Nice. I was just writing about mathematics and use of symbols:
On Saturday, November 3, 2012 3:01:55 PM UTC-4, 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
> 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
> 'This - for example what distinguish the colors from the point of the
> projective plane - one can only know in immediate alive intuition.'
> 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 illusory.
> 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?"
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