Founding Mathematics on Semantic Conventions (eBook, PDF)

Founding Mathematics on Semantic Conventions (eBook, PDF)

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This book presents a new nominalistic philosophy of mathematics: semantic conventionalism. Its central thesis is that mathematics should be founded on the human ability to create language - and specifically, the ability to institute conventions for the truth conditions of sentences.This philosophical stance leads to an alternative way of practicing mathematics: instead of "building" objects out of sets, a mathematician should introduce new syntactical sentence types, together with their truth conditions, as he or she develops a theory.Semantic conventionalism is justified first through critici...

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