The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993

(ed.)
Oxford, England: Clarendon Press (1998)
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Abstract

The Philosophy of Mathematics Today gives a panorama of the best current work in this lively field, through twenty essays specially written for this collection by leading figures. The topics include indeterminacy, logical consequence, mathematical methodology, abstraction, and both Hilbert's and Frege's foundational programmes. The collection will be an important source for research in the philosophy of mathematics for years to come. Contributors Paul Benacerraf, George Boolos, John P. Burgess, Charles S. Chihara, Michael Detlefsen, Michael Dummett, Hartry Field, Kit Fine, Bob Hale, Richard G. Heck, Jnr., Geoffrey Hellman, Penelope Maddy, Karl-Georg Niebergall, Charles D. Parsons, Michael D. Resnik, Matthias Schirn, Stewart Shapiro, Peter Simons, W.W. Tait, Crispin Wright.

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2003

Call number

QA8.P45 1998

ISBN(s)

9780199262625   9780198236542   0199262624   0198236549

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Chapters

What Mathematical Truth Could Not Be--1.Paul Benacerraf
Die Grundlagen der Arithmetik, §§82–3.George Boolos & Richard Kimberly Heck
Occam's razor and scientific method.John P. Burgess
Tarski's Thesis and the Ontology of Mathematics.Charles Chihara
Constructive existence claims.Michael Detlefsen
Neo-Fregeans: In Bad Company?Michael Dummett
Do We Have a Determinate Conception of Finiteness and Natural Number?Hartry Field
The Limits of Abstraction.Kit Fine
Iis Platonism Epistemologically Bankrupt?Bob Hale
Beyond definitionism—but not too far beyond.Geoffrey Hellman
Naturalizing mathematical methodology.Penelope Maddy
Hilbert's Finitism and the Notion of Infinity.Karl-Georg Niebergall & Matthias Schirn
Finitism and intuitive knowledge.Charles Parsons
Holistic mathematics.Michael D. Resnik
Logical consequence: Models and modality.Stewart Shapiro
Structure and Abstraction.Peter Simons
Zermelo's Conception of Set Theory and Reflection Principles.W. W. Tait
Zermelo (1930) is concerned with impredicative second-order set theory. He treats the general case of set theory with urelements, but it will be enough to consider only the case of pure set theory, ie without urelements. In this context, Zermelo's theory is the axiomatic second-order theory T2 in the language of pure set theory whose axioms are Extensionality, Regu. [REVIEW]Ww Tait
On the harmless impredicativity of N=('Hume's Principle').Crispin Wright
Response to Dummett.Crispin Wright
Response to Michael Dummett.Crispin Wright

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Author's Profile

Matthias Schirn
Ludwig Maximilians Universität, München

Citations of this work

Antireductionism and Ordinals.Beau Madison Mount - 2019 - Philosophia Mathematica 27 (1):105-124.

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