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Mikael Johansson wrote

*> His name is Pál Erdös -- not Paul Eotvos; I presume?
*

Yes. That's who I meant when I referred to how he believed

that "God's Book" contained all, and only, the most elegant

proofs. Erdos was always saying "That's in The Book!"

when shown a really exquisite proof. I was spoofing when

I suggested that God's Book, in it's appendix, might also have

all the true relationships, with an asterisk next to the

ones that had proofs, (and two asterisks next to the ones

that could be proved by pre-singularity humans!), no matter

how ugly the proofs.

*> ...if it is unprovable whether there exists infinitely many
*

*> prime pairs, then the existence of an upper bound on the
*

*> prime pairs is unprovable, and thus -- perchance -- one might
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*> argue that the unprovability proves the theorem.
*

That's great! Whether you are right or not! It makes my head

hurt, and that's the purpose of my little story about the

mathematician at the party, namely as an aid to keeping clear

what I know about provability and unprovability.

Let me take a swing: Okay, so the student says that he

has a proof that (the existence of infinitely many) is

unprovable. So he has a proof (in his trembling fingers)

that it's unprovable whether there is an upper bound.

That means that for each integer (beyond the small ones,

of course) we cannot prove whether or not it is an upper

bound.

Interestingly, suppose that his proof proves that for each

integer N greater than 3^163^641^6969 + 86^86 + 42 you

can neither prove nor disprove (i.e. such proofs do not

exist) that N is an upper bound. Then that would mean

that any pair greater than that would have to be

composite (because we can always, brutally if need be,

establish whether or not a given number is prime), and

as you say, that would prove the finitetude of the prime

pairs.

It doesn't help any if his paper merely proves that there

exists some number Z such that you can neither prove nor

disprove that any number greater than Z is an upper bound.

Your observation kicks in once more. The student has been

unmasked as a charletan.

But what if his paper just proves that you cannot prove that any

number greater than 42 is an upper bound? (Slightly different!)

Just because we can't prove it, it may nonetheless be the case

that 3^163^641^6969 + 86^86 + 42 is in fact an upper bound

(although we could never possibly learn that). Then we would

have to hail the student and his proof after all.

Thanks,

Lee

**Next message:**Jim Fehlinger: "Re: "analog computer" = useless hypothesis?"**Previous message:**Lee Corbin: "Re: "analog computer" = useless hypothesis?"**Next in thread:**J. R. Molloy: "NSF boosts cognitive neuroscience"**Reply:**J. R. Molloy: "NSF boosts cognitive neuroscience"**Reply:**scerir: "Re: Unprovability"**Maybe reply:**CurtAdams@aol.com: "Re: Unprovability"**Maybe reply:**zeb haradon: "Re: Unprovability"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]

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