On Sun, 23 Jul 2006 01:25:46 -0400, email@example.com wrote:
> > >Lester Zick wrote: >> On Sat, 22 Jul 2006 03:07:19 -0400, firstname.lastname@example.org wrote: >> >Lester Zick wrote: >> >> On Fri, 21 Jul 2006 14:14:26 -0600, Virgil <email@example.com> wrote: >> >> > >> >[...] >> >> >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. >> > >> >No. P may be false and validly imply true q. >> >> I don't follow this. If P is false then any Q demonstrated of P is >> false too. > >Let P = Margaret Thatcher is a man, and all men are politicians. >Let Q = Margaret Thatcher is a politician. > >P is false, and validly implies Q, which is true.
Well sure but you're using compound predicates which are false to begin with and don't really imply Q except to the extent they're false.If I were simply to say "Margaret Thatcher is a male politician" the effect would be exactly the same. The proposition is just false. Q may or may not be true but not because P is false.
>> >> Otherwise the truth of Q >> >> remains problematic. >> > >> >Yes. >> > >> >> 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. >> > >> >Yes and no: Q is true or false regardless of whether P implies it >> >or not. On the other hand, our _knowledge_ of the truth of Q is >> >only supported by (our knowledge of) the truth of P. >> >> So what do we do about it? We're still forced to rely on the truth of >> axioms for our knowledge of the truth of Q. > >Yep. Usually the truth of the premises would have to be established >empirically.
Truth can't be established empirically. The only thing which can be established empirically is inconsistency or a lack of inconsistency.
> Unless they are analytic, logical truths.
Which cannot be shown to be true through syllogistic inference.
> In the >case of mathematical axioms, it could be argued that the axioms >are stipulative,
Of course they're stipulative. The difficulty is that they're assumed true.
> and possess neither truth nor falsehood, but >are only applicable in this situation or that -- that is, they >are true of some things, false of others.
I agree. But that leaves us not knowing which are actually true and which not.
>> >We may be about to have a problem due to confusing a proposition "p" >> >with a formula "P". >> >> Formulas are proposition cast in formulaic terms. > >Formulae are the forms of propositions. Some are sufficiently determined >so as to be a proposition rendered in symbolic form. Of course, all >propositions are rendered in symbolic form, when they are put into >some language or other. Well, I guess I could concretely render >the proposition "I don't like you" by beating you. Not much >symbolism there.
Not necessarily. Certainly there are those who love to be beaten.