here's another thing. assume p -> q. like those guys up there said a million times, if p is true, then the entire statement p -> q is true. q is not necessarily true, and is not necessarily false. it's just that p -> q as a statement is still valid, because it has not been proven to be false.
for example: assuming the statement "'Ed is a dog" implies "Ed has four legs'" is true: if Ed is, indeed, a dog, then he has four legs if Ed is not a dog, then he may or may not have four legs, but since you haven't proven the implication false, it is still true, since you have not proven that there exists an Ed that is a dog but does not have four legs.
my main point is, you're saying "if one's hypothesis is false, how can one derive a conclusion that is true?", and you're way off base. your hypothesis, that Ed is a dog, isn't saying that your conclusion, that Ed has four legs, is correct if Ed isn't a dog. it's just saying that, as a statement, "Ed is a dog implies Ed has four legs" is still valid, and makes no comment whatsoever on whether or not Ed the non-dog, indeed, has four legs.
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Date: 2003-08-29 01:50 am (UTC)for example: assuming the statement "'Ed is a dog" implies "Ed has four legs'" is true:
if Ed is, indeed, a dog, then he has four legs
if Ed is not a dog, then he may or may not have four legs, but since you haven't proven the implication false, it is still true, since you have not proven that there exists an Ed that is a dog but does not have four legs.
my main point is, you're saying "if one's hypothesis is false, how can one derive a conclusion that is true?", and you're way off base. your hypothesis, that Ed is a dog, isn't saying that your conclusion, that Ed has four legs, is correct if Ed isn't a dog. it's just saying that, as a statement, "Ed is a dog implies Ed has four legs" is still valid, and makes no comment whatsoever on whether or not Ed the non-dog, indeed, has four legs.