Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 12/14/04 

Date: Tue, 14 Dec 2004 05:38:28 -0600

On 13 Dec 2004 04:54:52 -0800, "Charlie-Boo" <chvol@aol.com> wrote:

>
>David C. Ullrich wrote:
>
>> You _really_ need to work on the irony detector. Truth
>> and provability are _different_ things - when you define
>> one to be the other you exhibit amazing ignorance of the
>> most basic issues.
>
>> ************************
>>
>> David C. Ullrich
>
>The definitions of Turing Machines and Lambda Calculus are very
>different, too, aren't they?

For heaven's sake, at some point you should just accept that
you've made a fool of yourself and drop it. I mean you have
plenty of experience with this phenomenon...

Ok. To answer your question: Yes, those two definitions
are very different.

I can't imagine what your point is. Two comments:

(i) If someone asked for the definition of a Turing Machine
and someone else replied with the definition of the Lambda
Calculus that person would indeed be exhibiting blithering
confusion.

(ii) On the other hand, it's true that the set of functions
computable by TM's is the same as the set of functions
computable by the LC. _Guessing_ what your point might
be here, I have to point out that truth and provability
are _not_ equivalent.

(Validity and provability are equivalent. And truth _in
that one particular model_ is equivalent to provability
_in that one particular formal system_. A very curious
formal system, btw, since there's no procedure to recognize
whether a proof is valid.)

>C-B

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

David C. Ullrich

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