Philosophy of Mathematics

accept analogous apples application argument arithmetic assertion axioms calculation Chihara claim concept conclusion connexions consistency consistency proof construction contradiction correct count criterion definition describe discussion Dummett empirical proposition example expansion experience explain expression fact false finitist Foundations of Mathematics Frege G. E. M. Anscombe geometry give Gödel's idea inconsistency infinite intuition intuitionism intuitionist justified language language-game lectures logic mathe mathematical logic mathematical proof mathematical propositions mathematician matics meaning measure method Michael Dummett miscounted natural necessary proposition necessity notion ostensive definition paradox particular philosophy of mathematics physical position possible predicate problem proof provable proved question real numbers reason Remarks result rule rules of inference Russell Russell's Russell's paradox seems sense sentence sequence set theory simply someone sort speak square statement stein Superprime suppose symbols theorem things tiles tion true truth understand Wittgen Wittgenstein says Wittgenstein's philosophy Wittgenstein's views words Wright