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Re: An Introduction to Connective Knowledge

You say, "For one thing, as people such as Mill and Kitcher argue, the rules of mathematics depend on empirical verification for their importance: we say that one plus one is two, not out of some innate sense of goodness, but because when we put one sheep together with another, we observe that there are two." Not exactly. While it's true that empirical verification is possible, it is not necessary. Proof of the existence of integers, the existence of addition, and that one plus one equals two may be had via axiomatic set theory. Granted, "axiomatic" set theory relies on a set of presumed axioms, and the point of those axioms is to arrive at a theory that is empirically verifiable, but nevertheless, empirical verification is not necessary to argue that one plus one equals two. [Comment] [Permalink]