terrified that they will be victims of school shootings because of the availability heuristic. It is so easy to think of examples (they are very available to memory) that people believe the event is very common. It is not. And there is a downside to this. We happen to believe that there is an enormous gun violence problem in the United States. According the the Centers for Disease Control and Prevention, there were 39,773 firearm deaths in the US in 2017. Fifteen of those deaths were in school shootings, according to the Post. 60% of those deaths were suicides. When people pay attention to the school shooting risk (low), they often fail to notice the much larger risk.

And examples like this are by no means unique. The authors of this book have been teaching psychology since the 1990’s. We have been able to make the exact same arguments about the misapplication of the availability heuristics and keep them current by simply swapping out for the “fear of the day.” In the 1990’s it was children being kidnapped by strangers (it was known as “stranger danger”) despite the facts that kidnappings accounted for only 2% of the violent crimes committed against children, and only 24% of kidnappings are committed by strangers (US Department of Justice, 2007). This fear overlapped with the fear of terrorism that gripped the country after the 2001 terrorist attacks on the World Trade Center and US Pentagon and still plagues the population of the US somewhat in 2020. After a well-publicized, sensational act of violence, people are extremely likely to increase their estimates of the chances that they, too, will be victims of terror. Think about the reality, however. In October of 2001, a terrorist mailed anthrax spores to members of the US government and a number of media companies. A total of five people died as a result of this attack. The nation was nearly paralyzed by the fear of dying from the attack; in reality the probability of an individual person dying was 0.00000002.

The availability heuristic can lead you to make incorrect judgments in a school setting as well. For example, suppose you are trying to decide if you should take a class from a particular math professor. You might try to make a judgment of how good a teacher she is by recalling instances of friends and acquaintances making comments about her teaching skill. You may have some examples that suggest that she is a poor teacher very available to memory, so on the basis of the availability heuristic you judge her a poor teacher and decide to take the class from someone else. What if, however, the instances you recalled were all from the same person, and this person happens to be a very colorful storyteller? The subsequent ease of remembering the instances might not indicate that the professor is a poor teacher after all.

Although the availability heuristic is obviously important, it is not the only judgment heuristic we use. Amos Tversky and Daniel Kahneman examined the role of heuristics in inductive reasoning in a long series of studies. Kahneman received a Nobel Prize in Economics for this research in 2002, and Tversky would have certainly received one as well if he had not died of melanoma at age 59 in 1996 (Nobel Prizes are not awarded posthumously). Kahneman and Tversky demonstrated repeatedly that people do not reason in ways that are consistent with the laws of probability. They identified several heuristic strategies that people use instead to make judgments about likelihood. The importance of this work for economics (and the reason that Kahneman was awarded the Nobel Prize) is that earlier economic theories had assumed that people do make judgments rationally, that is, in agreement with the laws of probability.

Another common heuristic that people use for making judgments is the  representativeness heuristic (Kahneman & Tversky 1973). Suppose we describe a person to you. He is quiet and shy, has an unassuming personality, and likes to work with numbers. Is this person more likely to be an accountant or an attorney? If you said accountant, you were probably using the representativeness heuristic. Our imaginary person is judged likely to be an accountant because he resembles, or is representative of the concept of, an accountant. When research participants are asked to make judgments such as these, the only thing that seems to matter is the representativeness of the description. For example, if told that the person described is in a room that contains 70 attorneys and 30 accountants, participants will still assume that he is an accountant.

inductive reasoning :  a type of reasoning in which we make judgments about likelihood from sets of evidence

inductively strong argument :  an inductive argument in which the beginning statements lead to a conclusion that is probably true

heuristic :  a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

availability heuristic :  judging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

representativeness heuristic:   judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

Type 1 thinking : fast, automatic, and emotional thinking.

Type 2 thinking : slow, effortful, and logical thinking.

• What percentage of workplace homicides are co-worker violence?

Many people get these questions wrong. The answers are 10%; stairs; skin; 6%. How close were your answers? Explain how the availability heuristic might have led you to make the incorrect judgments.

• Can you think of some other judgments that you have made (or beliefs that you have) that might have been influenced by the availability heuristic?

7.3 Problem Solving

• Please take a few minutes to list a number of problems that you are facing right now.
• Now write about a problem that you recently solved.
• What is your definition of a problem?

Mary has a problem. Her daughter, ordinarily quite eager to please, appears to delight in being the last person to do anything. Whether getting ready for school, going to piano lessons or karate class, or even going out with her friends, she seems unwilling or unable to get ready on time. Other people have different kinds of problems. For example, many students work at jobs, have numerous family commitments, and are facing a course schedule full of difficult exams, assignments, papers, and speeches. How can they find enough time to devote to their studies and still fulfill their other obligations? Speaking of students and their problems: Show that a ball thrown vertically upward with initial velocity v0 takes twice as much time to return as to reach the highest point (from Spiegel, 1981).

These are three very different situations, but we have called them all problems. What makes them all the same, despite the differences? A psychologist might define a  problem   as a situation with an initial state, a goal state, and a set of possible intermediate states. Somewhat more meaningfully, we might consider a problem a situation in which you are in here one state (e.g., daughter is always late), you want to be there in another state (e.g., daughter is not always late), and with no obvious way to get from here to there. Defined this way, each of the three situations we outlined can now be seen as an example of the same general concept, a problem. At this point, you might begin to wonder what is not a problem, given such a general definition. It seems that nearly every non-routine task we engage in could qualify as a problem. As long as you realize that problems are not necessarily bad (it can be quite fun and satisfying to rise to the challenge and solve a problem), this may be a useful way to think about it.

Can we identify a set of problem-solving skills that would apply to these very different kinds of situations? That task, in a nutshell, is a major goal of this section. Let us try to begin to make sense of the wide variety of ways that problems can be solved with an important observation: the process of solving problems can be divided into two key parts. First, people have to notice, comprehend, and represent the problem properly in their minds (called  problem representation ). Second, they have to apply some kind of solution strategy to the problem. Psychologists have studied both of these key parts of the process in detail.

When you first think about the problem-solving process, you might guess that most of our difficulties would occur because we are failing in the second step, the application of strategies. Although this can be a significant difficulty much of the time, the more important source of difficulty is probably problem representation. In short, we often fail to solve a problem because we are looking at it, or thinking about it, the wrong way.

problem :  a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

problem representation :  noticing, comprehending and forming a mental conception of a problem

Defining and Mentally Representing Problems in Order to Solve Them

So, the main obstacle to solving a problem is that we do not clearly understand exactly what the problem is. Recall the problem with Mary’s daughter always being late. One way to represent, or to think about, this problem is that she is being defiant. She refuses to get ready in time. This type of representation or definition suggests a particular type of solution. Another way to think about the problem, however, is to consider the possibility that she is simply being sidetracked by interesting diversions. This different conception of what the problem is (i.e., different representation) suggests a very different solution strategy. For example, if Mary defines the problem as defiance, she may be tempted to solve the problem using some kind of coercive tactics, that is, to assert her authority as her mother and force her to listen. On the other hand, if Mary defines the problem as distraction, she may try to solve it by simply removing the distracting objects.

As you might guess, when a problem is represented one way, the solution may seem very difficult, or even impossible. Seen another way, the solution might be very easy. For example, consider the following problem (from Nasar, 1998):

Two bicyclists start 20 miles apart and head toward each other, each going at a steady rate of 10 miles per hour. At the same time, a fly that travels at a steady 15 miles per hour starts from the front wheel of the southbound bicycle and flies to the front wheel of the northbound one, then turns around and flies to the front wheel of the southbound one again, and continues in this manner until he is crushed between the two front wheels. Question: what total distance did the fly cover?

Please take a few minutes to try to solve this problem.

Most people represent this problem as a question about a fly because, well, that is how the question is asked. The solution, using this representation, is to figure out how far the fly travels on the first leg of its journey, then add this total to how far it travels on the second leg of its journey (when it turns around and returns to the first bicycle), then continue to add the smaller distance from each leg of the journey until you converge on the correct answer. You would have to be quite skilled at math to solve this problem, and you would probably need some time and pencil and paper to do it.

If you consider a different representation, however, you can solve this problem in your head. Instead of thinking about it as a question about a fly, think about it as a question about the bicycles. They are 20 miles apart, and each is traveling 10 miles per hour. How long will it take for the bicycles to reach each other? Right, one hour. The fly is traveling 15 miles per hour; therefore, it will travel a total of 15 miles back and forth in the hour before the bicycles meet. Represented one way (as a problem about a fly), the problem is quite difficult. Represented another way (as a problem about two bicycles), it is easy. Changing your representation of a problem is sometimes the best—sometimes the only—way to solve it.

Unfortunately, however, changing a problem’s representation is not the easiest thing in the world to do. Often, problem solvers get stuck looking at a problem one way. This is called  fixation . Most people who represent the preceding problem as a problem about a fly probably do not pause to reconsider, and consequently change, their representation. A parent who thinks her daughter is being defiant is unlikely to consider the possibility that her behavior is far less purposeful.

Problem-solving fixation was examined by a group of German psychologists called Gestalt psychologists during the 1930’s and 1940’s. Karl Dunker, for example, discovered an important type of failure to take a different perspective called  functional fixedness . Imagine being a participant in one of his experiments. You are asked to figure out how to mount two candles on a door and are given an assortment of odds and ends, including a small empty cardboard box and some thumbtacks. Perhaps you have already figured out a solution: tack the box to the door so it forms a platform, then put the candles on top of the box. Most people are able to arrive at this solution. Imagine a slight variation of the procedure, however. What if, instead of being empty, the box had matches in it? Most people given this version of the problem do not arrive at the solution given above. Why? Because it seems to people that when the box contains matches, it already has a function; it is a matchbox. People are unlikely to consider a new function for an object that already has a function. This is functional fixedness.

