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PY 4813 -- Philosophy of Mathematics

The TWiki page for the second half of the PY4813 Philosophy of Mathematics class

Schedule

Additional Reading for the lectures

Here is some additional reading for the indivdual lectures.

Hilbert

• MathFormalism -- This contains various articles by Hilbert and others. Advisable are:
  • HilbertUberDasUnendliche. Reprinted in BenacerrafPhilosophyOfMathematics.
  • Zach's Stanford Encyclopedia Entry: http://www.seop.leeds.ac.uk/entries/hilbert-program/

Intuitionism

• MathIntuitionism
  • IntuitBrouwer
  • IntuitHeyting
  • IntuitDummett
    • DummettPhilosophicalBasisOfIntuitionisticLogic
    • DummettElementsOfIntuitionism -- I cannot recommend reading the whole book (at least not with a straight face), but § 1.2 and chapter 7 (here esp. §§7.2 and 7.3) are very instructive

Benacerraf's Dilemma and Platonism

• BenacerrafMathematicalTruth -- THE classic paper and a must-read. Follow the link for an online version of the text.
  • HaleWrightBenacerrafsDilemmaRevisited -- A good overview of various response and an outline of the Neo-Fregean response.

• BenacerrafWhatNumbersCouldNotBe -- another classic by Benacceraf
  • MathematicalReference -- The Twiki bibliography contains various issue pertaining to reference to abstract objects - an issue raised in the Benacerraf paper

• ParsonsMathematicalIntuition -- Defence of the idea of mathematical intuition, as defended by Godel (see e.g. his GodelWhatIsCantor)

Nominalism

• MathNominalism
  • MacBrideListeningToFictions - a great article on various aspects of Field's Nominalism (including link to online version)
  • Further Readings:
    • QuineWordAndObject §55 - for the Indispensability Argument
    • BurgessWhyImNotANominalist
    • BurgessRosenSubjectWithNoObject
    • ChiharaConstructibilityAndMathematicalExistence
    • FieldScienceWithoutNumbers
    • FieldOnConservativenessAndIncompleteness
    • HellmanOnNominalism
    • ShapiroConservativenessAndIncompleteness

Neo-Logicism

• NeoFregeanProgramme (with a nice categorization of the various issues)
  • MacBrideSpeakingWithShadows - a very good article surveying (and more) the philosophy behind Neo-Logicism

Exam Preparation

• RevisionClassforPY4813.pdf: Handout of the Revision class, with readings for exam preparation

• Clark / Demopoulos - Logicism.pdf (published in ShapiroOxfordHandbook)

• HaleWright_BenacerrafDillema.pdf: Hale/Wright paper outlining Benacerraf's dilemma and discussing various platonist strategies.

Additional Resources

• http://www.seop.leeds.ac.uk/contents.html

• http://arche-wiki.st-and.ac.uk/~ahwiki/bin/view/Arche/MathsBibliographies

• http://www.rep.routledge.com/

-- PhilipAEbert / MarcusRossberg - 21 Mar 2005

Attachment	Action	Size	Date	Who	Comment
PY4813_Formalism.pdf	manage	99.0 K	17 Apr 2005 - 18:12	PhilipAEbert
NonConstrProofEx.pdf	manage	54.5 K	18 Apr 2005 - 19:21	MarcusRossberg
PY4813_Benacerraf.pdf	manage	126.0 K	19 Apr 2005 - 10:35	PhilipAEbert
PY4813_Intuitionism_Dummett.pdf	manage	56.3 K	23 Apr 2005 - 16:13	MarcusRossberg
PY4813_Nominalism.pdf	manage	85.4 K	26 Apr 2005 - 15:29	MarcusRossberg
PY4813_NeoLogicism.pdf	manage	109.7 K	03 May 2005 - 14:27	PhilipAEbert
RevisionClassforPY4813.pdf	manage	93.3 K	10 May 2005 - 10:36	MarcusRossberg	Handout with readings for exam preparation
Logicism-_Peter.pdf	manage	474.7 K	11 May 2005 - 14:15	MarcusRossberg	Clark / Demopoulos - Logicism
HaleWright_BenacerrafDillema.pdf	manage	345.6 K	14 May 2005 - 14:40	PhilipAEbert

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