The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations

abstract algebraic algorithm analytic applied approach arithmetic arithmetical mean axiomatic axioms calculus Cambridge category theory century complexity concept consider constraints defined definition differential distributive category ematical equation errors example finite formal foundations functor fundamental group Gauss geometry given idea intensive quantities interpretation intuitive knowledge Lagrange Lakatos language Leibniz linear logic manifold math mathematical objects mathematical theory mathematicians means mechanics method natural numbers Newton nonstandard analysis notion number theory observations ontological order theories partial recursive partial recursive functional particular philosophy of mathematics philosophy of science physical theory possible predicates prime number principle problem procedure PROLOG proof question recursion theory recursive function reduction relation representation revolution scientific sense set theory set-theoretic space spacetime species of structures Suppes symbolic constructs theorem theory elements theory nets tion Turing variable