Mental set is a type of fixation in which the problem solver gets stuck using the same solution strategy that has been successful in the past, even though the solution may no longer be useful. It is commonly seen when students do math problems for homework. Often, several problems in a row require the reapplication of the same solution strategy. Then, without warning, the next problem in the set requires a new strategy. Many students attempt to apply the formerly successful strategy on the new problem and therefore cannot come up with a correct answer.

The thing to remember is that you cannot solve a problem unless you correctly identify what it is to begin with (initial state) and what you want the end result to be (goal state). That may mean looking at the problem from a different angle and representing it in a new way. The correct representation does not guarantee a successful solution, but it certainly puts you on the right track.

A bit more optimistically, the Gestalt psychologists discovered what may be considered the opposite of fixation, namely  insight . Sometimes the solution to a problem just seems to pop into your head. Wolfgang Kohler examined insight by posing many different problems to chimpanzees, principally problems pertaining to their acquisition of out-of-reach food. In one version, a banana was placed outside of a chimpanzee’s cage and a short stick inside the cage. The stick was too short to retrieve the banana, but was long enough to retrieve a longer stick also located outside of the cage. This second stick was long enough to retrieve the banana. After trying, and failing, to reach the banana with the shorter stick, the chimpanzee would try a couple of random-seeming attempts, react with some apparent frustration or anger, then suddenly rush to the longer stick, the correct solution fully realized at this point. This sudden appearance of the solution, observed many times with many different problems, was termed insight by Kohler.

Lest you think it pertains to chimpanzees only, Karl Dunker demonstrated that children also solve problems through insight in the 1930s. More importantly, you have probably experienced insight yourself. Think back to a time when you were trying to solve a difficult problem. After struggling for a while, you gave up. Hours later, the solution just popped into your head, perhaps when you were taking a walk, eating dinner, or lying in bed.

fixation :  when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

functional fixedness :  a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

mental set :  a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

insight :  a sudden realization of a solution to a problem

Solving Problems by Trial and Error

Correctly identifying the problem and your goal for a solution is a good start, but recall the psychologist’s definition of a problem: it includes a set of possible intermediate states. Viewed this way, a problem can be solved satisfactorily only if one can find a path through some of these intermediate states to the goal. Imagine a fairly routine problem, finding a new route to school when your ordinary route is blocked (by road construction, for example). At each intersection, you may turn left, turn right, or go straight. A satisfactory solution to the problem (of getting to school) is a sequence of selections at each intersection that allows you to wind up at school.

If you had all the time in the world to get to school, you might try choosing intermediate states randomly. At one corner you turn left, the next you go straight, then you go left again, then right, then right, then straight. Unfortunately, trial and error will not necessarily get you where you want to go, and even if it does, it is not the fastest way to get there. For example, when a friend of ours was in college, he got lost on the way to a concert and attempted to find the venue by choosing streets to turn onto randomly (this was long before the use of GPS). Amazingly enough, the strategy worked, although he did end up missing two out of the three bands who played that night.

Trial and error is not all bad, however. B.F. Skinner, a prominent behaviorist psychologist, suggested that people often behave randomly in order to see what effect the behavior has on the environment and what subsequent effect this environmental change has on them. This seems particularly true for the very young person. Picture a child filling a household’s fish tank with toilet paper, for example. To a child trying to develop a repertoire of creative problem-solving strategies, an odd and random behavior might be just the ticket. Eventually, the exasperated parent hopes, the child will discover that many of these random behaviors do not successfully solve problems; in fact, in many cases they create problems. Thus, one would expect a decrease in this random behavior as a child matures. You should realize, however, that the opposite extreme is equally counterproductive. If the children become too rigid, never trying something unexpected and new, their problem solving skills can become too limited.

Effective problem solving seems to call for a happy medium that strikes a balance between using well-founded old strategies and trying new ground and territory. The individual who recognizes a situation in which an old problem-solving strategy would work best, and who can also recognize a situation in which a new untested strategy is necessary is halfway to success.

Solving Problems with Algorithms and Heuristics

For many problems there is a possible strategy available that will guarantee a correct solution. For example, think about math problems. Math lessons often consist of step-by-step procedures that can be used to solve the problems. If you apply the strategy without error, you are guaranteed to arrive at the correct solution to the problem. This approach is called using an  algorithm , a term that denotes the step-by-step procedure that guarantees a correct solution. Because algorithms are sometimes available and come with a guarantee, you might think that most people use them frequently. Unfortunately, however, they do not. As the experience of many students who have struggled through math classes can attest, algorithms can be extremely difficult to use, even when the problem solver knows which algorithm is supposed to work in solving the problem. In problems outside of math class, we often do not even know if an algorithm is available. It is probably fair to say, then, that algorithms are rarely used when people try to solve problems.

Because algorithms are so difficult to use, people often pass up the opportunity to guarantee a correct solution in favor of a strategy that is much easier to use and yields a reasonable chance of coming up with a correct solution. These strategies are called  problem solving heuristics . Similar to what you saw in section 6.2 with reasoning heuristics, a problem solving heuristic is a shortcut strategy that people use when trying to solve problems. It usually works pretty well, but does not guarantee a correct solution to the problem. For example, one problem solving heuristic might be “always move toward the goal” (so when trying to get to school when your regular route is blocked, you would always turn in the direction you think the school is). A heuristic that people might use when doing math homework is “use the same solution strategy that you just used for the previous problem.”

By the way, we hope these last two paragraphs feel familiar to you. They seem to parallel a distinction that you recently learned. Indeed, algorithms and problem-solving heuristics are another example of the distinction between Type 1 thinking and Type 2 thinking.

Although it is probably not worth describing a large number of specific heuristics, two observations about heuristics are worth mentioning. First, heuristics can be very general or they can be very specific, pertaining to a particular type of problem only. For example, “always move toward the goal” is a general strategy that you can apply to countless problem situations. On the other hand, “when you are lost without a functioning gps, pick the most expensive car you can see and follow it” is specific to the problem of being lost. Second, all heuristics are not equally useful. One heuristic that many students know is “when in doubt, choose c for a question on a multiple-choice exam.” This is a dreadful strategy because many instructors intentionally randomize the order of answer choices. Another test-taking heuristic, somewhat more useful, is “look for the answer to one question somewhere else on the exam.”

You really should pay attention to the application of heuristics to test taking. Imagine that while reviewing your answers for a multiple-choice exam before turning it in, you come across a question for which you originally thought the answer was c. Upon reflection, you now think that the answer might be b. Should you change the answer to b, or should you stick with your first impression? Most people will apply the heuristic strategy to “stick with your first impression.” What they do not realize, of course, is that this is a very poor strategy (Lilienfeld et al, 2009). Most of the errors on exams come on questions that were answered wrong originally and were not changed (so they remain wrong). There are many fewer errors where we change a correct answer to an incorrect answer. And, of course, sometimes we change an incorrect answer to a correct answer. In fact, research has shown that it is more common to change a wrong answer to a right answer than vice versa (Bruno, 2001).

The belief in this poor test-taking strategy (stick with your first impression) is based on the  confirmation bias   (Nickerson, 1998; Wason, 1960). You first saw the confirmation bias in Module 1, but because it is so important, we will repeat the information here. People have a bias, or tendency, to notice information that confirms what they already believe. Somebody at one time told you to stick with your first impression, so when you look at the results of an exam you have taken, you will tend to notice the cases that are consistent with that belief. That is, you will notice the cases in which you originally had an answer correct and changed it to the wrong answer. You tend not to notice the other two important (and more common) cases, changing an answer from wrong to right, and leaving a wrong answer unchanged.

Because heuristics by definition do not guarantee a correct solution to a problem, mistakes are bound to occur when we employ them. A poor choice of a specific heuristic will lead to an even higher likelihood of making an error.

algorithm :  a step-by-step procedure that guarantees a correct solution to a problem

problem solving heuristic :  a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

confirmation bias :  people’s tendency to notice information that confirms what they already believe

An Effective Problem-Solving Sequence

You may be left with a big question: If algorithms are hard to use and heuristics often don’t work, how am I supposed to solve problems? Robert Sternberg (1996), as part of his theory of what makes people successfully intelligent (Module 8) described a problem-solving sequence that has been shown to work rather well:

• Identify the existence of a problem.  In school, problem identification is often easy; problems that you encounter in math classes, for example, are conveniently labeled as problems for you. Outside of school, however, realizing that you have a problem is a key difficulty that you must get past in order to begin solving it. You must be very sensitive to the symptoms that indicate a problem.
• Define the problem.  Suppose you realize that you have been having many headaches recently. Very likely, you would identify this as a problem. If you define the problem as “headaches,” the solution would probably be to take aspirin or ibuprofen or some other anti-inflammatory medication. If the headaches keep returning, however, you have not really solved the problem—likely because you have mistaken a symptom for the problem itself. Instead, you must find the root cause of the headaches. Stress might be the real problem. For you to successfully solve many problems it may be necessary for you to overcome your fixations and represent the problems differently. One specific strategy that you might find useful is to try to define the problem from someone else’s perspective. How would your parents, spouse, significant other, doctor, etc. define the problem? Somewhere in these different perspectives may lurk the key definition that will allow you to find an easier and permanent solution.
• Formulate strategy.  Now it is time to begin planning exactly how the problem will be solved. Is there an algorithm or heuristic available for you to use? Remember, heuristics by their very nature guarantee that occasionally you will not be able to solve the problem. One point to keep in mind is that you should look for long-range solutions, which are more likely to address the root cause of a problem than short-range solutions.
• Represent and organize information.  Similar to the way that the problem itself can be defined, or represented in multiple ways, information within the problem is open to different interpretations. Suppose you are studying for a big exam. You have chapters from a textbook and from a supplemental reader, along with lecture notes that all need to be studied. How should you (represent and) organize these materials? Should you separate them by type of material (text versus reader versus lecture notes), or should you separate them by topic? To solve problems effectively, you must learn to find the most useful representation and organization of information.
• Allocate resources.  This is perhaps the simplest principle of the problem solving sequence, but it is extremely difficult for many people. First, you must decide whether time, money, skills, effort, goodwill, or some other resource would help to solve the problem Then, you must make the hard choice of deciding which resources to use, realizing that you cannot devote maximum resources to every problem. Very often, the solution to problem is simply to change how resources are allocated (for example, spending more time studying in order to improve grades).
• Monitor and evaluate solutions.  Pay attention to the solution strategy while you are applying it. If it is not working, you may be able to select another strategy. Another fact you should realize about problem solving is that it never does end. Solving one problem frequently brings up new ones. Good monitoring and evaluation of your problem solutions can help you to anticipate and get a jump on solving the inevitable new problems that will arise.

