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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: 1,969
Registered: 12/4/12
Re: Mathematics and the Roots of Postmodern Thought
Posted: Mar 31, 2013 12:03 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 3/30/2013 9:38 PM, Shmuel (Seymour J.) Metz wrote:
> In <D8OdnVFB9IWK6MvMnZ2dnUVZ_rSdnZ2d@giganews.com>, on 03/30/2013
> at 12:15 AM, fom <fomJUNK@nyms.net> said:
>

>> If one wishes to argue that "real" space is curved
>> but that the curvature is so slight as to be negligible,

>
> That would be Physics rather than Mathematics.
>


Which accounts for the scare quotes in my statements.

>> If the sensible impressions relate to each other in the Euclidean
>> sense, that is precisely Kant's thesis.

>
> <http://en.wikipedia.org/wiki/Geometry#Geometry_beyond_Euclid>:
>
> "Immanuel Kant argued that there is only one, absolute, geometry,
> which is known to be true a priori by an inner faculty of mind:
> Euclidean geometry was synthetic a priori.[3]"
>
> <http://en.wikipedia.org/wiki/Non-Euclidean_geometry#Importance>:
>
> "The philosopher Immanuel Kant's treatment of human knowledge had a
> special role for geometry. It was his prime example of synthetic a
> priori knowledge; not derived from the senses nor deduced through
> logic - our knowledge of space was a truth that we were born with."
>
> That doesn't sound like a pragmatic appeal to observation.
>


Both of these excerpts refer to "truth" which is a semantical
concept. Kant's concerns were epistemological. In

http://plato.stanford.edu/entries/kant-spacetime/#IntPhiQueAboSpaTim

you can find a more complete discussion of the complexities
involved with interpreting Kant.


But, when words like "absolute" are used to describe
Kant's position, it is almost clearly by someone who
has not read "Critique of Pure Reason". The following
is excerpted from the web link:

Kant consistently writes in the Critique of ideality and reality in the
more familiar modern sense, where mind-dependence is at issue. Kant's
usage serves to shift the philosophical discussion concerning space from
a focus on relationalism and absolutism to one on idealism and realism.
Hence when he reflects on the Newtonian and Leibnizian conceptions of
space and time in general terms in the Transcendental Aesthetic, he
eschews a discussion of the relative merits of absolutism and
relationalism in favor of discussing the common mistake of his
predecessors. For instance, after outlining his conception of space and
time, Kant claims: ?Those, however, who assert the absolute reality
[absolute Realität] of space and time, whether they take it to be
subsisting or only inhering, must themselves come into conflict with the
principles [Principien] of experience? (A39/B56). The former group, also
called ?the mathematical investigators of nature,? is clearly identified
with the Newtonians, and the latter, the ?metaphysicians of nature,?
with the Leibnizians (cf. Shabel 2005, 31, 45-9). So transcendental
idealism is articulated as a kind of replacement for the Leibnizian and
Newtonian conceptions of space and time, but it is not their status as
relationalist and absolutist conceptions, respectively, that calls for
their replacement. Rather, it is their status as representatives of a
separate and overarching conception of space, a conception according to
which space (like time) is said to bear an ?absolute reality.?






















Date Subject Author
3/25/13
Read Mathematics and the Roots of Postmodern Thought
David Petry
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fom
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David Petry
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fom
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fom
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David Petry
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scattered
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David Petry
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fom
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David Petry
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fom
3/26/13
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fom
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3/25/13
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3/25/13
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David Petry
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fom
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David Petry
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fom
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fom
3/25/13
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fom
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fom
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fom
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fom
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fom
3/29/13
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Shmuel (Seymour J.) Metz
3/29/13
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fom
3/30/13
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Shmuel (Seymour J.) Metz
3/31/13
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fom
3/30/13
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Jesse F. Hughes
3/26/13
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fom
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Jesse F. Hughes
4/1/13
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4/1/13
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fom
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