Re: Godel's Incompleteness Theorems

[Tim Gwinn <***>]

> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of John M
> Sent: Sunday, March 28, 2004 11:41 AM
> To: ***
> Subject: Re: Godel's Incompleteness Theorems
>
>
> Tim, hi,
>
> I never understood Goedel (did not put effort in it either) but your words
> switched on a light in the darkness of my head:
> [TG]: > Godel's
> > theorems say that the idea that one can turn every mathematical system
> into
> > a strictly syntactic, axiomatic system, while retaining most or
> all of the
> > richness of the original system, is false....<

[JM]
> Is this not a formulation to describe the reductionism of math as
> practiced?
> The continuation uses other words galore, but is fittable into such image.


I'm not sure I follow, but let me try this. A formalization, turning a
mathematical system into an entirely axiomatic and syntactic one, would be
entirely compatible with the notion of reductionism. Nonformalizable systems
like Number Theory or Category Theory, on the other hand, would not.


> > Rather than imposing "limitations" or "strictures", Godel's theorems
> > effectively demonstrate that the universe of mathematics is far broader
> and
> > richer than only axioms plus algorithms. <
> The wholeness of mathematics vd the "math' reduced to axioms + algorithms.

[JM]
> Seems that Goedel was a "RR" of mathematics?

That is an interesting way to put it. I suppose in some sense it is true. :)

Regards,
Tim