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MATHEMATICAL REASONING CANNOT
THE PSYCHOLOGICAL INTERPRETATION
THE LOGICIST TRADITION
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algebra allows analysis applied argument Aristotle arithmetic axiom of comprehension axiomatic axioms Beth Cantor Chapter character characteristic co-ordination of actions combinations concepts concerned conclusion conscious consists construction correspondence decision problem deduction demonstration Descartes discovery discussion domain elementary elements empiricism entities epistemology Euclidean Euclidean geometry example existence fact formal formalisation formula Frege function generalisation genetic geometry Godel number hypothesis independent INRC interpretation introspection intuitionism inverse Kant latter Leibniz logic logician logico-mathematical experience machine mathematicians means metamathematics method natural numbers natural thought non-contradiction non-Euclidean geometry normative objects observe perceptual philosophy physical Piaget Platonism Platonist Poincare possible postulate premisses principles propositions psychological pure mathematics question reasoning reflective abstraction relations result schemas Section self-evidence semantic semantic tableau sense sensory-motor seriation set theory solution spatial intuition stage starting structures subject's activities system F tableau theorems theory tion triangle true validity verify viewpoint whilst