Wittgenstein's Philosophy of Mathematics

ISBN-13: 9780415861960 / Angielski / Miękka / 2013 / 198 str.

Pasquale Frascolla

Opis

Wittgenstein's role was vital in establishing mathematics as one of this century's principal areas of philosophic inquiry. In this book, the three phases of Wittgenstein's reflections on mathematics are viewed as a progressive whole, rather than as separate entities. Frascolla builds up a systematic construction of Wittgenstein's representation of the role of arithmetic in the theory of logical operations. He also presents a new interpretation of Wittgenstein's rule-following considerations - the community view of internal relations'.

Recenzje

'A welcome addition to the literature on Wittgenstein.' - Philosophia

Spis treści

Preface Abbreviations I. The Philosophy of Arithmetic of the Tractatus 1. Preliminaries 2. Systematic Exposition 3. The Knowledge of Forms: Vision and Calculation 4. Foundations of Mathematics (I) II. Verificationism and its Limits. The Intermediate Phase (1929-'33) 1. Introduction 2. Finite Cardinal Numbers: the Arithmetic of Strokes 3. Mathematical Propositions 4. The Mathematical Infinite 4.1 Quantifiers in Mathematics 4.2 Recursive Arithmetic and Algebra 4.3 Real Numbers 4.4 Set Theory 5. Foundations of Mathematics (II) III. From Facts to Concepts. The Later Writings on Mathematics (1934-'44) 1. The Crisis of Verificationism: Rule-Following 2. Mathematical Proofs as Paradigms 3. The Problem of Strict Finitism 4. Wittgenstein's Quasi-Revisionism 4.1 Cantor's Diagonal Proof and Transfinite Cardinals 4.2 The Law of Excluded Middle 4.3 Consistency References

O autorze

Pasquale Frascolla