Subject: Re: Falsity implies anything.
Date: Sun 11/29/98 10:07 PM
From: Alex Bogomolny
The statement "If I have a computer, then you have a computer" does not say that I have a computer even if you do not. I may or may not have a computer. However, if you do not have a computer, the statement is correct.
There may be differences in opinion as to what kind of logic (and there are several) one should prefer. However, I feel perfectly comfortable with the one known as the Mathematical Logic.
Forget for a moment about your examples and your general dissatisfaction with logic. How should I define the implication "=>"? I feel that from truth may only follow truth. And to distinguish, from falsity may follow anything. Why? For truth, I do not need any justification at all. So truth may as well follow from falsity. If we stop here then there would not be any difference between F=>A and T=>A. For this reason, I feel we also have to accept F=>F. Falsity implies everything.
This only says that F=>F and F=>T both are true. It does not say that if A=>B and A is false then B is true. Therefore, I do not feel that F=>F is absurd. It might be meaningless in the sense of not providing a lot of information - but this is a different matter.
All the best,