> > >Truth of "If P then Q" need not require assuming the truth of "P". > > > > Never said it did. I just said the truth of any Q demonstrated of P > > requires the assumption of truth for P. > > But that only means that the truth of Q is conditional on the truth of > P, and does not require that P be true, unless one claims that Q is > unconditionally true. > > > Otherwise the truth of Q > > remains problematic. It's an old and ongoing problem in Aristotelian > > syllogistic inference: the truth of any conclusion is only supported > > by the truth of the premises involved. > > Precisely. > > > > >If P and Q are compound statements such that Q is false whenever P is > > >false, then "If P then Q" will be true regardless of the truth of P. > > > > Don't quite follow the logic here. The whole "If" conditional is an > > assumption of truth on the face of it. > > It is an assumption of relative truth, but not of any absolute truth.
There is vast confusion in the use of the terms "relative truth", "absolute truth", "conditional truth", "unconditional truth", "trivially true", "vacuously true", "contingent truth", "necessary truth", and other locutions. It's an embarrassment.
I addressed the topic of the relation of truth to validity in my postings to sci.logic on June 22, 23, and 24 of this year.