Just out of curiosity, if anyone knows about this and perhaps can correct or
confirm my understanding :
doesn't Godel's proof, insofar as it demonstrates (among other things) that
the number system cannot be reduced to logic (at least the Russell/Whitehead
attempt), lead necessarily to a recognition of numbers as existent (not as
abstract sets or classes), and hence lend support to an affirmation of the
existence of ideal objects outside the human head? This would seem to be a
good field in which to explore Ilyenkov's notion of the ideal as well.
btw, is the reading Vygotsky's "crisis" or Laszlo's?
Paul H. Dillon
----- Original Message -----
From: Dewey Dykstra, Jr. <dykstrad@email.boisestate.edu>
To: <xmca@weber.ucsd.edu>
Sent: Thursday, October 04, 2001 3:18 PM
Subject: Re: reality of math objects
> >Thanks for the quote, Eric. Check out lchc.ucsd.edu/People/Joe Goguen for
> >a paper called the reality of mathematical objects. Ditto Anna Sfard at
> >Haifa, but I do not know her web address. An examination of what sort of
> >reality is represented by mathematical symbols is not just an historical
> >question,but a hot current topic with big implications for pedagogy.
> >mike
>
> For that matter one might check out Target Article 40
> (http://www.douglashospital.qc.ca/fdg/kjf/40-TADYK.htm ) on the Karl
> Jaspers Forum http://www.mcgill.ca/douglas/fdg/kjf
>
> There are indeed major pedagogical implications concerning the
> reality of entities and the relationship of our explanations of these
> entities to their "true natures."
>
> Dewey
>
> --
> (As of 12/21/01 the mailserver email.boisestate.edu will cease to
> exist. My new address is: dewey@mac.boisestate.edu)
> +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> Dewey I. Dykstra, Jr. Phone: (208)426-3105
> Professor of Physics Dept: (208)426-3775
> Department of Physics/MCF421/418 Fax: (208)426-4330
> Boise State University dykstrad@email.boisestate.edu
> 1910 University Drive Boise Highlanders
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>
> "As a result of modern research in physics, the ambition and hope,
> still cherished by most authorities of the last century, that physical
> science could offer a photographic picture and true image of reality
> had to be abandoned." --M. Jammer in Concepts of Force, 1957.
>
> "If what we regard as real depends on our theory, how can we make
> reality the basis of our philosophy? ...But we cannot distinguish
> what is real about the universe without a theory...it makes no sense
> to ask if it corresponds to reality, because we do not know what
> reality is independent of a theory."--S. Hawking in Black Holes
> and Baby Universes, 1993.
>
> +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
>
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