# Deduction

## The Basic Idea

Like many of the concepts we come across in behavioral science, deduction, or deductive reasoning can seem terribly complicated, especially when applied to abstract or hypothetical situations. Thankfully, it’s something we do in our everyday lives, often without paying it too much attention.

Deduction is simply the logic we use when we draw from something we observe generally, and apply it to a specific case. Consider the below example;

• All horses have four legs.
• Bill is a horse.
• Therefore, Bill has four legs.

It helps to think of deduction as the opposite of induction – which happens when we move in the other direction, from a specific case to a generality.

• Bill is a horse.
• Bill has four legs.
• Therefore, all horses have four legs.

The degree to which we can rely on deduction depends on whether our argument is sound and valid. Deduction has been highly influential in philosophy, mathematics, computer science and more recently, artificial intelligence. Many economic decision-making models are also based on principles of deduction.1

## Theory, meet practice

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## Key Terms

Logic/logical reasoning – an abstract theory of examining or thinking about arguments. Logic and logical reasoning follow a series of steps, known as inferences, which allow us to reach a conclusion based on an argument or ‘premise’ we know to be valid.

Deductive reasoning – a psychological process of deriving predictions from generally accepted premises or theories. Often summarised as ‘moving from the general to the specific’, although some scholars argue that this definition is too narrow.

Inductive reasoning – where we start with an argument or premise that is likely valid, and supplies some evidence to support a wider theory. Sometimes summarised as ‘moving from the specific to the general’, but again this is disputed as there are examples of inductive arguments that do not fall into this definition.

## History

The origins of deduction as a theory stretch back to ancient times, when ideas of logic and reasoning were pondered by the great mathematicians and philosophers of Ancient Greece. Pythagoras and Thales used deduction to develop their geometry theorems, and some years later Aristotle wrote extensively about syllogisms, which are essentially deductive arguments that have two premises or known facts, and a conclusion. For example – “All men are mortal; Socrates is a man; therefore Socrates is mortal” is an example of an Aristotle syllogism.2

Deduction attracted renewed attention in the 15th and 16th century, as the Scientific Revolution swept across Europe. Francis Bacon, considered the ‘father of empiricism’, turned deduction upside down through his scientific method, which took an experimental approach based heavily on inductive reasoning, or testing ideas and eliminating them when there wasn’t enough evidence to support them. This was a stark departure from previous studies of deduction, which were typically based on observations people took from the world (and of course, subject to a whole load of bias!). The French philosopher René Descartes also supported the scientific method, famously arguing that “I think, therefore I am” is the only statement that passes all tests of reasonable doubt.3

Fast-track to the 20th century, and we see the emergence of natural deduction through the work of Stanisław Jaśkowski and Gerhard Gentzen. Natural deduction reverts back to the ancient view of logic, seeing it as a linear process of inference as opposed to a complex, axiom-based approach. Many developments in calculus and computer science originated from natural deduction.4

When psychologists talk about deduction today, it’s usually in the simplified sense of people applying theories they know to be true, to cases and stimuli in their everyday lives. While using deduction as a heuristic or ‘mental short-cut’ can sometimes backfire; overall, deduction is considered a rational, and useful, decision-making tool.

## Aristotle

Aristotle was a philosopher and polymath of Ancient Greece who is considered the father of the study of logic, the world’s first zoologist, and a pioneer in the field of ethics (amongst many, many other areas of expertise!). A student of Plato, Aristotle’s work on deduction is the first known approach to the concept.

## Rene Descartes

Often referred to as the ‘father of modern philosophy’ Descartes was a French philosopher, mathematician and scientist of the Scientific Revolution. Along with Sir Francis Bacon, he was a major proponent of the ‘scientific method’ in scholarly pursuits. He rejected Aristotle’s theory that our senses are what determine our knowledge, and instead promoted an experimental approach based on reason and observation. He is famous for his four rules for deductive logic, ideas that paved the way for the emergence of rationalism in later years.

## Sherlock Holmes

Arthur Conan Doyle’s fictional detective is probably the best known advocate for deductive reasoning. This is slightly ironic, since Sherlock Holmes relied more on abductive reasoning to solve his crimes – considering causes and effects instead of just fitting an observation into a neat theory.5 Nevertheless, we can learn a lot about human logic and inference from him.

## Consequences

Deduction is the backbone of human logic. If scholars had not devoted so much time to the study of deduction, we might never have seen the emergence of rationalism and ‘The Age of Reason’ in the 17th and 18th centuries.

In contemporary times, deduction has been explored as a psychological process, helping to explain how people process large amounts of stimuli and information in order to make decisions. Sometimes we use deduction subconsciously, performing actions on the basis that we expect a generally held theory to apply in a specific situation. On the other hand, Daniel Kahneman’s famous book Thinking, Fast and Slow6 describes deduction as something that requires deliberate effort, especially when it comes to making complex decisions. In general, deduction is commonly accepted as a psychological tool that we human beings deploy on a regular basis.

