The Philosophy of Mathematics: An Introductory Essay |
Contents
EXPOSITION | 32 |
CRITICISM | 52 |
MATHEMATICS AS THE ACTIVITY OF INTUITIVE CONSTRUC | 119 |
Copyright | |
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actual infinities admit analysis antinomies apple applied mathematics arguments assert axioms Brouwer Cantor's cardinal number Cauchy sequence classical mathematics consider consistency deduced defined definition elementary arithmetic elements empirical concepts entities Euclidean geometry exact and inexact example excluded middle existential exists experience false finite methods formal systems formalist Frege Gödel Hilbert ideal imply incompatible inexact concepts infinite totalities instances integers internally inexact intuition intuitionism intuitionist logic intuitionist mathematics Kant Kant's Leibniz logical relations logicist mathe mathematical concepts mathematical theories mathematicians matics means metamathematics natural numbers negative candidate neutral candidates non-empirical one-one correspondence particular perceptual characteristics perceptual objects philosophy of mathematics physical Plato positive candidate possible postulates precisely principle priori programme pure and applied pure mathematics purely exact rational numbers real numbers reason recursive functions regarded rules Russell sense similar sitions stroke stroke-expressions subject-matter symbols synthetic tion transfinite true truth truth-functional