saying a theorem is wrong because the hypotheses are not true is bad logic.
If the objection is true, and the hypothesis is false, that seems like a great objection! If, on the other hand, he provided no evidence towards his objection, then it seems that the bad logic is in not offering evidence, not attacking the hypothesis directly.
Am I missing something, or just reading this in an overly pedantic way?
You’re missing something by reading this in an insufficiently pedantic way.
The pedantic way is as follows. The theorem’s claim is “If A, then B”, where A is the hypothesis. Claiming that A is false does not invalidate the theorem; in fact, if A could be proven to be false, then “If A, then B” would be vacuously true, and so in a way, arguing with the hypotheses only supports the theorem.
You could, however, claim that the theorem is useless if the hypothesis never holds. One example of this is “If 2+2=5, then the moon is made of green cheese”. This is a true statement, but it doesn’t tell us anything about the moon because 2+2 is not 5.
If the objection is true, and the hypothesis is false, that seems like a great objection! If, on the other hand, he provided no evidence towards his objection, then it seems that the bad logic is in not offering evidence, not attacking the hypothesis directly.
Am I missing something, or just reading this in an overly pedantic way?
You’re missing something by reading this in an insufficiently pedantic way.
The pedantic way is as follows. The theorem’s claim is “If A, then B”, where A is the hypothesis. Claiming that A is false does not invalidate the theorem; in fact, if A could be proven to be false, then “If A, then B” would be vacuously true, and so in a way, arguing with the hypotheses only supports the theorem.
You could, however, claim that the theorem is useless if the hypothesis never holds. One example of this is “If 2+2=5, then the moon is made of green cheese”. This is a true statement, but it doesn’t tell us anything about the moon because 2+2 is not 5.