Please note that this as  an  effective problem-solving sequence, not  the  effective problem solving sequence. Just as you can become fixated and end up representing the problem incorrectly or trying an inefficient solution, you can become stuck applying the problem-solving sequence in an inflexible way. Clearly there are problem situations that can be solved without using these skills in this order.

Additionally, many real-world problems may require that you go back and redefine a problem several times as the situation changes (Sternberg et al. 2000). For example, consider the problem with Mary’s daughter one last time. At first, Mary did represent the problem as one of defiance. When her early strategy of pleading and threatening punishment was unsuccessful, Mary began to observe her daughter more carefully. She noticed that, indeed, her daughter’s attention would be drawn by an irresistible distraction or book. Fresh with a re-representation of the problem, she began a new solution strategy. She began to remind her daughter every few minutes to stay on task and remind her that if she is ready before it is time to leave, she may return to the book or other distracting object at that time. Fortunately, this strategy was successful, so Mary did not have to go back and redefine the problem again.

Pick one or two of the problems that you listed when you first started studying this section and try to work out the steps of Sternberg’s problem solving sequence for each one.

a mental representation of a category of things in the world

an assumption about the truth of something that is not stated. Inferences come from our prior knowledge and experience, and from logical reasoning

knowledge about one’s own cognitive processes; thinking about your thinking

individuals who are less competent tend to overestimate their abilities more than individuals who are more competent do

Thinking like a scientist in your everyday life for the purpose of drawing correct conclusions. It entails skepticism; an ability to identify biases, distortions, omissions, and assumptions; and excellent deductive and inductive reasoning, and problem solving skills.

a way of thinking in which you refrain from drawing a conclusion or changing your mind until good evidence has been provided

an inclination, tendency, leaning, or prejudice

a type of reasoning in which the conclusion is guaranteed to be true any time the statements leading up to it are true

a set of statements in which the beginning statements lead to a conclusion

an argument for which true beginning statements guarantee that the conclusion is true

a type of reasoning in which we make judgments about likelihood from sets of evidence

an inductive argument in which the beginning statements lead to a conclusion that is probably true

fast, automatic, and emotional thinking

slow, effortful, and logical thinking

a shortcut strategy that we use to make judgments and solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

udging the frequency or likelihood of some event type according to how easily examples of the event can be called to mind (i.e., how available they are to memory)

judging the likelihood that something is a member of a category on the basis of how much it resembles a typical category member (i.e., how representative it is of the category)

a situation in which we are in an initial state, have a desired goal state, and there is a number of possible intermediate states (i.e., there is no obvious way to get from the initial to the goal state)

noticing, comprehending and forming a mental conception of a problem

when a problem solver gets stuck looking at a problem a particular way and cannot change his or her representation of it (or his or her intended solution strategy)

a specific type of fixation in which a problem solver cannot think of a new use for an object that already has a function

a specific type of fixation in which a problem solver gets stuck using the same solution strategy that has been successful in the past

a sudden realization of a solution to a problem

a step-by-step procedure that guarantees a correct solution to a problem

The tendency to notice and pay attention to information that confirms your prior beliefs and to ignore information that disconfirms them.

a shortcut strategy that we use to solve problems. Although they are easy to use, they do not guarantee correct judgments and solutions

Introduction to Psychology Copyright © 2020 by Ken Gray; Elizabeth Arnott-Hill; and Or'Shaundra Benson is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

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Inductive vs. Deductive Writing

by Purdue Global Academic Success Center and Writing Center · Published February 25, 2015 · Updated February 24, 2015

Dr. Tamara Fudge, Kaplan University professor in the School of Business and IT

There are several ways to present information when writing, including those that employ inductive and deductive reasoning . The difference can be stated simply:

• Inductive reasoning presents facts and then wraps them up with a conclusion .
• Deductive reasoning presents a thesis statement and then provides supportive facts or examples.

Which should the writer use? It depends on content, the intended audience , and your overall purpose .

If you want your audience to discover new things with you , then inductive writing might make sense.   Here is n example:

My dog Max wants to chase every non-human living creature he sees, whether it is the cats in the house or rabbits and squirrels in the backyard. Sources indicate that this is a behavior typical of Jack Russell terriers. While Max is a mixed breed dog, he is approximately the same size and has many of the typical markings of a Jack Russell. From these facts along with his behaviors, we surmise that Max is indeed at least part Jack Russell terrier.

Within that short paragraph, you learned about Max’s manners and a little about what he might look like, and then the concluding sentence connected these ideas together. This kind of writing often keeps the reader’s attention, as he or she must read all the pieces of the puzzle before they are connected.

Purposes for this kind of writing include creative writing and perhaps some persuasive essays, although much academic work is done in deductive form.

If your audience is not likely going to read the entire written piece, then deductive reasoning might make more sense, as the reader can look for what he or she wants by quickly scanning first sentences of each paragraph. Here is an example:

My backyard is in dire need of cleaning and new landscaping. The Kentucky bluegrass that was planted there five years ago has been all but replaced by Creeping Charlie, a particularly invasive weed. The stone steps leading to the house are in some disrepair, and there are some slats missing from the fence. Perennials were planted three years ago, but the moles and rabbits destroyed many of the bulbs, so we no longer have flowers in the spring.

The reader knows from the very first sentence that the backyard is a mess! This paragraph could have ended with a clarifying conclusion sentence; while it might be considered redundant to do so, the scientific community tends to work through deductive reasoning by providing (1) a premise or argument – which could also be called a thesis statement, (2) then evidence to support the premise, and (3) finally the conclusion.

Purposes for this kind of writing include business letters and project documents, where the client is more likely to skim the work for generalities or to hunt for only the parts that are important to him or her. Again, scientific writing tends to follow this format as well, and research papers greatly benefit from deductive writing.

Whether one method or another is chosen, there are some other important considerations. First, it is important that the facts/evidence be true. Perform research carefully and from appropriate sources; make sure ideas are cited properly. You might need to avoid absolute words such as “always,” “never,” and “only,” because they exclude any anomalies. Try not to write questions: the writer’s job is to provide answers instead. Lastly, avoid quotes in thesis statements or conclusions, because they are not your own words – and thus undermine your authority as the paper writer.

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3.4: Inductive and Deductive Reasoning

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Learning Objectives

Students will be able to

• Identify and utilize deductive and inductive reasoning

Ask somebody who has a job as to why they have a job and there is a good chance they have a reason or multiple reasons. Most likely they will respond by saying that they need the money for their basic necessities. They may even respond that they just want to keep busy or that their parents told them they had to. The point is that there are reasons.

Definition: Reasoning

Reasoning is the act of drawing a conclusion from assumed fact(s) called premise(s) .

Examples \(\PageIndex{1}\)

Identify the premise(s) and conclusion in each case of reasoning:

a) "Martha wants to buy a new smartphone, so she decides to get a job."

b) The traffic app notifies Pedro that the traffic on Interstate 215 North will cause him to arrive at his destination at 3 p.m., an hour later than he expected. The app also shows that Interstate 15 North will allow him to arrive at his destination at 2:30 p.m. Pedro decides to take the Interstate 15 North.

a) The premise is that Martha wants to buy a new smartphone and the conclusion is that she decides to get a job.

b) There are two premises in this example. One, that the traffic on Interstate 215 North will cause Pedro to arrive at his destination at 3 p.m, and the other that Interstate 15 North will allow him to arrive at his destination at 2:30 p.m. The conclusion is that Pedro takes the Interstate 15 North.

There are many different forms of reasoning defined by scholars, two of which are defined below.

Definitions: Inductive and Deductive Reasoning

Inductive reasoning: uses a collection of specific instances as premises and uses them to propose a general conclusion .

Deductive reasoning: uses a collection of general statements as premises and uses them to propose a specific conclusion .

Notice carefully how both forms of reasoning have both premises and a conclusion. The important difference between these two types is the nature of the premises and conclusion. Applying these definitions to some examples should illuminate the differences and similarities.

Examples \(\PageIndex{2}\)

Identify the premises and conclusion of the reasoning below. Identify the type of reasoning used and explain your choice.

a) “When I went to the store last week I forgot my purse, and when I went today I forgot my purse. I always forget my purse when I go to the store”

b) “Every day for the past year, a plane flies over my house at 2 p.m. A plane will fly over my house every day at 2 p.m.”

c) "All electronic devices are useful. My cell phone is an electronic device. Therefore, my cell phone is useful."

d) Spicy food makes me teary. Habanero sauce is spicy food. Habanero sauce makes me teary.

a) The premises are:

• When I went to the store last week I forgot my purse.
• When I went today I forgot my purse.

