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Topic: [HM] Language of Discovery
Replies: 23   Last Post: Mar 15, 2001 1:04 PM

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Gordon Fisher

Posts: 367
Registered: 12/3/04
Re: [HM] Language of Discovery
Posted: Feb 25, 2001 5:01 PM
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Alexander Zenkin wrote:


<< But if we trust in Plato and Kant as to that ideas exist
"outside, before and independently from a human-being", then
all mathematical achievements are certainly scientific
discoveries :-) >>

<< From this point of view, there is a quite interesting
question: whether G.Cantor was an inventor or a discoverer
of his famous diagonal argument and his minimal transfinite
integer "OMEGA"? :-) >>

Since you brought up Kant in this connection, I will seize the occasion
to ask any philosophically minded participants in this virtual
get-together whether they interpret Kant to have held that mathematical
ideas exist independently of humans, in the manner which Plato did. I
take him to have proposed something more like this: Humans are so
constituted that they must understand the world in certain restrictive
ways. He used as an example a proposed necessity for humans to interpret
space using a euclidean geometry, presumably including its notorious
parallel postulate. Legions of commenters thereafter have derogated old
Kant for having missed the boat on non-euclidean geometries, which have
turned out, it appears, to have some relevance in interpreting space
(and time), at least on large enough scales. (This has happened since
Einstein through us a curve -- pardon me, Alexander, if this attempt at
humor doesn't get through to you in Russia, since it's based on the sport
of American baseball.)

My own belief, of some standing, is that while Kant chose an unfortunate
example to illustrate his theories of the transcendental aesthetic, and
how people necessarily perceive space and time and such things, his
arguments can still be cogently taken to apply to such propositions as:
humans necessarily perceive and conceive of space in terms of _some_
geometry_ our brains, minds, or whatever, being the way they are.

Somehow I'm reminded of Rainer Rilke's fantasy (in his prose piece Malte
Laurid Brigge) of the fellow who had to take to his bed permanently
because he became aware of our earth's motion around our sun, and it
made him dizzy.

Gordon Fisher

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