Strategies for Decision Making – Week 2 Lecture

Introduction to Logic

We have been looking so far at the general structure of logic and critical thinking. This week, we’ll focus more on deduction and induction.

For our purposes, we can divide arguments up into two categories: deductive and inductive. Many logicians also recognize a third category (abduction), but we won’t be looking at that in this course work.

As was mentioned last week, deductive arguments are those in which the truth of the premises guarantee the truth of the conclusion. Consider the following argument:

1. If the moon is made out of cheese, then it is tasty.

2. The moon is made out of cheese.

3. Therefore, the moon is tasty.

This is a deductively valid argument. If the premises are true, then the conclusion must follow out of necessity. Of course, the second premise is false, but deductive validity has to do with the argument’s structure, not the truth of the premises.

This tends to trip people up. Typically, when we use “valid” and “invalid” in everyday language, we mean something like “correct” and “incorrect.” But that’s not what logicians mean by those terms, and it’s not how we’ll be using them in this class. For our purposes, an argument is deductively valid if has the right structure. Consider again the argument we just looked at, which has the following structure:

1. If P, then Q.

2. P.

3. Therefore, Q.

The structure of the argument is a valid form of inference. If premises one and two are true, then premise three follows of necessity. It’s important to emphasize the “if” part of this explanation. When testing for validity, you are not looking to see if the premises are in fact true. Rather, you assume them to be true for the sake of argument and then see whether the conclusion follows given the truth of the premises. If the conclusion does follow, then the argument is valid. If the premises are in fact true, then the argument is sound. With that in mind, we can now define validity and soundness:

Validity: An argument is deductively valid if the truth of its premises guarantee the truth of its conclusion.

Soundness: An argument is sound if it has a valid structure and has true premises.

There are many different forms that valid arguments may take. Several are outlined in your book.

Validity applies to deductive arguments only. This is because deductive arguments are designed so as to guarantee certainty: if the premises of a deductive argument are true, then the conclusion must follow. This isn’t the case with inductive arguments, which merely render the conclusion more probable.

There are many different types of inductive reasoning. Several mentioned in the book include reasoning by analogy, statistical induction, enumerative induction, and higher-level induction. Inductive arguments attempt to generalize from the basis of experience.

Although the textbook uses the term “inductive validity,” we will be referring to inductive arguments as either strong or weak. Whereas validity in the context of deductive arguments is an all-or-nothing concept, strength and weakness come in degrees. Inductive arguments can admit of varying degrees of strength. In general, an inductive argument is strong if it lends good support to its conclusion, and weak if it doesn’t. Keep these points in mind as you do the readings and exercises for this week.