Re: OUTGOEDELING A HUMAN?

abo says...

stevendaryl3...@xxxxxxxxx (Daryl McCullough) wrote:

I'm claiming that "true" doesn't have an absolute meaning,
and neither does "corresponds with the way the world is".
Does "This sentence is not true" correspond with the way
the world is, or not?

It does not.

So if you are defining "true" to mean "corresponds with
the way the world is", and you are saying that the Liar
does not correspond with the way the world is, then aren't
you saying that the Liar is not true? So does that mean
that "The Liar is not true" corresponds with the way the
world is? But the Liar *is* the sentence "The Liar is not
true".

When I said one can block the inference, I didn't mean that one is
blocking a logically valid inference. That of course would be ad hoc
and close to (if not actually) inconsistent. The inference from ""This
sentence is paradoxical" is paradoxical" to ""This sentence is
paradoxical" is true" depends on an assumed property of truth, given
by the schema if S, then "S is true." One can reject the validity of
the schema (which is not a logical validity) and block the reasoning.

But only at the cost of making "truth" even more mysterious.
You've proved sentence S, but you're not allowed to conclude
that S is true? I don't think that this alternative has anything
going for it.


Of course, one then has to explain *why* one can reject this. As this
is my last post for the moment, I'll have to refer to postings that I
made to sci.logic about 8 years ago, which I regrouped here:

http://www.andrewboucher.com/papers/paradoxes.htm

Are you the same person as Andrew Boucher? Anyway, it seems
clear to me that throwing out standard set theory and (in particular)
Cantor's theorem is going *way* overboard as a way to respond to
the Liar paradox. The Liar paradox is not even expressible in ZFC.
Why in the world should ZFC be affected by the Liar paradox?

That seems very weird.

--
Daryl McCullough
Ithaca, NY

.

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