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Topic: Mathematics and the Roots of Postmodern Thought
Replies: 101   Last Post: Apr 7, 2013 10:38 PM

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fom

Posts: 1,968
Registered: 12/4/12
Re: Mathematics and the Roots of Postmodern Thought
Posted: Mar 29, 2013 8:29 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 3/29/2013 12:50 PM, Shmuel (Seymour J.) Metz wrote:
> In <otadneXBRZ4yqM_MnZ2dnUVZ_oudnZ2d@giganews.com>, on 03/26/2013
> at 06:56 PM, fom <fomJUNK@nyms.net> said:
>

>> I think that what you want to assert as a foundation for mathematics
>> -- that is, the closeness of one's sensibility to what is expressed
>> by mathematical explanation -- will be found in Kant.

>
> Given the existence of models for non-Eucldiean Geometry in Eucldean
> Geometry, I find it hard to take Kant seriously.
>


Kant actually called for the development of non-Euclidean
geometries. It is a small paper translated by Ewald in
"From Kant to Hilbert". Ewald refers to the fact as
"surprising" given what is usually presented in the
historical accounts.

Also, I read somewhere recently that Kant never mentions
the parallel postulate in "Critique of Pure Reason". I
have not made an exhaustive search, but, I keep my eyes
open for it. I have not found it yet.

Suppose one is willing to understand Kant with respect to
changes in the nineteenth century as one understands
Newton's theory of gravity with respect to Einstein's
theories. Then Frege's retraction and Russell's
analysis of projective geometry as the a priori
condition of external form speak to the possibility
of considering a revised version of Kant's theses.

When I sought definitive modern references to
explain these matters to me, the books recommended
did just the opposite. Stewart Shapiro actually calls
for some sort of structural framework along the lines
of a Kantian scheme. Jeffrey Boolos has a wonderful
statement that none of the foundational movements
of the late nineteenth and early twentieth century
had disproved Kant. It would be more correct to
say that he lists the various critics of Kant
by name.

In any case, David had been looking for some explanation
for mathematics that was "real" in the sense of one's
innate knowledge of these matters. Kant's
discussion of sensible intuition as a ground
for mathematical insight should appeal to him.
It will also provide a foundation for interpreting
the history that followed.

I have been avoiding discussions of Kant precisely
because I am aware of the historical context.
Besides, the key to that in which I am really interested
is the misrepresentation of Leibniz. I do not
need Kant for that.

=====================

Here is Frege and Russell


> "The more I have thought the matter
> over, the more convinced I have become
> that arithmetic and geometry have
> developed on the same basis -- a
> geometrical one in fact -- so that
> mathematics in its entirety is
> really geometry"
>
> Frege



> "..., I shall deal first with projective
> geometry. This, I shall maintain, is
> necessarily true of any form of
> externality, and is, since some such
> form is necessary to experience,
> completely a priori."
>
> Russell






Date Subject Author
3/25/13
Read Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
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fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
scattered
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/25/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
Virgil
3/26/13
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David Petry
3/26/13
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fom
3/26/13
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dan.ms.chaos@gmail.com
3/26/13
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dan.ms.chaos@gmail.com
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
3/26/13
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dan.ms.chaos@gmail.com
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
Frederick Williams
4/2/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/29/13
Read Re: Mathematics and the Roots of Postmodern Thought
Shmuel (Seymour J.) Metz
3/29/13
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fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Shmuel (Seymour J.) Metz
3/31/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
3/26/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
3/30/13
Read Re: Mathematics and the Roots of Postmodern Thought
Jesse F. Hughes
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
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fom
4/1/13
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dan.ms.chaos@gmail.com
4/1/13
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Frederick Williams
4/1/13
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4/1/13
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fom
4/1/13
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Frederick Williams
4/1/13
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David Petry
4/1/13
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David Petry
4/1/13
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dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
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dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
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dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
dan.ms.chaos@gmail.com
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
fom
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
Virgil
4/2/13
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fom
4/1/13
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fom
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fom
4/1/13
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fom
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Read Re: Mathematics and the Roots of Postmodern Thought
Virgil
4/1/13
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Jesse F. Hughes
4/1/13
Read Re: Mathematics and the Roots of Postmodern Thought
David Petry
4/1/13
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Jesse F. Hughes
4/1/13
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rt servo
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fom
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Jesse F. Hughes
4/1/13
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fom
4/1/13
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Virgil
4/1/13
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David Petry
4/1/13
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fom
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Jesse F. Hughes
4/6/13
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Rotwang
4/7/13
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4/1/13
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fom
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