A is something which we do not know the truth value of, for example: A = It will rain tomorrow. It might happen, it might not. So possibly A is true, and possibly ~A is also true. What is wrong with the below reductio ad absurdum? Where I will take A as the assumed premise, show that it leads to a contradiction and then assert the negation of A as the conclusion.
Assume A. Possibly ~A (which we know is true). A & possibly ~A is a contradiction. Therefore ~A. If this works, I have proved that it will not rain tomorrow...which of course cannot be...so where does the problem lie? If we assume A, can we not say 'possibly ~A'? (I looked at some modal logic....but I don't think possibly ~A is the same as '~A is true in some possible world'.) Thanks very much guys