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

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From: MoeBlee on 22 Mar 2010 21:22

On Mar 22, 7:58 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:
> I didn't bother reading it
> carefully.

But you're standard theorist. So it follows that none of the standard
theorists bothered to read it carefully. This is dire.

MoeBlee

From: Jesse F. Hughes on 22 Mar 2010 21:44

"Jesse F. Hughes" <jesse(a)phiwumbda.org> writes:

> "Jesse F. Hughes" <jesse(a)phiwumbda.org> writes:
>
>>> Although I don't necessarily agree with the idea of killfiling someone
>>> merely because one disagrees with them, Clarke is only doing the
>>> same thing to Hughes that Daryl McCullough, another poster in this
>>> thread, has done to me. And Clarke has killfiled Hughes for the exact
>>> same reason that McCullough has killfiled me -- because both Hughes
>>> and I have repeatedly posted statements with which Clarke and
>>> McCullough, respectively, disagree. The so-called "cranks" and the
>>> standard theorists have more in common with each other than either
>>> would like to admit.
>
> Two points I failed to make: First, I don't see why you think Clarke
> is a crank.

Actually, I should also say that Newberry is not a crank -- at least
not by the standards of sci.math. He's fairly passionate about
replacing FOL with an alternative, which is certainly crank*ish*, but
he's perfectly coherent and relatively competent. (I'm not sure he
has the knowledge necessary to complete his project, but he's still
relatively knowledgeable about the subject.)

Compare his writings to AP, James S. Harris, Meuckenheim. Newberry is
not in the same league.

--
Jesse F. Hughes

"Had you told it like it was, it wouldn't be like it is."
-- Albert King

From: Nam Nguyen on 22 Mar 2010 23:10

Jesse F. Hughes wrote:

> He's fairly passionate about
> replacing FOL with an alternative, which is certainly crank*ish*

Huh? Why is being passionate (without qualification) about replacing
the current FOL with an alternative being equated to _crank_ish,
especially when the current FOL has fundamental weaknesses in it?

From: Nam Nguyen on 22 Mar 2010 23:13

Aatu Koskensilta wrote:
> Nam Nguyen <namducnguyen(a)shaw.ca> writes:
>
>> If that's case, and you have to say if it is or isn't, then an example
>> of a "nontrivial" metamathematical theorem would be the following modified
>> GIT:
>>
>> (1) _If_ PA is consistent, then for any consistent formal system T
>> sufficient strong to carry out basic notions of arithmetic,
>> there's a formula G(T) which is syntactically undecidable in T
>> but of which a certain encoded formula, say, encoded(G(T)) is
>> provable in PA.
>>
>> Would (1) be an interesting theorem?
>
> It's hard to say, since your statement of this theorem is rather
> opaque. For instance, what is encoded(G(T))?
>

Is G(T), to you, a formula written in L(T) or in the language of arithmetic
[i.e. L(PA)]?

From: Newberry on 23 Mar 2010 01:25

On Mar 22, 5:42 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.

It is meaningless only if ~(Ex)Px is necessarly true. If ~(Ex)Px is
contingent then

(Ax)(Px -> Qx)

is merely neither true nor false. In arithmetic it would indeed be
meaningless.

> --
> "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....