The conclusion is:

• I always forget my purse when I go to the store

This is an example of inductive reasoning because the premises are specific instances, while the conclusion is general.

b) The premise is:

• Every day for the past year, a plane flies over my house at 2 p.m
• A plane will fly over my house every day at 2 p.m.

c) The premises are:

• All electronic devices are useful.
• My cell phone is an electronic device.
• My cell phone is useful.

d) The premises are:

• Spicy food makes me teary.
• Habanero sauce is spicy food.
• Habanero sauce makes me teary.

This is an example of deductive reasoning because the premises are general statements, while the conclusion is specific.

Marcus Coetzee

Inductive and deductive reasoning can help us to solve complex strategic and social problems.

Article on #Strategy .

By Marcus Coetzee, 18 June 2021.

1. Introduction

Strategy emerges from how we think about the complex problems facing our organizations. These problems might relate to our environment, the challenges faced by our beneficiaries or something inside our organization. To become better at developing strategies, we must learn how to think more clearly and avoid cognitive biases.

My ability to think strategically has benefited immensely from understanding the differences between inductive and deductive reasoning, and understanding when and how to apply them. Inductive reasoning involves ‘bottom up thinking’ – constructing theories from details. In contrast, deductive reasoning involves ‘top down thinking’ – starting with a theory and assuming details that must be true if the theory is valid.

We all have our preferences for one of these types of reasoning when solving complex problems that affect organizations and communities. Nevertheless, it is beneficial to master both types of reasoning so that we can use them when the need arises.

This article summarizes what I have learned so far while diving into this topic. It is a detailed and technical article that will interest people who want to enhance how they use reasoning to solve problems.

2. Terminology

Here is some of the terminology I use in this article:

‘Theories’ include beliefs, principles, generalizations, rules, patterns, conjectures and conclusions that describe a part of the world that is greater than what was observed. These theories are used to explain or predict that which was not observed or not yet observed.

‘Observations’ include experiences, cases and instances.

‘ Hypotheses ’ are clear statements that are the building blocks for theories. For example, it was raining this morning when I left my apartment. I hypothesized that drops of water would fall on me when I went outdoors. This hypothesis is a core component of our theory of rain.

‘Scientific’ is when we use inductive or deductive reasoning in a way that conforms with the standards prescribed by the philosophy of science , which explores the nature of scientific theories and methodologies. For example, the Principle of Falsification requires that a scientific theory is able to be disproved and should specify how this might be done.

3. Inductive reasoning

In this section I will introduce inductive reasoning and provide several examples. I will explain how inductive reasoning is intrinsically constrained by the need to make generalizations. I will also explain when and when not to use inductive reasoning. 

This section closes with a detailed example of how I used inductive reasoning to infer an informal theory that homelessness has increased in South Africa as a result of the Covid-19 pandemic and is unlikely to be alleviated any time soon.

3.1 What is inductive reasoning?

Inductive reasoning is commonly referred to as ‘bottom up’ thinking. It involves using details to infer theories that cover more than what was observed – i.e. creating generalizations based upon a set of observations. The statement of probable truth that we reach through inductive reasoning is sometimes called a ‘conjecture’.

The flowchart below illustrates the process of inductive reasoning.

We use inductive reasoning in our lives everyday to make sense of the world. Many of the theories we formulate are not scientific or academic but rather personal.

People are more likely to consider the theories that they develop through inductive reasoning to be true if their theories are associated with intense emotions, and if their repeated and different types of observations fit their theory. For example, someone will be more inclined to believe that their community is unsafe if they are a victim of crime, and if they know other people who have had similar experiences, and if they hear stories about their dangerous community on the radio.

In contrast, when inductive reasoning is used formally in statistics and quantitative research, then the strength of the resulting theory depends primarily on the sample design and research methodology. Let us assume that the researchers have a sample frame (with the details of the population that is being studied), and are able to draw a probability sample (where there is a positive and known chance of everyone being included in the sample). This would enable them to specify the exact statistical probability that their theory will apply to people, things and events that were not observed but are in the ambit of the theory.

3.2. Three examples of inductive reasoning

The best way to understand inductive reasoning is to see examples of how it is being used. Here are three that were on my mind when I wrote this article.

The first example relates to the National Income Dynamics Study – Coronavirus Rapid Mobile Survey (NIDS-CRAM) . Enumerators phoned a nationally representative sample of South Africans during ‘hard lockdown’ to understand their social and economic circumstances. This yielded many insights about how South Africans were struggling with the symptoms of poverty such as a shortage of food and access to social services. This is an example of inductive reasoning because the detailed results of the interviews were used to create a broader theory about the socio-economic circumstances of all South Africans.

The second example relates to the stories of government corruption and ‘state capture’ that have filled the South African news cycle for several years. Investigative journalists and the Zondo Commission of Inquiry into Allegations of State Capture have uncovered many instances of large-scale corruption. Many South Africans, including myself, have inferred a theory about the nature and incidence of corruption in government and state-owned enterprises. Then when I heard of a massive tender (approx USD 15 billion) being awarded on short notice for the supply of electricity, I predicted that government corruption is most likely involved in the tender process. Time is revealing the truth of the matter. This is inductive reasoning because I used several observations about corruption to notice patterns and develop a personal theory about government corruption, from which I make informal predictions.

The third example relates to a project I’m currently working on in East Africa . I am part of a team that is working on a study of non-tariff barriers in the East African Community. We are gathering official statistics on trade in the region, as well as information from traders, transporters, clearing agents and border officials. There are several data gathering methodologies involved. We will primarily use inductive reasoning to assimilate this data and infer a theory about the negative impact of these trade barriers on the region and how best to mitigate them. This is inductive reasoning because we use a multitude of observations to develop a theory about how non-tariff barriers are affecting all trade in the region.

3.3. Inductive theories vary in their probability that they will apply to things that were yet not observed

The Problem of Induction was described by the philosopher David Hume in the 18th century. He explained why generalizing a set of observations can never be true – at the most they can be described as highly probable . This is the inherent risk that we all experience when making generalizations about a broader group or set of phenomena. However, this should not belittle the value of inductive reasoning since our mental models rely on this process. We should simply accept that the ‘map is not the territory’.

When conducting scientific research, it may be possible to specify the probability that the theory is true for observations that were not used to build the theory (i.e. for other people or future events that are not yet observed). 

When we cannot specify the probability that an inductive reasoning is true, the proponents of the theory must be transparent about the process and compromises with data and methodology that were required along the way. This enables others to judge for themselves how probable they believe the theory to be.

3.4. When to use inductive reasoning

Inductive reasoning is useful when you want to develop a general theory based upon a limited set of observations because you don’t have the means to investigate or measure everything.

It is also useful when you already understand the conceptual areas that you want to explore but want to understand the likely incidence or frequency that certain things are true. For example, I spent three years working on a study to assess the likelihood that certain demographic and background factors were associated with students dropping out of South African universities.

It can also be useful when you want to investigate the strength of relationships between things and the extent to which certain variables correlate with each other.

Finally, inductive reasoning is useful when you want to make a prediction about the future based on historical trends (e.g. unemployment rate and types of skills that the economy will need.)

3.5. Inductive reasoning needs the right data to work effectively

Flawed and improbable theories are created when we take data from one situation and generalize it to other situations that are very different from the one where the original data was obtained. The problem here is not so much with inductive reasoning per se, but rather with its poor use. This might involve:

• Attempting to generalize findings from one group to another with different characteristics. For example, a group of policy-makers might attempt to use a set of observations about the challenges faced by informal businesses in the Khayelitsha township in Cape Town to develop a theory about the challenges faced by all businesses in South Africa, regardless of their context or size. This resulting theory is likely to have some flaws.
• Attempting to generalize findings to different contexts. For example, mosquito nets that have been treated with insecticide have proven effective in randomized control trials at reducing the incidence of malaria in Africa with no harmful side effects. However, when these nets were given to certain fishing communities in Zambia, it was discovered   that these fishermen were using them to filter fish and other insects from rivers, lakes and wetlands which then damaged these ecosystems as an unintended consequence.
• Attempting to use associations between things to assume a causal relationship. For example, we know that high levels of vitamin D are associated with reduced Covid-19 symptoms , but this does not necessarily mean that taking vitamin D supplements will achieve the same since there might be other factors at play. People with ill-health or who are too sick to go outdoors will tend to have poor vitamin D levels.

The quality of the theories developed using inductive reasoning are also influenced by the quality of our mental models. For example, believers in the QAnon conspiracy have assimilated a disparate set of observations into a theory that a bunch of satanic power-hungry pedophiles are trying to take over the United States government.

I believe that we must learn to guard against theories where inductive reasoning has been used incorrectly since they can easily be used for nefarious purposes, or at the very least, these theories will mislead or misinform us.

3.6. Detailed example of inductive reasoning

While writing this article, I audited my belief that the social problem of homelessness has increased in South Africa as a result of the Covid-19 pandemic and is unlikely to be alleviated any time soon. The following flowchart shows a simplified version of how I unconsciously used inductive reasoning to infer this theory. You must read the flowchart from left to right.

Because this theory was developed informally and largely unconsciously, I can’t specify the probability that it is true for other neighborhoods in Cape Town and for other cities in South Africa. Neither am I an expert in homelessness. Nevertheless, I will refine my personal theory as I learn more about this problem and how it has recently worsened. 

4. Deductive reasoning

This section introduces deductive reasoning and provides several examples to show how it is different from inductive reasoning. I will explain when to use it and when not to use it. The section will conclude with a detailed example of how I might use deductive reasoning to develop a theory about the financial problems facing a non-profit organization.

4.1 What is deductive reasoning?

Deductive reasoning is commonly referred to as ‘top-down’ thinking. It involves adopting a theory, which was most likely developed using inductive reasoning, and then deducing details that must be true if the theory is valid.

