'When Are Relations Neither True Nor False? [Logic]

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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