On 11/3/2012 2:01 PM, Evgenii Rudnyi wrote:
Some more quotes from Bas C Van Fraassen Scientific Representation: Paradoxes of Perspective. This time on what Weyl has said on isomorphism between mathematics and reality.

p. 208 "Herman Weyl expressed the fundamental insight as follows in 1934:

'A science can never determine its subject-matter expect up to isomorphic representation. The idea of isomorphism indicates the self-understood, insurmountable barrier of knowledge. [...T]oward the "nature" of its objects science maintains complete indifference.' (Weyl 1934:19)

The initial assertion is clearly based on two basic convictions:

o  that scientific representation is mathematical, and
o  that in mathematics no distinction cuts across structural sameness."

p. 209 "Weyl illustrates this with the example of a color space and an isomorphic geometric object. ... The color space is a region on the projective plane. If we can nevertheless distinguish the one from the other, or from other attribute spaces with that structure, doesn't that mean that we can know more that what science, so conceived, can deliver? Weyl accompanies his point about this limitation with an immediate characterization of the 'something else' which is then left un-represented.

'This - for example what distinguish the colors from the point of the projective plane - one can only know in immediate alive intuition.' (Ibid.)"

p. 210 "We seem to be left with four equally unpalatable alternatives:

o  that either the point about isomorphism and mathematics is mistaken, or

o  that scientific representation is not at bottom mathematical representation 
alone, or

o  that science is necessarily incomplete in a way we can know it to be 
incomplete, or

o  that those apparent differences to us, cutting across isomorphism, are 

In his comment about immediate alive intuition, Weyl appears to opt for the second, or perhaps the third, alternative. But on the either of this, we face a perplexing epistemological question: Is there something that I could know to be the case, and which is not expressed by a proposition that could be part of some scientific theory?"

It seems to me he left out the most likely case: that our science is incomplete in a way we know.


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