Re: The fallacy of strengthened liar's paradox.

On Tue, 25 Dec 2007 17:05:34 -0800 (PST), Newberry
<newberryxy@xxxxxxxxx> wrote:

On Dec 25, 8:15 am, herbzet <herb...@xxxxxxxxx> wrote:
Newberry wrote:

On Dec 25, 6:01 am, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
On Mon, 24 Dec 2007 15:11:50 -0800 (PST), Newberry

<newberr...@xxxxxxxxx> wrote:
Let P be the sentence "This sentence is meaningless." Is it true or
false? [...]

This gives us the basic insight that all self-referential, paradoxical
sentences, including possibly Goedel's sentence, are probably
meaningless.

You're jumping a bit from one example to _all_ such sentences.

It is a bit conjecture.

But much more important: There's nothing _literally_ self-referetial
about "Godel's sentence" - your lovely anlysis is irrelevant there.
The sentence in question is just an ordinary assertion about positive
integers, with no problem whatever regarding what it means,
any more than there's a problem with "If n and m are even positive
integers then n + m is even."

One of those number is the Goedel number of the sentence ITSELF.

Under a different coding scheme the same sentence does not refer
to itself.

I was mainly disputing the idea that the strengthened liar defeats the
3-valued approach. The side note about Goedel's sentence is just an
afterthought.

A totally wrong afertthought.

But anyway here is what Torkel Franzen says about self-
reference:

QUOTE:
But sentences constructed in the proof that every arithmetical
property P has a provable fixpoint are self-referential in a stronger
sense: they are sentences A of the form

There is an m such that m has the property P and property Q

where it is provable in PA that the only number that has the property
P is the Goedel number of the sentence itself. It is in this sense
that the sentence A "says of itself it has property Q."
END OF QUOTE [p. 45]

And in particular, it's not _literally_ self-referential,
so that any paradoxes or meaninglessnesses associated with
sentences like "this sentence is false" simply don't come up.

************************

David C. Ullrich
.

Relevant Pages

  • Re: The fallacy of strengthened liars paradox.
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  • Re: The fallacy of strengthened liars paradox.
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