Topics Logic

Question I know affirming the consequent is a fallacy, so that any argument with that pattern is invalid. But what what about analytically true premises, or causal premises? Are these not really instances of the fallacy? They seem to take its form, but they don't seem wrong. For example: 1. If John is a bachelor, he is an unmarried man. 2. John’s an unmarried man. 3. Therefore he’s a bachelor. How can 1 and 2 be true, and 3 be false? Yet it looks like affirming the consequent. 1. X is needed to cause Y. 2. We’ve got Y. 3. Therefore there must have been X. Again, it seems like the truth of 1 and 2 guarantee the truth of 3. What am I missing?

Accepted:
January 31, 2013

Comments

Your particular argument:

1. If John is a bachelor, he is an unmarried man.

2. John's an unmarried man.

3. Therefore he's a bachelor.

isn't a valid argument. You may think it is because you believe that (3) just follows logically from (2). But it doesn't. It follows from (2) and the definition of "bachelor" as unmarried man.

You asked, "How can 1 and 2 be true, and 3 be false?" Suppose that John is divorced and not remarried; he'd be unmarried but not a bachelor. You can patch up the argument by changing (1) to (1*) "If John is a bachelor, he is a never-married man" and changing (2) to (2*) "John is a never-married man." The argument still wouldn't be formally valid, which is the sense of "valid" that Prof. George uses in his reply. But it would be valid in that the premises couldn't be true unless the conclusion were true, because (2*) by itself implies that John is a bachelor. An argument that isn't formally valid -- i.e., an argument whose form alone doesn't guarantee its validity -- can be valid in the sense that the truth of its premises guarantees the truth of its conclusion.

The last sentence of Prof. George's reply suggests that definitions are crucial in enabling conclusions to follow from premises. I think that suggestion is true only if logical implication is a relation holding between items of language such as sentences rather than (as I prefer to say) a relation holding between non-linguistic propositions. The proposition that my car is red implies the proposition that my car exists, and the implication holds regardless of how we define words.