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Deductive & Inductive Arguments

Ok, so you made it to Chapter 10. Congratulations! If you have been doing the activities as well as the readings, you are developing an impressive and practical logical mind/toolkit.

This chapter builds on the two ways arguments go bad (Chapter 2). Learning the meaning of the words in this chapter will deepen your knowledge of logic and prepare you for further study in symbolic logic. 

So, let’s get started with the difference between deductive and inductive.

 

Section 1: Deductive and Inductive
Can you see the different ways the premises support the conclusion in the following arguments?

 

Deductive
All philosophers have a brain.
Bob is a philosopher.
Therefore, Bob has a brain.

 

Inductive
Most philosophers have a brain.
Sam is a philosopher.
So, Sam probably has a brain.

 

This distinction describes how the premises support the conclusion. In deductive arguments, the truth of the premise(s) guarantees the conclusion. That is, it is impossible for the conclusion to be false if we assume the premises are true in a good/valid deductive argument.

In inductive arguments, the premise(s) provide probabilistic support. That is, it is improbable, but possible, that the conclusion is false in good/strong inductive arguments.

Argument 1 is a deductive argument because the conclusion must follow if we assume the premises are true. In example 1, it is impossible for the conclusion (i.e. Bob has a brain) to be false if the premises are assumed true. So, it is a valid deductive argument.

In Argument 2, it’s improbable that the conclusion is false if we assume the premises are true. It’s possible, but unlikely, that Sam doesn’t have a brain.

In short, deductive and inductive refer to how the arguer is claiming the premises support the conclusion. In a deductive argument, the arguer is claiming the conclusion must follow if we assume the premises are true. In an inductive argument, the arguer is claiming the conclusion probably follows if we assume the premises are true. 

 

Many websites present misconceptions about deduction and induction, which include the following:

Misconception 1: Deductive arguments always move from general to specific whereas inductive arguments move from specific to general.

Correction: Actually, some deductive arguments move from specific to general claims, and some inductive arguments move from general to specific. I will provide some examples in the activity.

Misconception 2: Deductive arguments are based on facts. Inductive arguments aren’t.

Correction: Actually, the truth of the premises has nothing to do with whether an argument is deductive or inductive. Rather, deduction and induction is all about how the arguer claims the premises support the conclusion if we assume the premises are true. Both deductive and inductive arguments can have false premises.

Misconception 3: Science is only about inductive thinking.

Correction: Actually, science uses both inductive and deductive thinking. I will illustrate in the exercise.

 

Before concluding, I should emphasize one final clarification. Deductive and inductive refer to how the arguer is claiming the premises support the conclusion. For example, the following is a deductive argument because I am claiming the conclusion must follow if the premises are assumed true:

 

All whales are mammals.

Shamu is a mammal.

So, Shamu is a whale.

 

This argument is deductive because I am claiming the conclusion must follow. But, of course, the conclusion does not follow even if we assume the two premises are true, so it is an invalid deductive argument. Just because x is a mammal and "all whales are mammals" does not mean it must be the case that "x is a whale."   X could be a nonwhale mammal, like a cat.

 

Exercise: Identify the following arguments as inductive or deductive

1. In my experience, most people are happier when they have the Epicurean goods of friends, self-sufficiency, and time for reflection. Therefore, I think you will probably be happier if you focus on getting these three goods.

2. You cannot achieve peace of mind until you recognize what is under your control and what isn't under your control, and then not worry about what isn't under your control. What others think of you isn't ultimately under your control precisely because it's their thinking. Therefore, don't worry about what others think of you (Stoicism).

3. All tigers are animals. Tigger is a tiger. Therefore, Tigger is an animal.

4. Humans usually use new technologies in times of war to destroy instead of build. The atomic bomb is a great example. Therefore, we will probably use strong artificial intelligence to destroy in times of war (if we ever invent it).

5. We are going to have at least one day in which the temperature rises above 100 in Austin because this has happened in Austin for at least the last 300 years.

6. Consciousness is either a physical thing or a nonphysical thing. Since it is not a physical thing, it must be nonphysical.

7. Since the universe is like a watch, it is probably designed.

8. There are only two people in this house: Blaise and Catherine. Neither wear glasses. Therefore, Blaise doesn't wear glasses.

9. If God exists there is good in the world. God exists, so there is good in the world.

10. Many inexplicable phenomena have eventually been explained by science, so consciousness will eventually have a scientific explanation.

11. Since every action has an equal and opposite reaction, this action will have an equal and opposite reaction.

12. Which of the two argument types (i.e. deductive or inductive) seem to add something new to the premises? Which seems to have its conclusion contained within its premises?

13. “Three is a prime number. Five is a prime number. Seven is a prime number. Therefore, all odd numbers between two and eight are prime numbers” (Patrick Hurley's Concise Introduction to Logic).

14. Some people incorrectly define deductive arguments as those that move from general claims to specific claims (e.g. all apples are red, so this apple is red) and inductive as those that move from specific claims to general claims (e.g. each apple is red so all apples are red). Examine arguments five & thirteen, and explain why this definition is sometimes incorrect.

15. Imagine someone tells you that deductive arguments are based on facts and inductive arguments are based on opinions or observations. Explain why this is a misconception and how you would explain it to him.

16. Why is the deductive/inductive distinction important?

* 17. In Patrick Hurley's Concise Introduction to Logic, he lists several types of deductive argument: argument based on math, argument from definition, categorical syllogism, hypothetical syllogism, and disjunctive syllogism. He also lists several types of inductive arguments: predictions, analogies, generalizations, argument from authority, argument based on signs, and causal inference. Give an example of each and explain why it's deductive or inductive.

18. Bob lives in Texas, so he lives in the U.S.

19. Bob lives in Texas, so he wears a cowboy hat.

20. Bob is taller than his wife, and his wife is taller than his son. So, Bob is taller than his son.

 

Answers
1. Inductive. “Probably” is a clue.
2. Deductive. If we assume the premises are true, the conclusion must follow.
3. Deductive. It is impossible for the conclusion to be false if we assume the premises are true.
4. Inductive. The arguer is claiming the conclusion probably follows, not that it must follow.
5. Inductive. An argument generalizing from a sample is inductive because the conclusion is supported in a probabilistic way; the conclusion could be false even if we assume the premises true.
6. Deductive. If we assume the premises are true, the conclusion must follow. Of course, you might reject the premise as false, but deduction and induction have nothing to do with the truth or falsity of the premises (or conclusion). Deduction or Induction is about how the premises support the conclusion.
7. Inductive.
8. Deductive
9. Deductive. If we assume the premises are true, then the conclusion must follow.
10. Inductive
11. Deductive. We aren’t generalizing; rather we are assuming a general law is true and then inferring a case from it.
12. Inductive arguments add something new whereas deductive arguments seem to have the conclusion contained within the premises. This definition may help you better understand the distinction between deductive and inductive.
13. Deductive. Notice it moves from particular claims to general claims, so not all deductive arguments move from general to specific.
14. See 13 and 5.
15. Answers will vary, but both types of arguments could have all the correct facts. Logic is about the quality of inferences, not the truth or falsity of premises.
16. The distinction helps us better understand any argument. Is the arguer arguing for a necessary or probabilistic connection between premises and conclusion?
17. Research
18. Deductive
19. Inductive
20. Deductive

 

Value and Application
There are only two ways premises can support a conclusion. The words “deductive” and “inductive” give us a way to talk about these two ways and to thereby better analyze and evaluate any particular argument.

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