The flowchart below illustrates the process of deductive reasoning.

Deductive thinking is closely associated with an experimental approach in science and academia. It is a straightforward method for checking the validity of the theory and then refining or discarding it. 

The Theory of Falsifiability by Karl Popper is pertinent as it states that a scientific theory is one that is capable of being disproved, and is valid until one of its hypotheses are proven to be false.

4.2. Three examples of deductive reasoning

Here are three examples of deductive reasoning that I have encountered in my work.

The first example relates to the Theory of Change, which is part of the doctrine of non-profit organizations and social enterprises. It starts with a theory about the end-state that must be achieved (i.e. the vision) and broadly how this can happen (i.e. mission). Deductive reasoning is then used to work backwards from the vision and map the key activities, outputs and outcomes that will achieve this end-state. A Theory of Change uses deductive reasoning because it starts with a theory of what can be achieved and deduces hypotheses that must be true for it to be valid.

The second example relates to the strategic work that I have done with the association of hospices in South Africa. During this time, we developed a theory using inductive reasoning about how the private sector will start to compete with traditional hospices, and how we should respond. Then we used deductive reasoning to deduce that private commercial hospices will seek to dominate the profitable market segments as soon as medical aid schemes pay properly for palliative care. This would present a threat to hospices since patients with medical aids cross-subsidize the services that hospices provide to poor communities. There is also the risk that hospices will consequently receive fewer bequests than before. Emerging evidence suggests that this hypothesis is true as some businesses have recently entered this market and begun to sell their services. Therefore our theory remains valid for now. This uses deductive reasoning since we started with the theory about competition from the private sector and unpacked the details of what must happen for our theory to hold ground.

The third example relates to randomized control trials (RCTs) which are based on deductive reasoning since they create testable hypotheses. Researchers then seek to falsify/disprove these hypotheses in order to test the validity of their theories that a certain type of intervention would produce a specific type of change. Examples of RCTs include:

• testing the efficacy of Covid vaccines
• testing whether marketing or financial training provides the greatest benefits for entrepreneurs
• testing whether money for mobile airtime and data, and travel subsidies can help young people to find work
• A/B testing by Instagram to test whether new features increase user engagement.

4.3. The best times to use deductive reasoning

The best time to use deductive reasoning is when there are diminishing returns to gathering more information using the inductive approach – i.e. as the new information adds few insights to what is already known. It is also useful when you are trying to understand the key drivers/causes of a problem or solution as opposed to things that are associated with it.

4.5. Common mistakes when using deductive reasoning

There are four common mistakes that I have noticed people make when using deductive reasoning to solve complex social problems. 

The first mistake is when one attempts to prove the validity of a theory by testing hypotheses that are not logically (or only partially related) to the theory. For example, let us assume that we were testing the market demand for a social enterprise that sells fortified food to feeding schemes and humanitarian agencies. A false hypothesis might be that ‘these potential customers have big annual budgets’ since this alludes to their ability to afford the food. However, I would argue that this would be a poor hypothesis since a big organizational budget does not necessarily mean that they spend a lot of money on food. Neither does it mean that they will want to buy the type of food that the social enterprise sells.

The second mistake is when one attempts to prove a theory by testing hypotheses that are not mutually exclusive (see MECE principle ) since it would be difficult to isolate which of the hypotheses are true. For example, let us assume that your organization runs a diversion programme to rehabilitate young offenders and is trying to understand the efficacy of its activities. It would be poor practice to compare the effectiveness of its counseling programmes on young people versus unemployed people since these categories may overlap. Similarly, it would be unwise to hypothesize that a diversion programme and a counseling programme would be required to rehabilitate these youth since counseling is an integral part of diversion.

The third mistake is when one uses hypotheses where it is impossible to gather evidence to prove or disprove them. For example, a small non-profit organization that runs drama workshops in communities should be cautious about hypothesizing that they improve community cohesion.

The final mistake is when one tries to create an initial theory when insufficient information exists in the first place, and when inductive reasoning should first be used.

4.6. Detailed example of deductive reasoning

For this example, let us assume that a large non-profit organization needs our help with a formal assessment of some pressing problems that threaten its existence.

Then let us assume, that after some initial conversations and after reviewing some documents, we used inductive reasoning to develop a theory that the organization is struggling financially and at risk of running itself into the ground.

The following flowchart gives an example of the types of hypotheses that we might deduce from this theory.

Now that we have deduced some hypotheses, we should be able to identify the type of evidence that we need to determine which of these sub hypotheses are true. For example, let’s look at the evidence and actions that we might need to prove/disprove hypothesis 1.1 (‘the organization is in debt’). We might need to do the following:

• Review the balance sheet in the audited financial statements for the past three years and in the latest unaudited statement or management accounts.
• Calculate the debt and current ratios over the past three financial years.
• Review the components of current liabilities and long-term liabilities.
• Review a list of trade creditors.

We might discover that some of our hypotheses are valid and others are invalid. For example, Hypothesis 1.1 (‘The organization is in debt’) might be currently be invalid while Hypothesis 1.2 (‘financial reserves are deteriorating’) might be valid. 

Next we could use this feedback to refine our hypotheses and original ideas, and write them as follows:

• Hypothesis 1.1 – The organization’s assets are declining and the ratio between assets and liabilities is deteriorating overall.
• Hypothesis 1.2 – Financial reserves are deteriorating and being used to fund the shortfall in the budget and pay creditors, and will only last 12 months at the current rate of consumption. 

Then the hypothesis tree comes together. If all the evidence supports the hypotheses, then our theory that ‘the organization is struggling financially and is at risk of running itself into the ground’ would be sound. This deductive approach would also reveal some of the causes of the problem that would need to be addressed and make it easier to present our findings to the board of directors.

5. Conclusion

We use inductive and deductive reasoning all the time in our lives and work. We use it both formally and informally. The strategy, policy and research that we see around us is underpinned by one of these forms of reasoning, and possibly both.

This article has explained the differences in inductive and deductive reasoning. The former seeks to assimilate observations to develop probable theories to describe the unknown or predict the future, whereas the latter seeks to test the soundness of theories by using evidence to validate hypotheses. Both forms of reasoning are equally important. They work together to provide us with useful theories. They have enabled the human race to be as successful as it is.

However, we should be mindful of the limitations of these two types of reasoning. When used incorrectly, they can result in improbable or unsound theories that can limit our options and distort our thinking. They can also be used nefariously to promote flawed theories for a political or geopolitical agenda.

We should also strive to be able to use inductive and deductive reasoning more explicitly when required. I believe there is immense value in learning how to improve our reasoning – the purpose of this article. It will improve our ability to understand this complex world we live in and make much better decisions.

6. Further reading

Here are some of the links that were the most useful in researching this topic.

• Crafting Cases: The Definitive Guide to Issue Trees by Bruno Nogueira.
• Deductive vs Inductive Reasoning: Make Smarter Arguments, Better Decisions, and Stronger Conclusions posted on FS Blog 
• The McKinsey Way by Ethan Raisel (book)
• The Pyramid Principle: Logic in Writing and Thinking (book)

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• What is Inductive Reasoning...

What is Inductive Reasoning and Why is it Important?

8 min read · Updated on December 08, 2023

Inductive reasoning involves using logic to make generalizations and is one of the vital soft skills employers seek in new hires

If you've ever been in a position to make autonomous decisions or figure out new processes without any type of roadmap, you probably relied on inductive reasoning to get you through. The process of assimilating details into a conclusion is the basis of inductive reasoning. 

In this article, we'll explore exactly what inductive reasoning is and why it's important, especially as it relates to your career and job search. We'll also give you some inductive reasoning examples. 

What is inductive reasoning?

Inductive reasoning is fusing experience with knowledge to make predictions about something or generalize a situation. While your assumptions may not be 100% accurate, the evidence should reasonably support why you drew the conclusions you did. 

Statisticians, mathematicians, salespeople, researchers, managers, analysts, and technicians use inductive reasoning daily. Being able to identify patterns can help you to develop strategies and identify procedural gaps that directly affect efficiency, productivity, and profitability. 

For example, suppose you notice that your social media marketing content attracts the most engagement during the early evening on Wednesday and Friday. In that case, you can logically assume that that would be the best time to interact with potential consumers. 

Types of inductive reasoning

As with anything else, there are different types of inductive reasoning. You've probably used more than one, depending on the situation in which you found yourself. 

Generalized reasoning

This type of inductive reasoning is useful when making observations about a sample or population. 

Example:  

Many people over the age of 65 enjoy eating dinner before 5:00 pm

My restaurant has a slow time between the hours of 3:00 pm and 5:00 pm

Offering a type of early-bird incentive targeted to people over the age of 65 could boost profitability

Statistical reasoning

Perhaps you're the type of person who relies heavily on quantifiable data. This is the inductive reasoning type for that personality. Some people feel that statistical reasoning allows them to draw better conclusions. 

100 students at the local junior college earned an average score of 82 on their math exams

100 students at the local university earned an average score of 91 on their math placement exams

Students at the university level have better math skills than those at the junior college level

Bayesian reasoning

Bayesian inductive reasoning is an add-on to statistical reasoning. It applies additional logic to update the conclusions drawn from the already-present statistics. 

New data indicating the age range of university versus junior college math students became available

100 junior college students between the ages of 25 and 30 score an average of 85 on their math exams

100 university students between the ages of 25 and 30 score an average of 93 on their math scores

University students between 25 and 30 years of age have better math skills than their counterparts at the junior college level

Causal reasoning

With causal inductive reasoning, you seek out cause and effect. This type of inductive reasoning can be tricky, because it's so easy to draw the wrong conclusions about the effect of a thing that's happening. Additionally, a lot of people confuse correlations with causation . It's important to remember that correlation has to do with how two things relate, rather than something directly affecting something else.

