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Vladimir_Nesov comments on What independence between ZFC and P vs NP would imply - Less Wrong Discussion

1 Post author: alexflint 08 December 2011 02:30PM

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Comment author: Vladimir_Nesov 08 December 2011 06:07:37PM 2 points [-]

Math as about axioms and proofs (well-formed finite strings), and is often a useful tool in mapping the territory, but it is just that, one of the tools.

Your formalist ideology is noted, but please don't state its (disputable) claims as clear truths.

Comment author: shminux 08 December 2011 06:25:35PM 0 points [-]

Your formalist ideology is noted, but please don't state its (disputable) claims as clear truths.

Not sure what you mean by "formalist", or " claims as clear truth", but feel free to provide a different definition of mathematics acceptable to a mathematician.

Comment author: Vladimir_Nesov 08 December 2011 06:36:00PM *  2 points [-]

Mathematics seemingly studies mathematical structures, guided by rather elusive criteria for what is worth studying, with axioms and proofs not obviously constituting the whole of its focus. In philosophy of mathematics, asserting that only formal statements and proofs make sense is known as formalism:

It has been claimed that “Formalists, such as David Hilbert, hold that mathematics is no more or less than mathematical language. It is simply a series of games...”

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