On Wed, May 11, 2011 at 11:40 AM, Adam P. Goucher <apgoucher@gmx.com> wrote:
You claim that the first sentence is true and the second is false. Why is this any more correct than the claim that the first statement is false and the second statement is true? It's similar to statements like
1. Statement 2 is false 2. Statement 1 is false
You can assign the truth values (T, F) or (F, T) without contradiction.
In either case, the contrapositive of the true statement is false. So, we can assume wlog that the first statement is true, and its contra- positive is false.
There's a difference between "Statement 1 is true" and "The assumption that Statement 1 is true does not lead to a contradiction". For example "Statement 1 is true" and "Statement 2 is false" can't both be correct, and in this case, both ""The assumption that Statement 1 is true does not lead to a contradiction" and "The assumption that Statement 1 is false does not lead to a contradiction" are true. Andy