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

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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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Reprint years

2003

Call number

QA8.P45 1998

ISBN(s)

9780199262625   9780198236542   0199262624   0198236549

DOI

10.1093/mind/112.448.792

Other Versions

edition Schirn, Matthias (2003) "Philosophy Mathematics Today". Oxford University Press UK

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My notes

Chapters

Beyond definitionism—but not too far beyond.Geoffrey Hellman
Die Grundlagen der Arithmetik §§82-83.Richard Heck & George Boolos
Die Grundlagen der Arithmetik, 82-3.George Boolos & Richard G. Heck
Do We Have a Determinate Conception of Finiteness and Natural Number?Hartry Field
Hilbert's Finitism and the Notion of Infinity.Karl-Georg Niebergall & Matthias Schirn
Iis Platonism Epistemologically Bankrupt?Bob Hale
Naturalizing mathematical methodology.Penelope Maddy
Neo-Fregeans: In Bad Company?Michael Dummett
Response to Michael Dummett.Crispin Wright
Structure and Abstraction.Peter Simons
The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard Heck
The Finite and the Infinite in Frege's Grundgesetze der Arithmetik.Richard Heck
The Limits of Abstraction.Kit Fine
What Mathematical Truth Could Not Be--1.Paul Benacerraf
Zermelo's Conception of Set Theory and Reflection Principles.W. W. Tait
Logical Consequence: Models and Modality.  (pages 131–156)Stewart Shapiro
Tarski's Thesis and the Ontology of Mathematics.  (pages 157--172)Charles Chihara
Occam's razor and scientific method.  (pages 195--214)John P. Burgess
Holistic mathematics.  (pages 227--46)Michael D. Resnik
Finitism and intuitive knowledge.  (pages 249--270)Charles Parsons
On the harmless impredicativity of N=('Hume's Principle').  (pages 339--68)Crispin Wright
Response to Dummett.  (pages 389--405)Crispin Wright
Die Grundlagen der Arithmetik, §§82–3.  (pages 407-428)George Boolos & Richard Kimberly Heck
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]  (pages 469)Ww Tait
Constructive existence claims.  (pages 1998--307)Michael Detlefsen

Similar books and articles

Response to Michael Dummett.Crispin Wright - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press.
The Limits of Abstraction.Kit Fine - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press.
Structure and Abstraction.Peter Simons - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press.
Response to Dummett.Crispin Wright - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 389--405.
Naturalizing mathematical methodology.Penelope Maddy - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press.
Logical Consequence: Models and Modality.Stewart Shapiro - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 131–156.
Holistic mathematics.Michael D. Resnik - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 227--46.
Hilbert's Finitism and the Notion of Infinity.Karl-Georg Niebergall & Matthias Schirn - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press.
Finitism and intuitive knowledge.Charles Parsons - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 249--270.
Tarski's Thesis and the Ontology of Mathematics.Charles Chihara - 1998 - In Matthias Schirn, The Philosophy of Mathematics Today: Papers From a Conference Held in Munich From June 28 to July 4,1993. Oxford, England: Clarendon Press. pp. 157--172.

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Matthias Schirn
Ludwig Maximilians Universität, München

Citations of this work

Antireductionism and Ordinals.Beau Madison Mount - 2019 - Philosophia Mathematica 27 (1):105-124.
The Metametaphysics of Neo-Fregeanism.Matti Eklund - 2020 - In Ricki Bliss & James Miller, The Routledge Handbook of Metametaphysics. New York, NY: Routledge.

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