Example of correlation versus causation:

When it's hot outside ice cream sales go up

When it's hot outside people get more sunburns

People with sunburns eat more ice cream

While having a sunburn and eating ice cream both relate to being outside on a hot sunny day, there is nothing that says people with sunburns eat more ice cream. Numbers one and two are great causal reasoning assumptions. Number 3 is a faulty assumption based on the relationship between being in the sun, getting a sunburn, and being hot enough to buy more ice cream.

Predictive reasoning

Causal reasoning analyzes trends to find out why things happen. Predictive reasoning uses trends to make assumptions about what will happen next. Causal and predictive reasoning are often used together. If ABC causes DEF, then ABC predicts that GHI will happen. 

People enjoy being out in the sun during the summer

Being exposed to the UV rays of sunlight causes sunburns

Area hospitals see a surge of bad sunburns during the summer months

As you can see, the second thing is caused by the first. The third thing is predicted by the first thing. 

Why is inductive reasoning important?

Soft skills are highly sought after in the workforce. It's been said that hiring managers favor job applicants with the right soft skills when the availability of hard skills is lacking. 

• Soft skills are characteristics you possess that make you good at what you do
• Hard skills are things you know how to do because of experience and education

One of the top soft skills employers look for in a job applicant is creative problem-solving and innovation .  Many people associate deductive reasoning with creativity; however, inductive reasoning fits, too. The ability to put things together to draw conclusions and bring about transformative change will make you highly sought after in the workforce. 

What is the difference between inductive and deductive reasoning?

The two should definitely not be used interchangeably. Basically speaking, inductive reasoning uses a bunch of data to draw conclusions. With deductive reasoning, you start at the conclusion and work backward through the data to deduce what already happened. 

Inductive reasoning is what will (or is likely to) happen based on this set of data

Deductive reasoning centers on trying to find out why a thing happened the way that it did

There is some debate about which is better - deductive or inductive reasoning. While each has pros and cons, as long as they're used properly, neither is better than the other. It all depends on what's going on, what needs to happen, and how you should present yourself within a given field. 

Inject some inductive reasoning into your resume

Letting companies know they want to hire you starts with your resume . Your resume should contain a strong mix of both hard and soft skills. So, how would you indicate your ability to leverage inductive reasoning to solve problems?

Increased profitability by more than 75% after noticing that sales were improved by sharing customer testimonials with prospects

Slashed inventory shrink costs by onboarding a new supplier with a reputation for delivering undamaged goods

Reduced employee turnover after discovering that those with less than 5 years of experience kept quitting and revamped hiring processes to onboard staff with 5+ years of experience

Use the STAR method

As you fine-tune the story you want to tell with your resume, remember to use the STAR method . This method is the best way to talk about achievements succinctly. 

• Situation: What was going on?
• Task: What was being affected by the situation?
• Action: What action did you take?
• Result: What was the result of your action?

When you stick to the STAR method, you'll be able to hit the mark when demonstrating your qualifications and you'll come across as an achiever rather than a doer. It's also a great way to pique the hiring manager's interest and open the conversation to more details. 

Don't forget the cover letter

The number of hiring managers who read cover letters has increased ( almost doubled ) in the last couple of years. Your cover letter is a great place to showcase additional skills and expand on ideas in the resume. You want to avoid regurgitating the same details from your resume; however, it's perfectly fine to provide more details. 

To say the least, you can use the cover letter to persuade employers with tales of your excellence in logic and reasoning to solve complex problems. The cover letter is the best place for that type of narrative, because it allows you to speak to a prospective employer in a more personal language. 

Bring up your inductive reasoning abilities during an interview

In the spirit of ensuring that you impress the hiring manager, keep talking about your skills when you step into their office for the interview. You've already wowed them with your resume and cover letter; keep that going as you speak about your experience and education. 

Just like with your resume, use the STAR method to answer interview questions that involve you using inductive reasoning. 

Inductive reasoning skills can be improved

Only some people can take a set of circumstances to conclude or predict what will happen. If you don't fall into this category, no big deal - though you should avoid using it as a skill on your resume. It's never too late to learn a new skill or hone a skill you already have. 

This is especially true if you want to change careers. Perhaps you're moving from a field where inductive reasoning wasn't a thing but now it'll be something you have to rely on more often. Don't be afraid to let a hiring manager know that inductive reasoning is one of your weaknesses but that you're working on it. 

In conclusion

Your ability to make decisions based on imperfect or incomplete information can help you to stand out from the crowd of other job seekers. Positioning yourself as someone who understands and applies the concepts of the varying forms of inductive reasoning allows you to showcase a soft skill employers want.

TopResume has a team of expert resume writers standing by to help you demonstrate your inductive reasoning skills, whether you need a resume, a cover letter or new LinkedIn profile. 

Recommended reading:

Key Differences Between Hard Skills and Soft Skills

10 Best Places to Learn New Skills in 2022

What to Say in a Cover letter: 5 Things You Should Include

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Why Deductive and Inductive Reasoning Are Important for Competitive Intelligence Analysts

06/07/2022 08/07/2022 | Octopus

Why deductive and inductive reasoning are important for Competitive Intelligence analysts

Intelligence analysts must be able to reason inductively and deductively. So they can analyse data and reach accurate conclusions. This article is called Why deductive and inductive reasoning are important for Competitive Intelligence analysts. Inductive reasoning allows analysts to generalise from specific cases to broader principles. And deductive reasoning helps them deduce the consequences of those principles. Strong reasoning skills are essential for Competitive intelligence analysis and within other fields.

What are the two primary forms of reasoning?

Inductive reasoning is the process of reasoning from specific facts. From these facts, you create a general conclusion. Deductive reasoning comes from a general principle to a particular conclusion. Both forms of reasoning are important in intelligence analysis. 

Use inductive reasoning to develop hypotheses about events or situations. These hypotheses can then be tested using deductive reasoning. Conclusions reached with deductive reasoning agree with empirical tests and strengthen the hypothesis. Discard or change the hypothesis if you disagree.

Inductive and deductive reasoning

Inductive reasoning starts with a principle and then applies it to specific cases. But inductive reasoning is considered intuitive, while deductive reasoning is more logical.

Intelligence analysts use deductive reasoning to help them test these hypotheses against reality. In this way, analysts use scientific and logical methods to understand their world.

How do they differ?

Inductive reasoning is a process of logic that starts with individual observations. Then moving to general conclusions. Deductive reasoning starts with an overriding principle and then applied to specific cases. Inductive reasoning is often used where analysts must make inferences from incomplete information. 

What is Competitive Intelligence? Competitive Intelligence creates insight to give you more certainty, competitive advantage, knowing what’s next and what to do about it.

Deductive reasoning is often used in legal arguments. With lawyers arguing from a general legal principle to a specific case. These are similar to two types of reasoning but differ in important ways. 

Inductive reasoning proceeds from the specific to the general. While deductive reasoning proceeds from the general to the specific. Inductive reasoning is often less certain than deductive reasoning. Analysts using inductive reasoning may have a limited understanding of their working data. So makes it challenging to draw firm conclusions.

When is each most useful?

Inductive reasoning is often considered the less rigorous form of reasoning. But, when used correctly, inductive reasoning can be a powerful tool. 

The key benefit of this reasoning is that analysts can identify patterns and trends in data. By identifying patterns, analysts can make better predictions about future events, and understanding the underlying event causes gives a better chance of predicting future behaviour. 

Inductive reasoning is also helpful in confirming or disproving hypotheses. If you think you know why something happened, inductive reasoning tests the hypothesis. And if the data supports the hypothesis you can be more confident in the conclusions. Yet, don’t use inductive reasoning in place of deductive reasoning. 

So, when is deductive reasoning most useful? Deductive reasoning is often thought of as the pinnacle of intelligence analysis. Start with a general principle, then apply it to specific cases and conclude. 

It relies on observations and past experiences and is considered more reliable. Deductive reasoning can be more accurate, but it can be less flexible. It may be more important to consider a broader range of potential solutions in some situations rather than narrowing the options down to a single solution based on prior assumptions.

Simple examples

Deductive logic is a system of reasoning in which you conclude from two premises. An example of deductive reasoning would be as follows:

All men are mortal.

Socrates is a man.

So, Socrates is mortal.

Here is an example of inductive logic. You reason that if something has always been true, it is likely to be accurate in the future. For instance, if you always wake up at 7 am on weekdays, you might reason that you will wake up at 7 am tomorrow.

In conclusion, use both inductive and deductive reasoning to analyse and reach conclusions. Inductive reasoning allows analysts to make generalisations from specific observations. In contrast, deductive reasoning will enable them to arrive at particular conclusions based on their hypotheses. These skills are essential as analysts can understand their data to make better decisions. This article was about Why deductive and inductive reasoning are important for Competitive Intelligence analysts.

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Reasoning processes in clinical reasoning: from the perspective of cognitive psychology

Hyoung seok shin.

Department of Medical Education, Korea University College of Medicine, Seoul, Korea

Clinical reasoning is considered a crucial concept in reaching medical decisions. This paper reviews the reasoning processes involved in clinical reasoning from the perspective of cognitive psychology. To properly use clinical reasoning, one requires not only domain knowledge but also structural knowledge, such as critical thinking skills. In this paper, two types of reasoning process required for critical thinking are discussed: inductive and deductive. Inductive and deductive reasoning processes have different features and are generally appropriate for different types of tasks. Numerous studies have suggested that experts tend to use inductive reasoning while novices tend to use deductive reasoning. However, even experts sometimes use deductive reasoning when facing challenging and unfamiliar problems. In clinical reasoning, expert physicians generally use inductive reasoning with a holistic viewpoint based on a full understanding of content knowledge in most cases. Such a problem-solving process appears as a type of recognition-primed decision making only in experienced physicians’ clinical reasoning. However, they also use deductive reasoning when distinct patterns of illness are not recognized. Therefore, medical schools should pursue problem-based learning by providing students with various opportunities to develop the critical thinking skills required for problem solving in a holistic manner.

