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Philosophy and Mathematics
Definitions of Mathematics
The Nature of the Objects of Mathematics
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abbreviation abstraction algebraic application arithmetic assertion belongs Brouwer called cardinal number Carnap Chwistek combination concepts consider consistency consistency proof construct correlated David Hilbert deduced definition of number demonstrable denotes derived discussion elemental mathematics elements entities equal equation example excluded middle exists expression false falsity finite number follows formal formalist foundations of mathematics free variable Frege fundamental geometry given Heyting Hilbert implies infinite Intuitionism intuitionist involved irrational numbers language logistic Math Mathematik matics means metad metamathematical method natural number series negation normal formulae number system objects occurs operation order type paradoxes Pasch philosophy of mathematics point of view positive integers possible postulate set predicated problems proof properties propositional function pure rational numbers real numbers relation represents result Russell Russell's sequence structure substitution Symbolic Logic tautologies term symbols theorem theory of types tion transfinite true truth value whole numbers