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Woolsey's law and formal logic

Posted By: Bryce
Date: Thursday, 13 March 2008, at 12:46 p.m.

In Response To: Woolsey's law and formal logic (PersianLord)

The "IF" definitely does not go with the p: the "if" is part of the implication arrow. p=>q means "If p, then q." p=>q is true exactly when the contrapositive, ~q=>~p is true. That statement reads "IF not q, THEN not p."

"If you see clouds in the sky (p), then it will be raining.(q)

~q>~p :

It will not be raining, if you don't see clouds in the sky. "

This is an odd statement because your original p->q is false; clouds do not imply rain! The statement you wrote is ~p->~q, the inverse, which happens to be true, but not because the original statment is. Note that your statement says the same thing as "IF you don't see clouds in the sky, THEN it will not be raining"--this is "IF ~p, THEN ~q."

There may be some confusion here, in that the english sentence "A, if B" means the same thing as "if B, A." I'm not meaning to insult your knowledge of the language, just saying that your statement means different things depending on where you put the "if," and Stein is correct that you have it switched.

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