Inductive and deductive reasoning are often confused. This lesson introduces the concept of reasoning and gives you tips and tricks to keeping inductive and deductive reasoning straight.

## Using Reasoning

Andrew and Kevin are studying for their upcoming speech final. They have to define inductive and deductive reasoning and provide examples of each. Kevin says he has a great example for deductive reasoning: ‘Every time it hails, I get a dent in my car. Every time it hails, my dad gets a dent in his car. Every time it hails, my brother gets a dent in his car. Every time it hails, everyone will get a dent in their cars.’

Andrew says that Kevin does not have an example of deductive reasoning, but it is better as an example for inductive reasoning. Who is right?

In this lesson, you will learn about the concept of reasoning and how it is used in conjunction with logic for inductive and deductive arguments.

## Reasoning and Logic

First, let’s discuss the concept of reasoning. **Reasoning** is the action of constructing thoughts into a valid argument. This is something you probably do every day. When you make a decision, you are using reasoning, taking different thoughts and making those thoughts into reasons why you should go with one option over the other options available. When you construct an argument, that argument will be either valid or invalid. A **valid argument** is reasoning that is comprehensive on the foundation of logic or fact.

Now let’s discuss propositional logic. Inductive and deductive reasoning are both forms of propositional logic. **Propositional logic** is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences. For our purposes, this means that propositional logic uses a series of facts and reasoning to develop a conclusion. Inductive and deductive reasoning use propositional logic to develop valid arguments based on fact and reasoning. Both types of reasoning have a premise and a conclusion. How each type of reasoning gets to the conclusion is different.

Let’s discuss inductive reasoning first.

## Inductive Reasoning

**Inductive reasoning** is reasoning where the premises support the conclusion. The conclusion is the hypothesis, or probable. This means that the conclusion is the part of reasoning that inductive reasoning is trying to prove. Inductive reasoning is also referred to as ’cause and effect reasoning’ or ‘bottom-up reasoning’ because it seeks to prove a conclusion first. This is usually derived from specific instances to develop a general conclusion.

Kevin and Andrew are now arguing about math. Kevin says that all big brothers are good at math. Andrew is an only child, but he’s pretty sure that this argument cannot be valid.

Kevin makes a conclusion based on the following premises: ‘My older brother is good at math. My friend’s older brother is good at math. My neighbor’s big brother is a math tutor. Therefore, all older brothers are good at math.’

You’ve probably heard people use this type of reasoning in life. We know this can’t be true. You probably know that being an older brother doesn’t inherently make you good at math. What Kevin has done is made a generalized conclusion: all older brothers are good at math based on three premises of specific instances: Mine, my friend’s and my neighbor’s older brother are all good at math. These specific instances are not representative of the entire population of older brothers. Because inductive reasoning is based on specific instances, it can often produce weak and invalid arguments.

You can remember inductive reasoning like this: inductive reasoning is bottom-up reasoning; it starts with a probable conclusion and induces premises.

Now let’s talk about deductive reasoning.

## Deductive Reasoning

**Deductive reasoning** is reasoning where true premises develop a true and valid conclusion. In the case of deductive reasoning, the conclusion must be true if the premises are also true. Deductive reasoning uses general principles to create a specific conclusion. Deductive reasoning is also known as ‘top-down reasoning’ because it goes from general and works its way down more specific.

For example, ‘All cars have engines. I have a car. Therefore, my car has an engine.’

We know that the conclusion is true because it is based on generalized premises that are true without any exceptions. As long as the premises are true, then the conclusion will also be true. This probably seems like a simple example; however, you need to see the importance of having a true and unquestionable premise. For example: ‘All blondes have blue eyes. Kevin has blonde hair. Therefore, Kevin must have blue eyes.’

It is an untrue conclusion because it is based on an untrue premise, ‘all blondes have blue eyes.’ There are many exceptions to this statement. Even if the premise ‘Kevin has blonde hair’ is true, the conclusion cannot be true because it is based on untrue premises.

You can remember deductive reasoning like this: deductive reasoning is top-down reasoning. It starts with a true premise and deduces a true conclusion.

## Lesson Summary

Remember, **reasoning** is the action of constructing thoughts into a valid argument. A **valid argument** is reasoning that is comprehensive on the foundation of logic or fact. Inductive and deductive reasoning both strive to construct a valid argument. They do this by using **propositional logic**, which is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences.

Both inductive and deductive reasoning construct sentences, also known as premises to a conclusion. Check out this chart to compare and contrast deductive reasoning:

First, **inductive reasoning** is also known as ‘bottom-up reasoning,’ while **deductive reasoning** is known as ‘top-down reasoning.’ This is because inductive reasoning starts with a conclusion and deductive reasoning starts with a premise.

Next, inductive reasoning uses specific instances to develop a conclusion, while deductive reasoning uses generalized principles. Therefore, inductive reasoning moves from specific instances into a generalized conclusion, while deductive reasoning moves from generalized principles that are known to be true to a true and specific conclusion.

The accuracy of inductive reasoning is questionable. Because inductive reasoning uses specific premises to build a conclusion, the conclusion is probable but not absolutely true. Deductive reasoning can lead to an absolutely true conclusion if and only if the premises that lead to that conclusion are also true.

So, what do you think? Is Kevin’s example better for an inductive or deductive reasoning?

‘Every time it hails, I get a dent in my car. Every time it hails, my dad gets a dent in his car. Every time it hails, my brother gets a dent in his car. Every time it hails, everyone will get a dent in their cars.’

This is an example of inductive reasoning! It uses specific instances, and we know this is just a probable conclusion because when it hails, I don’t get a dent in my car…most of the time.

## Learning Outcomes

After you have finished with this lesson, you should be able to:

- Define reasoning, valid argument and propositional logic
- Compare and contrast inductive reasoning and deductive reasoning