Deduction is also the foundation on which most economic models of decision-making are built. The homo economicus is seen as a logical figure who makes decisions based solely on costs and benefits, therefore if a person’s deductive argument is that a particular action will bear more benefits than costs, they will likely pursue it. The idea of assumptions, a cornerstone of economic thought, is also heavily influenced by deduction. Decisions in the world of business and management also tend to rely on a set of assumptions or ‘premises’. Finally, the advancements we’ve seen in computer science, and more recently in big data and artificial intelligence, would never have come about were it not for groundbreaking studies in the fields of logic and mathematical deduction over the years.

## Controversies

Done right, deduction saves time and allows us to solve complex problems. Done wrong, we encounter all sorts of trouble.

If a deductive argument isn’t valid or sound, we end up with what’s referred to as a ‘fallacy’.7 A valid argument is one where the conclusion must be true, if the premise is known to be true. So, Socrates must be mortal because it is true that all men are mortal. If it happened to be the case that the conclusion could potentially be challenged, then the argument is invalid, and considered a fallacy. Similarly, an argument is only sound if it is also valid, and the premise is definitely known to be true. So let’s say we didn’t know whether Socrates was a man or woman, then our argument would not be sound. Since it’s pretty rare that we can be absolutely confident in the validity and soundness of our deductive arguments, deduction is sometimes challenged as an unrealistic model of reasoning.

Fallacies cause us to draw incorrect conclusions, and make illogical decisions. It’s useful to consider the role of biases here, as there are often the culprits of poor deductive reasoning. Check out our list of biases and heuristics here to see some examples of where deduction can go wrong.

## Case Study: The Wason Selection Task

One of the most famous experiments in deductive reasoning is The Wason Selection Task. Peter Wason developed the logic puzzle in 1966 to determine how good people are at solving tasks that require deductive reasoning.8

The experiment was set up as follows:

“You are shown a set of four cards placed on a table, each of which has a number on one side and a colored patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which card(s) must you turn over in order to test the truth of the proposition that if a card shows an even number on one face, then its opposite face is red?”

The correct solution is to turn over the brown card, and the card with the number 8. Did you figure it out?

The puzzle is solved by applying a “if P, then Q” argument structure, and deciding which cards you need to see to ensure the proposition is true. So in this case, If the brown card is even, it violates the rule, and if the card with 8 is not red, it violates the rule. It doesn’t really matter what colour is on the back of the 3 card, since the proposition makes no claims about odd numbers. Nor are we concerned by whether the red card is odd or even because although we are told that all even numbers are red, the proposition does not claim that all red cards are even, or odd for that matter.

What makes this experiment (and it’s 1993 replication) really interesting, is that although most people fail miserably at the task when it’s presented in this structure (<10% answer correctly), they perform much better when the same puzzle is applied in a more realistic context, or a scenario that’s easier to imagine.

For instance, Cosmides and Tooby (1993)  showed that people were able to solve similar puzzles when they considered them under social rules or norms. Their task involved the rule “In order to drink alcohol, you must be over 25”, and instead of numbers and colours, they asked participants to imagine a group of people in a bar, with some drinking beer and others drinking coca-cola. They wrote the ages of individuals on one side of the card, and the beverage they were consuming on the other. So a card that showed 16, couldn’t show ‘drinking beer’ on its’ flip-side. In this setting, the vast majority of people reached the correct solution, even though the fundamentals of the task were the same. This finding lends support to the evolutionary school of psychology, and the argument that human reasoning is influenced by contextual factors and stimuli in our environment.

## Related TDL Content

Reference Guide: Algorithm

An algorithm is essentially a sequence of concrete instructions that tell an operator what to do. Algorithms follow rule-based logic, and some arguments typical of deductive reasoning.

Reference Guide: Abductive Reasoning

Closely related to deduction, and the form of logic used by Sherlock Holmes. Abductive reasoning involves generating a hypothesis which is subsequently tested.

TDL Perspectives: Becoming an Applied Behavioral Scientist

Applied behavioral science is all about using the scientific method—abduction, deduction, induction—to find evidence-based solutions to the problems plaguing some kind of system. This article goes over the basics of what a career in applied behavioral science looks like.

## Sources

1. APA Dictionary of Psychology. Dictionary.apa.org. (2021). Retrieved 31 January 2021, from https://dictionary.apa.org/deduction.
2. Aristotle | Internet Encyclopedia of Philosophy. Iep.utm.edu. (2021). Retrieved 31 January 2021, from https://iep.utm.edu/aristotl/.
3. Descartes, Rene | Internet Encyclopedia of Philosophy. Iep.utm.edu. (2021). Retrieved 31 January 2021, from https://iep.utm.edu/descarte/.
4. Natural Deduction | Internet Encyclopedia of Philosophy. Iep.utm.edu. (2021). Retrieved 31 January 2021, from https://iep.utm.edu/nat-ded/
5. Carson, D. (2009). The abduction of Sherlock Holmes. International Journal of Police Science & Management, 11(2), 193-202.
6. Kahneman, D. (2011). Thinking, fast and slow. Macmillan.
7. Fallacies (Stanford Encyclopedia of Philosophy). Plato.stanford.edu. (2021). Retrieved 31 January 2021, from https://plato.stanford.edu/entries/fallacies/.