Introduction

It is hard to describe clinical reasoning in a sentence, because it has been studied by a number of researchers from various perspectives, such as medical education, cognitive psychology, clinical psychology, and so forth, and they have failed to reach an agreement on its basic characteristics [ 1 ]. Accordingly, clinical reasoning has been defined in various ways. Some researchers defined clinical reasoning as a crucial skill or ability that all physicians should have for their clinical decision making, regardless of their area of expertise [ 2 , 3 ]. Others focused more on the processes of clinical reasoning; thus, they defined it as a complex process of identifying the clinical issues to propose a treatment plan [ 4 - 6 ]. However, these definitions are not so different. Taking this into account, it can be concluded that clinical reasoning is used to analyze patients’ status and arrive at a medical decision so that doctors can provide the proper medical treatment.

In reality, properly working clinical reasoning requires three domains of knowledge: diagnostic knowledge, etiological knowledge, and treatment knowledge [ 6 ]. From the perspective of cognitive psychology, structural knowledge is needed to integrate domain knowledge and find solutions based on the learner’s prior knowledge and experience [ 7 ], and structural knowledge can be constructed as a form of mental model by understanding the relations between the interconnected factors involved in clinical issues [ 8 , 9 ]. In this cognitive process, critical thinking skills such as causal reasoning and systems thinking can play a pivotal role in developing deeper understanding of given problem situations. Causal reasoning is the ability to identify causal relationships between sets of causes and effects [ 10 ]. Causality often involves a series or chain of events that can be used to infer or predict the effects and consequences of a particular cause [ 10 - 13 ]. Systems thinking is a thinking paradigm or conceptual framework where understanding is defined in terms of how well one is able to break a complex system down into its component parts [ 14 , 15 ]. It is based on the premise that a system involves causality between factors that are parts of the system as a whole [ 14 ]. Systems thinking is a process for achieving a deeper understanding of complex phenomena that are composed of components that are causally interrelated [ 14 - 16 ]. As a result, causal reasoning and systems thinking are skills that can help people to better understand complex phenomena in order to arrive at effective and targeted solutions that address the root causes of complex problems [ 10 , 12 , 15 ].

If cognitive skills work properly, one can make correct decisions all of the time. However, human reasoning is not always logical, and people often make mistakes in their reasoning. The more difficult the problems with which they are presented, the more likely they are to choose wrong answers that are produced by errors or flaws in the reasoning process [ 17 , 18 ]. Individual differences in reasoning skills—such as systems thinking, causal reasoning, and thinking processes—may influence and explain observed differences in their understanding. Therefore, to better assist learners in solving problems, instructors should focus more on facilitating the reasoning skills required to solve given problems successfully.

In this review paper, the author focuses on the reasoning processes involved in clinical reasoning, given that clinical reasoning is considered as a sort of problem-solving process. Therefore, this paper introduces concepts related to the reasoning processes involved in clinical reasoning and their influences on novices and experts in the field of medical education from the perspective of cognitive psychology. Then, based on the contents discussed, the author will be able to propose specific instructional strategies associated with reasoning processes to improve medical students’ reasoning skills to enhance their clinical reasoning.

Concepts and nature of reasoning processes

Generally, reasoning processes can be categorized into two types: inductive/forward and deductive/backward [ 19 ]. In an inductive reasoning process, one observes several individual facts first, then makes a conclusion about a premise or principle based on these facts. Yet there may be the possibility that a conclusion is not true even though a premise or principle in support of that conclusion is true, because the conclusion is generalized from the facts observed by the learner, but the learner does not observe all relevant examples [ 20 ].

In general, in a deductive reasoning process, according to Johnson-Laird [ 20 ], one establishes a mental model or a set of models to solve given problems considering general knowledge and principles based on a solid foundation. Then, one makes a conclusion or finds a solution based on the mental model or set of models. To verify a mental model, one needs to check the validity of the conclusions or solutions by searching for counterexamples. If one cannot find any counterexamples, the conclusions can be accepted as true and the solutions as valid. Consequently, the initial mental model or set of models can be used for deductive reasoning.

Anderson [ 17 ] proposed three different ways of solving complex problems: means-ends analysis, working backward, and planning by simplification. A means-ends analysis is a process that gets rid of differences between the current state and the ideal state in order to determine sub-goals in solving problems, and the process can be repeated until the major goal is achieved [ 21 - 23 ]. It can be considered an inductive reasoning process, because the distinct feature of means-ends analysis where it achieves sub-goals in consecutive order is similar to inductive reasoning. Working backward is addressed as an opposite concept to means-ends analysis [ 17 ], because it needs to set up a desired result to find causes by measuring the gap between the current state and the ideal state; then, this process is repeated until the root causes of a problem are identified. According to Anderson [ 17 ], means-ends analysis (inductive reasoning) is more useful in finding a solution quickly when a limited number of options are given or many sub-goals should be achieved for the major goal; whereas working backward (deductive reasoning) spends more time removing wrong answers or inferences to find the root causes of a problem. In conclusion, inductive and deductive reasoning processes have different features and can play different roles in solving complex problems.

The use of reasoning processes

A number of researchers across different fields have used inductive and deductive approaches as reasoning processes to solve complex problems or complete tasks. For example, Scavarda et al. [ 24 ] used both approaches in their study to collect qualitative data through interviews with experts, and they found that experts with a deductive approach used a top-down approach and those with an inductive approach used a bottom-up approach to solve a given problem. In a study of Overmars et al. [ 25 ], the results showed that a deductive approach explicitly illustrated causal relations and processes in 39 geographic contexts and it was appropriate for evaluating various possible scenarios; whereas an inductive approach presented associations that did not guarantee causality and was more useful for identifying relatively detailed changes.

Sharma et al. [ 26 ] found that inductive or deductive approaches can both be useful depending on the characteristics of the tasks and resources available to solve problems. An inductive approach is considered a data-driven approach, which is a way to find possible outcomes based on rules detected from undoubted facts [ 26 ]. Therefore, if there is a lot of available data and an output hypothesis, then it is effective to use an inductive approach to discover solutions or unexpected and interesting findings [ 26 , 27 ]. An inductive approach makes it possible to directly reach conclusions via thorough reasoning that involves the following procedures: (1) recognize, (2) select, and (3) act [ 28 ]. These procedures are recurrent, but one cannot know how long they should be continued to complete a task, because a goal is not specified [ 26 ]. Consequently, an inductive approach is useful when analyzing an unstructured data set or system [ 29 ].

On the other hand, a deductive approach sets up a desired goal first, then finds a supporting basis—such as information and rules—for the goals [ 26 ]. For this, a backward approach, which is considered deductive reasoning, gradually gets rid of things proved unnecessary for achieving the goal while reasoning; therefore, it is regarded as a goal-driven approach [ 28 ]. If the output hypothesis is limited and it is necessary to find supporting facts from data, then a deductive approach would be effective [ 26 , 28 ]. This implies that a deductive approach is more appropriate when a system or phenomenon is well-structured and relationships between the components are clearly present [ 29 ]. Table 1 shows a summary of the features and differences of the inductive and deductive reasoning processes.

Features of Inductive and Deductive Reasoning Processes

The classification according to the reasoning processes in the table is dichotomous, but they do not always follow this classification absolutely. This means that each reasoning process shows such tendencies.

Considering the attributes of the two reasoning processes, an inductive approach is effective for exploratory tasks that do not have distinct goals—for example, planning, design, process monitoring, and so on, while a deductive approach is more useful for diagnostic and classification tasks [ 26 ]. In addition, an inductive approach is more useful for discovering solutions from an unstructured system. On the other hand, a deductive approach can be better used to identify root causes in a well-structured context. While both reasoning approaches are useful in particular contexts, it can be suggested that inductive reasoning is more appropriate than deductive reasoning in clinical situations, which focus on diagnosis and treatment of diseases rather than on finding their causes.

Reasoning processes by novices and experts

As mentioned above, which reasoning process is more effective for reaching conclusions can be generally determined depending on the context and purpose of the problem solving. In reality, however, learners’ choices are not always consistent with this suggestion, because they are affected not only by the problem itself, but also by the learner. Assuming that learners or individuals can be categorized into two types, novices and experts, based on their level of prior knowledge and structural knowledge, much research has shown that novices and experts use a different reasoning process for problem solving. For example, in a study of Eseryel et al. [ 30 ], novice instructional designers who possessed theoretical knowledge but little experience showed different patterns of ill-structured problem solving compared to experts with real-life experience. Given that each learner has a different level of prior knowledge relating to particular topics and critical thinking skills, selecting the proper reasoning process for each problem is quite complex. This section focuses on which reasoning process an individual uses depending on their content and structural knowledge.

Numerous studies have examined which reasoning processes are used by experts, who have sufficient content and structural knowledge, and novices, who have little content and structural knowledge, for problem solving. The result of a study of Hong et al. [ 31 ] showed that children generally performed better when using cause-effect inferences (inductive approach) than effect-cause inferences (considered a deductive approach). According to Anderson [ 17 ], people are faced with some difficulties when they solve problems using induction. The first difficulty is in formulating proper hypotheses and the second is that people do not know how to interpret negative evidence when it is given and reach a conclusion based on that evidence [ 17 ]. Nevertheless, most students use a type of inductive reasoning to solve problems that they have not previously faced [ 32 ]. Taken together, the studies suggest that novices generally prefer an inductive approach to a deductive approach for solving problems because they may feel comfortable and natural using an inductive approach but tend to experience difficulties during problem-solving processes. From these findings, it can be concluded that novices are more likely to use inductive reasoning, but it is not always productive.

