(March 1, 2012 at 7:33 pm)ChadWooters Wrote: But C can still be true if BOTH A and B are false. No?
A implies B is the premise C.
So if we go alone by that, A and B can be both false, and C can be true. Which is what he is arguing. That even if I prove that A ->B, I haven't proven B without proving A.
So the argument is saying, the premise A -> B would not be true without A being true. I explained why.
If that is true, and we say C is true, then it contradicts what he said, that proving A -> B doesn't prove B because I haven't proven A. Now I have proven A, because I say
Not A -> Not C. (= C-> A.)
And if A is true, then B is true.