'When Are Relations Neither True Nor False?
in [Math]
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From: MoeBlee on 22 Mar 2010 20:43 On Mar 22, 7:18 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Perhaps [you] [Transfer Principle] [are] convinced that there are two teams I thought we were going to form a league. But first we have to nominate captains and flip a coin to see who gets first pick. I nominate Aatu! (I hope he picks me! Or at least I hope I'm not left for the very last pick.) > You have no idea why Clarke killfiled me and neither do I (nor do I > care, of course). What do you mean you don't care?! How can you have human feelings and not care about such things?! > Yes, because what better indication of the worth of an idea than its > popularity? Really good ideas are rejected by most people but > accepted by a minority. The minority has to be more than one, of > course. Probably two or three is optimal. I think it's been proven that 2.78 is optimal. > Mind you, Clarke has not expressed agreement, but let's not dwell on > unpleasant details. Why not? It's never stopped us before. MoeBlee
From: Jesse F. Hughes on 22 Mar 2010 20:42 MoeBlee <jazzmobe(a)hotmail.com> writes: > On Mar 22, 7:00 pm, Transfer Principle <lwal...(a)lausd.net> wrote: >> So we know that in ZFC, if phi(x) is a one-place predicate of the form >> Ayex (psi(y)) for some one-place predicate psi, then phi(0) must hold >> by vacuous truth. There are two ways to avoid this. The first would be >> to change the laws of inference of FOL in order to avoid vacuous >> truth, >> and the other would be to change the axioms of ZFC in order to prevent >> the empty set 0 from existing. > > But that in itself doesn't block all instantances of vacuous > implication. Walker isn't interested in relevance logic, since Newberry isn't focused on vacuous implication. Newberry's pet peeve is that a statements like (Ax)(Px -> Qx) is true if ~(Ex)Px. He thinks that the latter statement should be neither true nor false (indeed, it should be considered *meaningless*) in this case. -- "I'd step through arguments in such detail that it was like I was teaching basic arithmetic and some poster would come back and act like I hadn't said anything that made sense. For a while I almost started to doubt myself." -- James S. Harris, so close and yet....
From: Nam Nguyen on 22 Mar 2010 20:50 J. Clarke wrote: > > Definition of "truth". Where does it come from? > In this context, it comes from Tarski's concept of truth: http://en.wikipedia.org/wiki/Semantic_theory_of_truth Note that Shoenfield's definition: >>> M(A) = T iff pm(M(a1),...,M(an)) the "concreteness" of truth, or falsehood, comes from the "concreteness" of an element being in, or not in, a set (the "predicate"/"relation" set).
From: MoeBlee on 22 Mar 2010 20:52 On Mar 22, 7:42 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > MoeBlee <jazzm...(a)hotmail.com> writes: > > On Mar 22, 7:00 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > >> So we know that in ZFC, if phi(x) is a one-place predicate of the form > >> Ayex (psi(y)) for some one-place predicate psi, then phi(0) must hold > >> by vacuous truth. There are two ways to avoid this. The first would be > >> to change the laws of inference of FOL in order to avoid vacuous > >> truth, > >> and the other would be to change the axioms of ZFC in order to prevent > >> the empty set 0 from existing. > > > But that in itself doesn't block all instantances of vacuous > > implication. > > Walker isn't interested in relevance logic, since Newberry isn't > focused on vacuous implication. Newberry's pet peeve is that a > statements like > > (Ax)(Px -> Qx) > > is true if ~(Ex)Px. He thinks that the latter statement should be > neither true nor false (indeed, it should be considered *meaningless*) > in this case. Okay, but still Transfer Principle's proposal wouldn't block all instances of what you just described, right? I mean, even if there's no empty set, then we'll still have situations in which ~ExPx, right? MoeBlee
From: Jesse F. Hughes on 22 Mar 2010 20:58
MoeBlee <jazzmobe(a)hotmail.com> writes: > On Mar 22, 7:42 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> MoeBlee <jazzm...(a)hotmail.com> writes: >> > On Mar 22, 7:00 pm, Transfer Principle <lwal...(a)lausd.net> wrote: >> >> So we know that in ZFC, if phi(x) is a one-place predicate of the form >> >> Ayex (psi(y)) for some one-place predicate psi, then phi(0) must hold >> >> by vacuous truth. There are two ways to avoid this. The first would be >> >> to change the laws of inference of FOL in order to avoid vacuous >> >> truth, >> >> and the other would be to change the axioms of ZFC in order to prevent >> >> the empty set 0 from existing. >> >> > But that in itself doesn't block all instantances of vacuous >> > implication. >> >> Walker isn't interested in relevance logic, since Newberry isn't >> focused on vacuous implication. Newberry's pet peeve is that a >> statements like >> >> (Ax)(Px -> Qx) >> >> is true if ~(Ex)Px. He thinks that the latter statement should be >> neither true nor false (indeed, it should be considered *meaningless*) >> in this case. > > Okay, but still Transfer Principle's proposal wouldn't block all > instances of what you just described, right? I mean, even if there's > no empty set, then we'll still have situations in which ~ExPx, > right? I've no idea what Walker's doing. I didn't bother reading it carefully. -- Jesse F. Hughes "Hey look, Captain, next time someone wants to tie us up, let's put up a fight." --Adventures by Morse |