"Not a good test taker..."- I don't understand.

someon
Thu, 09 Jul 2009 14:30:34 +0000

Again, it is not the theorem itself that is true. What is true is the if-then statement. For example, if I said: If all cows are blue, then some cows are blue, assuming that you allow that step as a valid rule of inference, the statement: If all cows are blue, then some cows are blue, is true. It doesn’t matter whether all cows are actually blue or not, the if-then statement is true. It doesn’t matter whether the rule “P and not P is false” is true or not in some sort of metaphysical sense- it is simply an axiom, and we say: If this axiom is true, then the following theorems follow. Mathematicians don’t care about whether their axioms are metaphysically true unless they are trying to apply the math to something. Most will tell you that trying to assert that some axiom is “true” is pointless.