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 
> 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 
> -- 

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