So I’ve been talking all year about how Philosophy is going to write this free Critical Thinking Text for the BC community. Meanwhile Mark Storey has actually done so. A complete draft should be ready to share in Fall Quarter. We will also be running a Critical Thinking Curriculum Development Seminar using this material through the Faculty Commons in the fall. Here’s a short excerpt:

Valid vs. Invalid

Every argument in the universe needs to “pass” two tests; the arguments must be logically good and factually good. We are speaking loosely at this point, but all deductive and inductive arguments must meet the same basic pair of demands: it must be the case that (a) its premises give good reason to believe the conclusion, and (b) the premises are actually true. The first concern pertains to the relation the premises have to the conclusion, and the actual truth or falsity of the premises is often irrelevant. The second concern pertains to the facts of the matter and to whether the claims of the premises correspond accurately to the world. Figuring out if an argument is logically good or not often involves a hypothetical thought experiment in which you don’t really care if the premises are actually true or not. Figuring out if the argument is factually good forces you to step out of the hypothetical thought experiment and rely on your knowledge of the real world. We’ll begin by focusing our attention on the first concern.

As we have seen, a deductive argument is any argument claiming either explicitly or implicitly that if the premises all are true, then the conclusion must be true. Deductive arguments are evaluated as either “valid” or “invalid.” A deductive argument is valid when it is indeed the case that if the premises are true then the conclusion must be true, and a deductive argument is invalid when it is not the case that if the premises are true then the conclusion must be true.

To determine if a deductive argument is valid or invalid, ask yourself a question:  Is it logically impossible for the premises to be true and at the same time and from the same perspective for the conclusion to be false? If “Yes,” then the argument is valid. If “No,” then the argument is invalid.

The distinction between valid and invalid arguments will become clearer after you’ve examined some examples. The following deductive arguments are all valid. Notice that it is impossible for the premises to be true and the conclusion false.

1. Every square has four sides. This figure is a square. Therefore this figure must have four sides.
2. Tom is older than Bob and Bob is older than Ed. So Tom must be older than Ed.
3. Some cats are pets. Thus, it must be that some pets are cats.
4. Alfredo is Sue’s (biological) father. Therefore, Alfredo must be older than Sue, because fathers are always older than their biological children.

 

The following deductive arguments are invalid. Notice that it is possible for the premises to be true and the conclusion false.

1. Javon is older than Betty. Therefore, Javon must be taller than Betty.
2. All members of the XYZ club are senior citizens. Thus it must be that all senior citizens are members of the XYZ club.
3. All members of the Hells Angels live in California. Joe lives in California. Therefore, it is certain that Joe is a member of the Hells Angels.
4. If the sun is out, then Vu is swimming. Vu is swimming. So it must be that the sun is out.

Each argument above is deductive because the claim in each case is that the conclusion must be true if the premises are true. However, some are valid deductive arguments and some are invalid, because some succeed in showing that their conclusions must be true if their premises are true, and some do not. That is, for the invalid arguments, it is logically possible for the premises to be true and the conclusion to be false. The premises are thus not guaranteeing the conclusion.

Suppose you are looking at a deductive argument trying to decide whether it is valid or invalid. How do you decide? Again, ask yourself a hypothetical question: Is it logically impossible for the premises to be true and at the same time the conclusion be false?

If you answer “Yes”—in other words—if the conclusion must be true if the premises are true, then the argument is valid. However, if your answer is “No” because the conclusion might be false even if the premises are true, then the argument is invalid. For example, suppose the Smiths are a big family living in Lynnwood, Washington:

1. All the Smiths are Catholics.
2. All Catholics live in Italy.
3. So, all the Smiths must live in Italy.

Is it impossible the premises could be true and the conclusion false? Yes! If the premises were true, the conclusion would certainly be true. This argument is therefore valid. It is logically good. The structure of the argument is such that if the premises were true (and they are not, but for now that’s irrelevant) the conclusion would be guaranteed to be true. We see this once we agree to do the thought experiment of asking about the possibility of the premises being true while the conclusion is false. Of course, given what we know about the Smiths (i.e., that they live in Lynnwood, Washington) the second premise is clearly false (and maybe the first premise, too), so the argument is factually bad, but we’ll get to that concern momentarily. For right now we are concerned only with the logical structure—or “bones”—of the argument. We’ll look at issues pertaining to the facts, or “truth value,” of the premises in shortly.

June 10, 2013