Mathematics and Its logics : philosophical essays / Geoffrey Hellman.

Format:

Book

Author/Creator:

Hellman, Geoffrey, author.

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Physical Description:

1 online resource (vii, 286 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extend]ability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic.

Contents:

Structuralism without structures

What is categorical structuralism?

On the significance of the Burali-Forti paradox

Extending the iterative conception of set : a height-potentialist perspective

On nominalism

Maoist mathematics? Critical study of J. Burgess and G. Rosen's A subject with no object : strategies for nominalistic interpretation of mathematics

Predicative foundations of arithmetic / with Solomon Feferman

Challenges to predicative foundations of arithmetic / with Solomon Feferman

Predicativism as a philosophical position

On the Gödel-Friedman program

Logical truth by linguistic convention

Never say 'never'! On the communication problem between intuitionism and classicism

Constructive mathematics and quantum mechanics : unbounded operators and the spectral theorem

If 'if-then' then what?

Mathematical pluralism : the case of smooth infinitesimal analysis.

Notes:

Title from publisher's bibliographic system (viewed on 05 Feb 2021).

ISBN:

1-316-99960-2

1-108-65741-9