Refutation of the \"Language-Only\" Interpretation of Math (The limitations of science)

by xeno6696 , Sonoran Desert, Saturday, February 13, 2010, 23:00 (5398 days ago) @ George Jelliss

xeno wrote: "Some time ago George attacked an assertion I made about a constant such as PI /// My argument was (and still is) that constants such as PI actually have an exact mathematical value"
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> It's true that pi has an exact mathematical value in Euclidean Geometry. But Euclidean Geometry is not the geometry of the "actual" world. It is a highly idealised system based on axioms. It provides a good approximation to the actual geometry of the real world for many practical purposes, but has been superseded by relativistic and quantum geometry for large and small scales. In Euclidean geometry for instance points and lines have no width and straight lines extend to infinity, and between any two points there is a continuum infinity of other points.
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> In reality the "perfect" circles of Euclid do not exist. The circumference and diameter of real circles can only be determined to within a certain degree of accuracy, and so their ratio (pi) is within similar error bars. 
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> The article to which xeno links seriously misrepresents the Formalist approach. After all, Euclid was arguably a Formalist. There are also Intuitionist and Constructivist schools which have a lot going for them. It's true that most mathematicians take the Platonist view that mathematics can be treated as a world of "existents", but this is not the same as the "real" world of the physicists. It is an "ideal" world of forms. It "exists" in mathematicians' collective imaginations.-You are correct that I was speaking of "pure mathematics," and I did forget myself in that, I apologize. You reference non-euclidean geometry, but its not as cut and dry as that. You are correct in maintaining Stenger's assertion that PI is only approximated in non-euclidean spaces, however it doesn't deal with the fact that the number represents a relationship that is independent of two observers. -How about e? This is a transcendental function that appears constantly in nature. Because it repeatedly appears are we to truly believe that it is a relativistic object? This sounds like a level of skepticism not seen since the Cynics.

--
\"Why is it, Master, that ascetics fight with ascetics?\"

\"It is, brahmin, because of attachment to views, adherence to views, fixation on views, addiction to views, obsession with views, holding firmly to views that ascetics fight with ascetics.\"