Re: This sentence is not true

LauLuna says...

On Feb 6, 10:39 pm, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:

Where is the flaw?

The flaw is that you are reasoning within an inconsistent system. From
an inconsistent system you can prove anything.

Oh, no. I'm reasoning about an (apparently) inconsistent system, not
within it.

Well, then what system are you reasoning *in*? Try writing your
argument as an informal proof, making it clear what axioms you
are assuming, what rules of inference.

This is another frequent confusion employed to reject any
reasoning from (the consideration of) paradoxes. I'm reasoning within
usual logic.

No, you are not. The predicate "is true" is not part of usual logic.
Tarski proved that it *can't* be. What is standard (as far as I
understand) is to *either* banish the predicate "is true", or to
restrict it to a particular language. If you take the first approach,
then sentence (1) is not expressible. If you take the second approach,
then there is nothing paradoxical about sentence (1) in the first place:

(1) Sentence (1) is not true_L.

where L is some specified language. In that case, sentence (1) is not
true in language L (because true_L is not available inside language L)
but is true inside a larger language that extends L with the predicate
true_L.

Whether a sentence is true or not depends on the interpretation
of the terms and predicates. The same sentence can be true
under one interpretation and false (or meaningless) under
another interpretation.

Let me say this is obvious but, as far as I can see, irrelevant to the
question.

Well, all I have used is a Tarskian scheme adapted to the possibility
of a sentence being incapable of stating anything and taking into
account the possibility that primitive truth bearers be propositions:

(T-) A sentence S is true (or expresses a true proposition)
according to some linguistic code C iff (there is something S says
according to C and) what S says according to C is the case.

Assuming (T-) seems to you to be too much?

I'm not objecting to your T-.

So, the alternatives are:

1. Either rejecting an interpretation of the truth predicate that is
long since widely used in Logic, Math and in common day life,

I think that's the way to go. The informal way that "true" is
used is inconsistent. There is nothing much lost by restricting
"true" to something that is language-specific, rather than absolute.
In any particular non-paradoxical context, it is usually possible
to figure out which truth predicate is meant, and the meaning of
particular sentences involving "true" are not substantially affected
by the choice.

So, let's put it in conditional:

(3) if (T-) holds, then (1) has no truth value (= is neither true nor
false)

Your T- only talks about truth within a "linguistic code C", but
your conclusion (3) makes no mention of such a code. So I would
consider (3) to be misleading. I would say, rather

if (T-) holds, and the word "true" is interpreted as true within
a linguistic code C, then (1) has no truth value in linguistic code C.

Would you say (3) can be proved? Let me add:

(4) if (T-) and (3) hold, then (2) is true

Would you say (4) can be proved?

If you make the linguistic code explicit, then (1) can be proved!

(1) Sentence (1) has no truth value according to linguistic code C.

That's true, but only in an extended language that goes beyond linguistic
code C. Sentence (2) says the same thing, and is true in exactly the same
way as sentence (1).

If yes, I suppose you will accept that tokenism can be proven from
(T-) or any equivalent scheme.

No, I don't.

--
Daryl McCullough
Ithaca, NY

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