Wittgenstein's philosophy of mathematics / Juliet Floyd.

Format:

Book

Author/Creator:

Floyd, Juliet, author.

Series:

Cambridge elements. Elements in the philosophy of mathematics, 2399-2883.

Cambridge elements. Elements in the philosophy of mathematics, 2399-2883

Language:

English

Subjects (All):

Wittgenstein, Ludwig, 1889-1951.

Wittgenstein, Ludwig.

Mathematics--Philosophy.

Mathematics.

Physical Description:

1 online resource (86 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

For Wittgenstein mathematics is a human activity characterizing ways of seeing conceptual possibilities and empirical situations, proof and logical methods central to its progress. Sentences exhibit differing 'aspects', or dimensions of meaning, projecting mathematical 'realities'. Mathematics is an activity of constructing standpoints on equalities and differences of these. Wittgenstein's Later Philosophy of Mathematics (1934-1951) grew from his Early (1912-1921) and Middle (1929-33) philosophies, a dialectical path reconstructed here partly as a response to the limitative results of Gödel and Turing.

Contents:

Cover

Title page

Copyright page

Wittgenstein's Philosophy of Mathematics

Contents

1 Introduction

1.1 Aims and Sources

1.2 Aspect Realism

2 Early Philosophy (1912-1928): Absolute Simplicity

2.1 "Final" Analysis

2.2 The General Form of Sentence, Form Series

2.3 Early Philosophy of Logic

2.4 Early Philosophy of Mathematics

2.5 Poincaré's Objections

2.6 Interpreting Form Series

3 Middle Philosophy (1929-1933): Relative Simplicity

3.1 Colloquial Language and "Effectiveness"

3.2 Satzsysteme and Statements of Gradation

3.3 Aspects: Sheffer's Strokes

3.4 Skolem Arithmetic and the Uniqueness Rule

3.5 Real Numbers: the Calculus Conception

3.6 Consistency

4 Later Philosophy (1937-1951): Fluid Simplicity

4.1 Language-Games to Forms of Life

4.2 Rule-Following: Paradigms and Proofs (RFM I)

4.3 Diagonal Proofs (RFM II)

4.4 Surveyability (RFM III)

4.5 Real Numbers (RFM V)

4.6 Wittgenstein, Gödel, and Turing (RFM I, II, V, VII)

List of Abbreviations

References

Acknowledgments.

Notes:

Title from publisher's bibliographic system (viewed on 30 Jul 2021).

ISBN:

1-108-68712-1

OCLC:

1261766616