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From: Nam Nguyen on 15 Apr 2010 23:15
Nam Nguyen wrote:
> Marshall wrote:
>> On Apr 14, 9:34 pm, Nam Nguyen <namducngu...(a)shaw.ca> wrote:
>>> Did you, as I mentioned
>>> before, define all the n-ary relations (sets) required by model-
>>> definition?
>>
>> Listing out all the tuples is only part of the buffoon-theoretic
>> version of the definition of model. So really that requirement
>> is only binding on you.
>
> Ah! So you'd ignore technical definition! No wonder why your arguments
> are cohesiveness and incorrect!

"...are not cohesive and incorrect" I meant.

>
> In the theory T = {Ax[x=a]} I know we could have a model because
> we could establish the 2-ary relation = which is the set {(a0,a0)}
> where a0 = {} by definition. So, T has a model, _by definition of model_ .
>
> That's how proofs, reasoning, and arguments are done, Marshall.
> By technical definitions, not by idiotic rambling and attacks!
>
> Naturally.
From: Newberry on 16 Apr 2010 01:36
On Apr 11, 8:18 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Newberry <newberr...(a)gmail.com> writes:
> > Such a proof in ZF that PA is consistent is obviously wothless.
>
> Why? Are all proofs in ZF worthless?

Proofs of consistency in ZFC certainly are worthless.

>
> --
> Aatu Koskensilta (aatu.koskensi...(a)uta.fi)
>
> "Wovon man nicht sprechan kann, darüber muss man schweigen"
>  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

From: Newberry on 16 Apr 2010 01:44
On Apr 11, 8:18 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
> Newberry <newberr...(a)gmail.com> writes:
> > If it absolutely certain that PA is consistent why don't we formalize
> > the reasoning?
>
> Absolute certainty is irrelevant.

Why is it irrelevant?

> Consistency proofs are every bit as
> formalizable as other proofs. We can formalize the trivial consistency
> proof for PA in the subtheory ACA of second-order arithmetic, in formal
> set theory, in Per-Martin L f's constructive type theory (by a detour
> through a double-negation interpretation), and so on.

Are these theories consistent?

> --
> Aatu Koskensilta (aatu.koskensi...(a)uta.fi)
>
> "Wovon man nicht sprechan kann, dar ber muss man schweigen"
>  - Ludwig Wittgenstein, Tractatus Logico-Philosophicus

From: Daryl McCullough on 16 Apr 2010 06:40
Newberry says...
>
>On Apr 11, 8:18=A0am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote:
>> Newberry <newberr...(a)gmail.com> writes:
>> > Such a proof in ZF that PA is consistent is obviously wothless.
>>
>> Why? Are all proofs in ZF worthless?
>
>Proofs of consistency in ZFC certainly are worthless.

That's certainly true, in the sense that nobody would pay
you much for such a proof, because graduate students do
these proofs for free, destroying the market.

Back when such proofs were rare, I'll bet they would fetch
a pretty penny, if you could find the right buyer.

A proof of the Beale Conjecture in ZFC is worth $100,000.
http://www.math.unt.edu/~mauldin/beal.html

--
Daryl McCullough
Ithaca, NY

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