Why Math is deeper than Sociology [quote]

Re:Why Math is deeper than Sociology [quote] by fauigerzigerk on Monday September 17, 2007 @04:13AM (#55604)

Mathematical statements are not unambiguous if you mean anything more than just syntactical consistency, which is by definition meaningless. Maths is a means to make statements about the world and thus depends on analysis and modeling. Modeling is by no means unambiguous as anyone who ever created a data model will be able to confirm. So maths is either meaningless or ambiguous if seen in its application context.

The issue goes even deeper. You could argue that the above argument is a semantic trick, because modeling is outside the realm of maths as a science. But even the formal foundations are in doubt if you consider Goedels incompleteness theorems (http://en.wikipedia.org/wiki/GAXdel%27s_incompleteness_theor...)

Sorry, the link is broken. Apparently this forum doesn't support umlauts in URLs

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Re:Why Math is deeper than Sociology [quote] by ced on Monday September 17, 2007 @08:45AM (#55651)

First, I do think that modelling is in the realm of physics, biology, etc. Mathematicians might make unambiguous statements about these, but they never claim that the model is a good representation of reality.

Second, Godel's incompleteness theorem is about incompleteness, not ambiguity. The statement x = y + 10 is unambiguous in the sense that all mathematicians would always interpret it in exactly the same way. There is no question that x = 12, y = 2 is consistent with that statement, and x=y is not.

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Re:Why Math is deeper than Sociology [quote] by anirbas on Monday September 17, 2007 @06:30AM (#55621)

http://en.wikipedia.org/wiki/Godel%27s_incompleteness_theore... redirects to the right page.

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