2. Deductive Arguments

 

Wireless Philosophy, Fundamentals, 5:41. Original title: CRITICAL THINKING - Fundamentals: Deductive Arguments

Summary

Picking up the distinction between deductive and ampliative arguments from the introductory video, Geoff Pynn takes the first of the two families on its own and works through the question it raises: when does a deductive argument actually give us a reason to believe its conclusion?

What makes an argument deductive

An argument is a set of statements, the premises, meant to give us a reason to believe a further statement, the conclusion. In some arguments the premises are meant to guarantee that the conclusion is true, and those are the deductive ones.

A good deductive argument is a powerful thing, since it guarantees its conclusion. But not every deductive argument is a good one, so there are several things to check before believing where one ends up.

Validity

Part of what the guarantee means is that it is impossible for the premises to be true while the conclusion is false. An argument meeting that condition is valid.

This is a technical use of the word. In everyday speech, "that's a valid point" means something like reasonable or cogent. In philosophy, valid always means just the one thing: if the premises are true, the conclusion must be true as well.

Validity describes the relationship between premises and conclusion. It does not say that either is actually true:

Premise 1: Beyoncé was born in Paris.
Premise 2: Everybody born in Paris loves cheese.
Conclusion: Therefore, Beyoncé loves cheese.

Both premises are false (Beyoncé was born in Houston, and surely some Parisians dislike cheese), yet the argument is valid: if the premises were true, the conclusion would have to be. Being valid is therefore not enough. Because the premises are false, this argument gives us no reason at all to believe its conclusion.

Soundness

A valid argument with true premises is called sound. Again the everyday sense of the word, roughly "compelling", is set aside in favour of the technical one. A deliberately boring example:

Premise 1: Beyoncé was born in Houston.
Premise 2: Everybody born in Houston was born in Texas.
Conclusion: Therefore, Beyoncé was born in Texas.

So the question of whether to believe the conclusion of a deductive argument becomes the question of whether the argument is sound, which splits into two separate checks: is it valid, and are its premises true? (Aaron Ancell's video on Soundness takes up the concept in detail.)

Checking validity: counterexamples

Sometimes validity is obvious, often it is not. One practical method is to look for a counterexample: a case, real or imagined, in which the premises are true and the conclusion is false.

Premise 1: Classical musicians appreciate opera.
Premise 2: Beyoncé is a pop star, not a classical musician.
Conclusion: Therefore, Beyoncé does not appreciate opera.

Suppose Beyoncé has listened to opera since she was a little girl and loves Mozart's Don Giovanni. Both premises stay true while the conclusion turns false, and that possibility is enough to show the argument is invalid. Even with true premises, it gives us no reason to accept its conclusion. More formal techniques for testing validity come later in the series.

Checking the premises takes knowledge, not logic

The second check is where logic runs out. If we do not know whether the premises are true, then even an argument that really is sound gives us no reason to believe its conclusion. Knowing an argument is valid without knowing its premises are true yields, at best, a conditional reason: should the premises turn out to be true, the conclusion will have to be accepted.

Establishing whether the premises are true is not something logic or philosophy can do for us. It takes research and empirical knowledge of the world. This is why critical thinking is more than logical skill: a brilliant logician who lacks the relevant facts still cannot tell whether a valid argument is worth anything.

Key takeaway

A deductive argument earns belief only by being sound, and soundness has two halves that must be checked separately. Logic settles validity; only knowledge of the world settles the premises. The more we know, the better we are able to evaluate deductive arguments.