[Corpora-List] PS:minimal changes in a paragraph (based on a corpus it appeared) ... (2nd attempt (after first one was deleted))

[Albretch Mueller]

> Godel showed that a formal system capable of doing arithmetic perfectly cannot be both complete and consistent …
~
 I agree with you. I think abusing Goedel's theory has become some
sort of new-age pastime, but I think you may be getting bit off course
with your colloquial explanations first the adverb "perfectly" was not
part of the statement in Goedel's theory and second and foremost, it
is not about us "humans" not being able to do arithmetic "perfectly",
not being "consistent" … "complete" (as we have limitations like
finite attention spans and finite lifetimes) …
~
 I would simply say that Goedel's never had in his mind (not even in
his wildest dreams) our own cognitive capacity he, very explicitly
indeed, was just referring to -formal systems- and to explain what
those beasts are and why Mathematicians fancied them so crazily (some
still do), I would first going through Frege's Begriffsschrift and
Hilbert (sort of trivialization of Euclid's work (my opinion more as a
semiotician than a Mathematician)), go as early as Euclid's's element
and explain what a proof is and why Mathematicians thought we could
make such a machine (syntactic device) capable to exhaustively -and
progressively- prove things for us.
~
 lbrtchx


On 8/9/11, Patrick Juola <juola at mathcs.duq.edu> wrote:
> On Tue, Aug 9, 2011 at 12:11 PM, Angus Grieve-Smith
> <grvsmth at panix.com>wrote:
>
>>   Russell continues:'IT IS A LANGUAGE THAT HAS ONLY SYNTAX AND NO
>> VOCABULARY WHATSOEVER.(My emphasis). Barring the omission of a vocabulary
>> I
>> maintain that it is quite a nice language. It aims at being the sort of
>> language that, if you add a vocabulary, would be a logically perfect
>> language.' He adds that actual languages are not logically perfect in this
>> sense...
>>
>>
>>     Then it's not a language, it's a model of a language.  I'm sure it's a
>> very nice model, and useful for all sorts of purposes.  But Gödel showed
>> that in general models can never completely capture reality,
>>
>
> No, he didn't.
>
>  |  One of the biggest mistakes a scientist can make is to reify their own
> model.  It is a dangerous form of hubris that can lead science off course
> for generations.
>
> And an even bigger mistake that scientists can make is to misunderstand what
> they read and then misapply it in a completely inappropriate way in a
> totally wrong discipline.
>
> Godel showed that a formal system capable of doing arithmetic perfectly
> cannot be both complete and consistent.  Since human beings are not formal
> systems, this is of limited application.   In particular, we know for
> independent reasons that a) humans can't do arithmetic perfectly, b) humans
> aren't consistent, and c) humans aren't "complete" (as they have limitations
> like finite attention spans and finite lifetimes).
>
> So, Godel's theorem only shows that if human beings were something we know
> they're not, they would have properties that we have already known them to
> have.
>

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