Introduction to the Philosophy of Mathematics

accept according argued argument assert assumptions axiom of choice axiom of infinity axiom of reducibility axioms of real Ayer Brouwer calculus Carnap Cauchy sequence claim commutative law concepts conclusion confirmed consider criticism Dedekind cuts deduced definition empirical example excluded middle existence explanation expressed false finitary finite cardinal number formal system formulae geometry Gödel's view Heyting Hilbert imply impredicative definitions infinite number intuitionism intuitionist intuitionist theory Körner L-true law of excluded least upper bound logical truths mathematical knowledge mathematical objects mathematical principles mathematical proofs mathematical propositions mathematical statements mathematical theory mathematical truths mathematicians meaningful Mill's natural number observational consequences ontological import philosophers philosophy of mathematics physical postulationism predicate premisses proof properties queer entities question rational numbers real number theory reference regard reject Robinson Russell semantical rules semantical system sensory observations sentence sequence set of objects set theory skepticism sort suggests syntactical system theorem Vaihinger valid variables