Nevertheless, there is still a controversy about which reasoning processes are used by experts or novices [ 33 ]. For example, experts in specific domains use an inductive approach to solving problems, but novices, who have a lower level of prior knowledge in specific domains, tend to use a deductive approach [ 23 ]. In contrast, according to Smith [ 34 ], studies in which more familiar problems were used concluded that experts preferred an inductive approach, whereas in studies that employed relatively unfamiliar problems that required more time and effort to solve, experts tended to prefer a deductive approach. In line with this finding, in solving physics problems, experts mostly used inductive reasoning that was faster and had fewer errors for problem solving only when they encountered easy or familiar problems where they could gain a full understanding of the situation quickly, but novices took more time to deductively reason by planning and solving each step in the process of problem solving [ 35 ].

Assuming that an individual’s prior knowledge consists of content knowledge such as knowledge of specific domains as well as structural knowledge such as the critical thinking skills required for problem solving in the relevant field, it seems experts use an inductive approach when faced with relatively easy or familiar problems; while a deductive approach is used for relatively challenging, unfamiliar, or complex problems. In the case of novices, it may be better to use deductive reasoning for problem solving considering that they have a lower level of prior knowledge and that even experts use deductive reasoning to solve complex problems.

Inductive and deductive reasoning in clinical reasoning

In medicine, concepts of inductive and deductive reasoning apply to gathering appropriate information and making a clinical diagnosis considering that the medical treatment process is a form of problem solving. Inductive reasoning is used to make a diagnosis by starting with an analysis of observed clinical data [ 36 , 37 ]. Inductive reasoning is considered as scheme-inductive problem solving in medicine [ 36 ], because in inductive reasoning, one first constructs his/her scheme (also considered a mental model) based on one’s experiences and knowledge. It is generally used for a clinical presentation-based model, which has been most recently applied to medical education [ 38 ].

In contrast, deductive reasoning entails making a clinical diagnosis by testing hypotheses based on systematically collected data [ 39 ]. Deductive reasoning is considered an information-gathering method, because one constructs a hypothesis first then finds supporting or refuting facts from data [ 36 , 40 ]. It has been mostly used for discipline-based, system-based, and case-based models in medical education [ 38 ].

Inductive and deductive reasoning by novice and expert physicians

A growing body of research explores which reasoning processes are mainly used by novices and experts in clinical reasoning. Novice physicians generally use deductive reasoning, because limited knowledge restricts them from using deductive reasoning [ 1 , 38 ]. Also, it is hard to consider deductive reasoning as an approach generally used by experts, since they do not repeatedly test a hypothesis based on limited knowledge in order to move on to the next stage in the process of problem solving [ 38 ]. Therefore, it seems that deductive reasoning is generally used by novices, while inductive reasoning is used by expert physicians in general. However, this may be too conclusive and needs to be further examined in the context of clinical reasoning.

In clinical reasoning, inductive reasoning is more intuitive and requires a holistic view based on a full understanding of content knowledge, including declarative and procedural knowledge, but also structural knowledge; thus, it occurs only when physicians’ knowledge structures of given problems are highly organized [ 38 ]. Expert physicians recognize particular patterns of symptoms through repeated application of deductive reasoning, and the pattern recognition process makes it possible for them to apply inductive reasoning when diagnosing patients [ 10 ]. As experts automate a number of cognitive sequences required for problem solving in their own fields [ 35 ], expert physicians automatically make appropriate diagnoses following a process of clinical reasoning when they encounter patients who have familiar or typical diseases. Such a process of problem solving is called recognition-primed decision making (RPDM) [ 41 , 42 ]. It is a process of finding appropriate solutions to ill-structured problems in a limited timeframe [ 10 ]. In RPDM, expert physicians are aware of what actions should be taken when faced with particular situations based on hundreds of prior experiences [ 10 ]. These prior experiences are called illness scripts in diagnostic medicine [ 10 ], and this is a concept similar to a mental model or schema in problem solving.

However, expert physicians do not always use inductive reasoning in their clinical reasoning. Jonassen [ 10 ] categorized RPDM into three forms of variations in problem solving by experts, and the first form of variation is the simplest and easiest one based on inductive reasoning, as mentioned above. The second type of variation occurs when an encountered problem is somewhat atypical [ 10 ]. Even expert physicians are not always faced with familiar or typical diseases when treating patients. Expert physicians’ RPDM does not work automatically when faced with atypical symptoms, because they do not have sufficient experiences relevant to the atypical symptoms. In this case, it can be said that they have weak illness scripts or mental models of the given symptoms. In the second variation, experts need more information and will attempt to connect it to their prior knowledge and experiences [ 10 ]. Deductive reasoning is involved in this process so that problem solvers can test their hypotheses in order to find new patterns and construct new mental models based on the newly collected data and previous experiences. The third variation of RPDM is when expert physicians have no previous experience or prior knowledge of given problem situations; in other words, no illness script or mental model [ 10 ]. Jonassen [ 10 ] argued that a mental simulation is conducted to predict the consequences of various actions by experts in the third variation. This process inevitably involves repetitive deductive reasoning to test a larger number of hypotheses when making a diagnosis.

Similarly, from the perspective of dual process theory as a decision-making process, decision making is classified into two approaches based on the reasoning style: type 1 and type 2 (or system 1 and system 2) [ 43 , 44 ]. According to Croskerry [ 44 ], the type 1 decision-making process is intuitive and based on experiential-inductive reasoning, while type 2 is an analytical and hypothetico-deductive decision-making process [ 44 , 45 ]. A feature that distinguishes the two processes is whether a physician who encounters a patient’s symptoms succeeds in pattern recognition. If a physician recognizes prominent features of the visual presentation of illness, type 1 processes (or system 1) are operated automatically, whereas type 2 (or system 2) processes work if any distinct feature of illness presentation is not recognized [ 44 ].

Only experienced expert physicians can use RPDM [ 10 , 46 ] or type 1 and 2 processes [ 43 ], because it can occur solely based on various experiences and a wide range of prior knowledge that can be gained as a result of a huge amount of deductive reasoning since they were novices. Consequently, it can be concluded that expert physicians generally use more inductive reasoning when they automatically recognize key patterns of given problems or symptoms, while sometimes they also use deductive reasoning when they additionally need processes of hypothesis testing to recognize new patterns of symptoms.

From the perspective of cognitive processes, clinical reasoning is considered as one of the decision-making processes that finds the best solutions to patients’ illnesses. As a form of decision making for problem solving, two reasoning processes have been considered: inductive and deductive reasoning. Deductive reasoning can be used to make a diagnosis if physicians have insufficient knowledge, sufficient time, and the ability to analyze the current status of their patients. However, in reality, it is inefficient to conduct thorough deductive reasoning at each stage of clinical reasoning because only a limited amount of time is allowed for both physicians and patients to reach a conclusion in most cases. A few researchers have suggested that using deductive reasoning is more likely to result in diagnostic errors than inductive reasoning, because evidence-based research, such as deductive reasoning, focuses mainly on available and observable evidence and rules out the possibility of any other possible factors influencing the patient’s symptoms [ 37 , 38 ]. However, when a physician encounters unfamiliar symptom and the degree of uncertainty is high, deductive reasoning is required to reach the correct diagnosis through analytical and slow diagnostic processes by collecting data from resources [ 44 ]. Taken together, in order to make the most of a limited timeframe and reduce diagnostic errors, physicians should be encouraged to use inductive reasoning in their clinical reasoning as far as possible given that patterns of illness presentation are recognized.

Unfortunately, it is not always easy for novice physicians to apply inductive or deductive reasoning in all cases. Expert physicians have sufficient capabilities to use both inductive and deductive reasoning and can also automate their clinical reasoning based on inductive reasoning, because they have already gathered the wide range of experiences and knowledge required to diagnose various symptoms. Novice physicians should make a greater effort to use inductive reasoning when making diagnoses; however, it takes experiencing countless deductive reasoning processes to structure various illness scripts or strong mental models until they reach a professional level. As a result, teaching not only clinical reasoning as a whole process but also the critical thinking skills required for clinical reasoning is important in medical schools [ 47 ]. For this, medical schools should pursue problem-based learning by providing students with various opportunities to gain content knowledge as well as develop the critical thinking skills —such as data analysis skills, metacognitive skills, causal reasoning, systems thinking, and so forth—required for problem solving in a holistic manner so that they can improve their reasoning skills and freely use both inductive and deductive approaches in any context. Further studies will be reviewed to provide detailed guidelines or teaching tips on how to develop medical students’ critical thinking skills.

Acknowledgments

Conflicts of interest

No potential conflict of interest relevant to this article was reported.

Author contributions

All work was done by HS.

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This will enable students, school children and other individual users to continue their learning journeys both safely and responsibly. We will continue to assess ways in which our services can be offered safely and responsibly to support all learners and educators, also those based in Russia. 

Supporting our employees 

At Kahoot!, we are not just a team in name, we are a team in practice. As such, we are committed to the well-being of our employees, especially those with ties to Ukraine, or those that in other ways are particularly affected by the war. We are providing these colleagues with any support we can. 

Acknowledging the current situation, the Kahoot! Group made an emergency aid donation to Save the Children and the Norwegian Refugee Council. This is a contribution to support life-saving assistance and protection for innocent Ukrainian children, families and refugees. 

As the situation in Ukraine continues to develop our teams across the company are actively monitoring the crisis so that we can respond in the most responsible and supportive way possible. 

Our hearts go out to the people of Ukraine, their loved ones, and anyone affected by this crisis. 

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