Re: Reply to Daryl McCullough on Liar paradox

On Mar 24, 7:30 am, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:
Newberry says...

Presumably you would *agree* with the following sentence (call
it "alternative sentence 42")

No sentence that has the same sequence of characters as sentence
number 42 in "Bob's Book of Paradoxes" is true.

(Where sentence number 42 is the sentence

What does this have to do withg the liar? Looking at different ways
to say the same thing has no bearing on the problem of evaluating
"This is false."

Trying to evaluate "This is false." is also a waste of time. Logic
shows it can have no value in the traditional sense. You have to show
why that is and how the situation can be changed, but the paradox
remains. You can only admit that some things cannot exist in English
and maintain certain desirable rules.

This has nothing to do with writing sentences that use novel means of
rererring to themself. The real problem is "This is false."

C-B



No sentence that is syntactically identical to sentence
number 42 in "Bob's Book of Paradoxes" is true.

Well, "has the same sequence of characters" means the same
thing as "is syntactically identical to"! To call one sentence
"true" and the other sentence "meaningless" is nonsensical.
It's not a resolution to the Liar paradox, it's just a replacement
of one paradox by another.

The whole point of *logic* is that you can do reasoning based on
the form of sentences without knowing all the facts. So, for
instance, we would like to be able to do logical inferences
of the form

1. No object satisfying <description 1> also satisfies <predicate 1>.
2. All objects satisfying <description 2> also satisfy <description 1>.
Therefore,
3. No object satsifying <description 2> also satisfies
<predicate 1>.

Your "resolution" makes such inferences impossible. For example,
let <description 1> be "is a sentence with the same sequence of
characters as sentence number 42", and let <predicate 1> be
"is true", and let <description 2> be "is a sentence that is
syntactically identical to sentence number 42". You can't do
the *logical* inference, to come up with conclusion 3, until
you know whether conclusion 3 happens to be sentence number 42.
Your resolution means that you can no longer say that anything
that follows from a true premises must be true.

So your resolution basically makes logical inference impossible
(at least about "truth" and "meaning"). I don't consider that a
resolution at all.

--
Daryl McCullough
Ithaca, NY

.

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