Re: [Marxism] Re: [PEN-L] More Godel

[Les Schaffer <schaffer@xxxxxxxxxxxxx>]

Carlos A. Rivera wrote:

> It references the book that influenced me about Godel, "Eternal Golden
> Braid: Godel, Escher, Bach".



Carlos:

check out Infinity and the Mind: *The Science and Philosophy of the
Infinite *, by Rudy Rucker. it is more mystical but less pomo than EGB,
but it has a better treatment, IMO, of Godel's proof (in schematic form)
as well as Cantor's work and also the construction of funny numbers. The
mathematican Robinson create something called hyper-real numbers which
give the notion of infinitesimals a firm axiomatic basis (something marx
hisself played aournd with). Godel was a big fan of Robinson, incidentally.

by all means check out Godel's own paper, but it is dense going, and as
someone who has taught a lot of math courses over the years i disagree
with Rod Holt's emphasis -- in this particular case -- to depend on
original sources for an appreciation of the work. which is why i quoted
Braithwaite's introduction to Godel's paper, also a very readable
account and i would be happy to scan it in sometime if people want to
read it. i suspect the equations wont OCR very well, and anyway, the
Dover book i think is under $10.

Rucker covers Godel numbering, the axiomatic system and the
self-reference stuff, gives you a good appreciation for the terrain of
the theorem.

les schaffer

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