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

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From: Newberry on 28 Mar 2010 23:41

On Mar 28, 4:37 am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
wrote:
> Newberry says...
>
>
>
>
>
>
>
> >On Mar 27, 4:56=A0am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
> >wrote:
> >> Newberry says...
>
> >> >L: ~T(L)
>
> >> >If v(L) =3D ~(T v F) then there is no contradiction. L is not true.
>
> >> But *if* T is a truth predicate, then "L is not true" is formalized
> >> by the statement ~T(L).
>
> >> >The argument usually goes "but that is what L says." But L does not
> >> >say anything.
>
> >> It says "L is not true".
>
> >> So your proposed resolution is complete nonsense.
>
> >It contains the string "L is not true", but it does not "say" that L
> >is not true
>
> That's completely silly.

Did you read this?
http://www.columbia.edu/~hg17/gaifman6.pdf

>
> --
> Daryl McCullough
> Ithaca, NY- Hide quoted text -
>
> - Show quoted text -

From: Jesse F. Hughes on 29 Mar 2010 00:04

Newberry <newberryxy(a)gmail.com> writes:

> On Mar 28, 5:50 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:

>> Anyway, I won't really defend my theory. My point is: you claim that
>> your approach may yield a theory in which truth and provability are
>> equivalent. Ignoring the fact that this is wishful thinking thus far,
>> so what? You do so only by redefining what truth means, so that
>> vacuously true statements are not true. I don't see any advantage to
>> that.
>
> Do you agree that Tarki's theorem does not apply to systems with
> gaps?

You keep saying so. Although I haven't looked up the reference, I
assume that you're not mistaken.

> DO you agree that if we say that the vacuous sentences are neither
> true nor false that we will have gaps?

Sure. I also think that if we simply say "1 + 1 = 2" is neither true
nor false (while every other formula is interpreted in the standard
way), then we have a theory with gaps. It does not follow, of course,
that truth and provability are the same in this theory, nor that my
new and improved notion of truth is sensible.

--
"There's lots of things in this old world to take a poor boy down.
If you leave them be, you can save yourself some pain.
You don't have to live in fear, but you best have some respect,
For rattlesnakes, painted ladies and cocaine." -- Bob Childers

From: Jesse F. Hughes on 29 Mar 2010 00:01

Newberry <newberryxy(a)gmail.com> writes:

> On Mar 28, 5:54 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:
>> Newberry <newberr...(a)gmail.com> writes:
>>
>> > But I can. In a system with gaps Tarski's theorem does not apply. We
>> > can then simply equate truth with provability.
>>
>> Your second sentence does not follow. You have to show that you have
>> a logic in which provability turns out to be equivalent to truth.
>> Tarski's theorem may not preclude this possibility, but it doesn't
>> follow that you can then "simply equate truth with provability."
>
> Did I say it follows? I meant that it is possible. In classical logic
> withuot gaps it is impossible. Why did you not interpret what I said
> this way?

"We can then simply equate truth with provability."

Hmm... No idea why I thought that meant it was a simple task, indeed,
that one could just equate truth with provability. I guess I'm just a
bit slow.

--
Jesse F. Hughes
"[Lancelot] sighed, defeated. 'It is as practical to hurry an acorn
toward treeness as to urge a damsel when her mind is set.'"
-- John Steinbeck, /The Acts of King Arthur and His Noble Knights/

From: Daryl McCullough on 29 Mar 2010 06:30

Newberry says...
>
>On Mar 28, 4:37=A0am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
>wrote:
>> Newberry says...
>>
>>
>>
>>
>>
>>
>>
>> >On Mar 27, 4:56=3DA0am, stevendaryl3...(a)yahoo.com (Daryl McCullough)
>> >wrote:
>> >> Newberry says...
>>
>> >> >L: ~T(L)
>>
>> >> >If v(L) =3D3D ~(T v F) then there is no contradiction. L is not true.
>>
>> >> But *if* T is a truth predicate, then "L is not true" is formalized
>> >> by the statement ~T(L).
>>
>> >> >The argument usually goes "but that is what L says." But L does not
>> >> >say anything.
>>
>> >> It says "L is not true".
>>
>> >> So your proposed resolution is complete nonsense.
>>
>> >It contains the string "L is not true", but it does not "say" that L
>> >is not true
>>
>> That's completely silly.
>
>Did you read this?
>http://www.columbia.edu/~hg17/gaifman6.pdf

Yes, and I think it's silly. He wants to associate truth
with sentence tokens (occurrences of sentences, rather
than sentences themselves), so that two identical sentences
may differ in truth values. There is a sense in which that
is necessary, when referring expressions are used (for example,
if I say "That is a cat", obviously some tokens are true,
when I'm pointing to a cat, and some tokens are false, when
I'm pointing to a dog).

However, if you have two sentence tokens, and they have
the same subject, and the same predicate, it's silly to
call one true and one false (or more generally, not true).
It's a silly resolution that doesn't resolve anything. If
"true" is a predicate applying to sentence *tokens*, then
we can invent a second predicate, "truthy" applying to
sentences:

A sentence X is truthy if at least one of its tokens is true.

Then you can form a new Liar paradox:

This sentence is not truthy.

--
Daryl McCullough
Ithaca, NY

From: Newberry on 30 Mar 2010 00:09

On Mar 28, 9:01 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:
> Newberry <newberr...(a)gmail.com> writes:
> > On Mar 28, 5:54 am, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote:
> >> Newberry <newberr...(a)gmail.com> writes:
>
> >> > But I can. In a system with gaps Tarski's theorem does not apply. We
> >> > can then simply equate truth with provability.
>
> >> Your second sentence does not follow. You have to show that you have
> >> a logic in which provability turns out to be equivalent to truth.
> >> Tarski's theorem may not preclude this possibility, but it doesn't
> >> follow that you can then "simply equate truth with provability."
>
> > Did I say it follows? I meant that it is possible. In classical logic
> > withuot gaps it is impossible. Why did you not interpret what I said
> > this way?
>
> "We can then simply equate truth with provability."

It does automatically folow but we can nevertheless do that. In
asystem without gaps we cannot.

>
> Hmm... No idea why I thought that meant it was a simple task, indeed,
> that one could just equate truth with provability. I guess I'm just a
> bit slow.
>
> --
> Jesse F. Hughes
> "[Lancelot] sighed, defeated. 'It is as practical to hurry an acorn
> toward treeness as to urge a damsel when her mind is set.'"
> -- John Steinbeck, /The Acts of King Arthur and His Noble Knights/