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From: jqb@netcom.com (Jim Balter)
Subject: Re: Putnam reviews Penrose.
Message-ID: <jqbDBIrMr.HGx@netcom.com>
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References: <3ss4sm$cjd@mp.cs.niu.edu> <3trb7c$em9@netnews.upenn.edu> <jqbDBID1x.8rD@netcom.com> <3ts2mt$aa3@netnews.upenn.edu>
Date: Mon, 10 Jul 1995 21:28:02 GMT
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In article <3ts2mt$aa3@netnews.upenn.edu>,
Matthew P Wiener <weemba@sagi.wistar.upenn.edu> wrote:
>In article <jqbDBID1x.8rD@netcom.com>, jqb@netcom (Jim Balter) writes:
>>In article <3trb7c$em9@netnews.upenn.edu>,
>>>>	         What does "arriving at" consist of?  Give us a definition
>>>>in a refutable form.
>
>>>How about "it's been published in a reputable journal".
>
>>Oh, wow.  So that's what it takes to know mathematical truths that
>>can't be proven.  Publish them in a reputable journal.
>
>Yes.  Goedel did it in 1931.  Were you napping, or what?
>
>>						         Of course, no
>>robot could do that.
>
>Not if the theorem was its Goedel sentence, no.

Ah, so Goedel published his own Goedel sentence in 1931?

And of course Goedel did not state that a formal system of sufficient
power cannot publish its own Goedel sentence, since such a silly
claim is trivially false.

Not every program is devoted to producing only a consistent set of
theorems as its output, any more than any human is.  Such silliness
must come of excessive time spent in circle jerks with fellow
Platonic mathematicians.

>>>Goedel does not record just what he did when he found an unprovable true
>>>statement.  Getting retardedly sarcastic about it won't change history.
>
>>Why, he put it on his list of consistent beliefs, of course.
>
>Yes.  Something no formal system could have done, apparently.

You can be astoundingly slow.  Goedel didn't have a consistent list of
beliefs, he had an inconsistent one, like any human.  And if he did have a
fully consistent set of beliefs, it could not have included his own Goedel
sentence, if he had one.  But of course you know he didn't have one through
"empirical observation".  But if you did have a Goedel sentence, then either
you couldn't 't empirically determine it, or you could and you could publish
it, along with your explanation that you can't prove it but you've discovered
empirically that it's your Goedel sentence and so you know it's true
nonetheless; in fact, since you know it's your Goedel sentence, you can prove
it's true by citing Goedel's theorem.  Which is a contradiction, so you cannot
empirically encounter your Goedel limitations whether you have them or not.
Unless you're a circle jerk.

-- 
<J Q B>

