Nice. I was just writing about mathematics and use of symbols: http://s33light.org/post/34935613677

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Craig 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 > 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 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?" > > Evgenii > -- > http://blog.rudnyi.ru/tag/bas-c-van-fraassen > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/at06iH1ons4J. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.