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Klappentext A distinguished philosopher surveys the mathematical views and influence of Plato! Aristotle! Leibniz! and Kant. He also examines the relationship between mathematical theories! empirical data! and philosophical presuppositions. 1968 edition. Inhaltsverzeichnis PrefaceIntroductionSOME OLDER VIEWS Plato's account Some views of Aristotle Leibniz's philosophy of mathematics Kant: some of his viewsMATHEMATICS AS LOGIC: EXPOSITION The programme The logic of truth-functions On the logic of classes On the logic of quantification On the logicist systemsMATHEMATICS AS LOGIC: CRITICISM The logicist account of logic The logicist conflation of empirical and non-empirical concepts The logicist theory of mathematical infinity The logicist account of geometryMATHEMATICS AS THE SCIENCE OF FORMAL SYSTEMS: EXPOSITION The programme Finite methods and infinite totalities Formal systems and formalizations Some results of metamathematicsMATHEMATICS AS THE SCIENCE OF FORMAL SYSTEMS: CRITICISM The formalist account of pure mathematics The formalist account of applied mathematics The concept of actual infinity The formalist conception of logicMATHEMATICS AS THE ACTIVITY OF INTUITIVE CONSTRUCTIONS: EXPOSITION The programme Intuitionist mathematics Intuitionist logicMATHEMATICS AS THE ACTIVITY OF INTUITIVE CONSTRUCTIONS: CRITICISM Mathematical theorems as reports on intuitive constructions Intuitionism and the logical status of applied mathematics The intuitionist conception of mathematical infinity Interrelations between formalism and intuitionismTHE NATURE OF PURE AND APPLIED MATHEMATICS Exact and inexact concepts Pure mathematics disconnected from perception Mathematical existence-propositions The nature of applied mathematics Mathematics and philosophyAppendix A. On the classical theory of real numbersAppendix B. Some suggestions for further readingIndex
