Re: Beyond Incompleteness

On Sun, 06 Jul 2008 21:39:10 +0100, John Jones <jonescardiff@xxxxxxx> said:
Chris Menzel wrote:
On Sun, 06 Jul 2008 15:04:00 +0100, John Jones <jonescardiff@xxxxxxx>
said:
Jesse F. Hughes wrote:
John Jones <jonescardiff@xxxxxxx> writes:

So 1+1=2 would be a possibly true statement as it deals with objects
and not systems. But if Godel says the system is incomplete or
inconsistent, and for that reason 1+1=2 cannot be a true statement
[...]
Why the heck would Goedel say something so stupid?

Better ask the other author here. He, Ross, said:

'Goedel doesn't accept there being any true statements. For Goedel,
"1+1=2" is not a true statement, just a theorem arising from
particular definitions which can never be true. '

Of the utterly clueless things said here about Gödel and his work,
this one arguably tops the list. The many ridiculous claims you in
particular have made about the incompleteness theorems can by and
large be chalked up to incompetence -- I suspect you've *tried* to
understand the mathematics of the theorems, but simply haven't the
ability or, at least, the work ethic to do so. (The proper response
would have been for you to acknowledge that you are out of your depth
and turn your philosophical attentions elsewhere, but that's another
matter.) But that the above claim is profoundly untrue can be
discovered simply by perusing the nontechnical parts of Gödel's own
philososophical writings or most any nontechnical discussion of his
life and work. One could make it with a straight face only if one
were *completely* unaware of anything Gödel wrote or believed.

I'm minded of Graham Priests' thinking here, who argues that no
knowledge of formal logic is required to do logic.

That is of course true (though I have no idea if Priest said it) in the
sense that one needs no formal logic to reason logically and think
clearly about such matters as validity and entailment; indeed, formal
logical systems are (among other things) an attempt to systematize our
informal logical intuitions in a clear and rigorous way.

Priest is *not* saying that no knowledge of formal logic is required to
do *formal logic*. Difficult as it is to imagine how anyone could think
otherwise, it is nonetheless evident that you do, given your repeated
denials of well-known, long established, often trivially provable
mathematical facts.

I also don't think that Godel saw his proofs as being anything other
than a means to persuade the formalists to pay attention to his
alogical ideas.

That Gödel was not a formalist is well known. He was a mathematical
realist/platonist of a very strong sort. But *even if*, as you claim,
Gödel himself saw his theorems as a means to other ends, e.g., refuting
formalism, mechanism, or the like -- and it is *highly* dubious that he
did -- it would alter nothing whatsoever of their *content* and their
consequences (e.g., that PA + "PA is inconsistent" is consistent if PA
is), about all of which you are deeply confused.

And its sad that most formalists here need persuading against their
will to attend to the true depth of logic.

Some day when you're all grown up and hopefully have learned a little
about humility, not to mention your own intellectual limitations, you'll
look back on these threads with profound embarrassment.

.

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