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The following are research topics within the MathematicsProject that have a more-or-less completed ArcheBibliography. Others may be found at MathematicsTopics.

Contents

The NeoFregeanProgramme

This contains a comprehensive but not complete selection of entries concerning the Neo-Fregean Programme.

• BadCompanyObjections - Worries about consistency, conservativeness and impredicativity of Abstractions Principles
  • NuisancePrinciple - Worries about per se consistent, but mutually inconsistent Abstraction Principles
• CaesarProblem - Whether Abstraction Prinicples are sufficient to impart a complete concepetion of the introduced objects.
• ContextPrinciple - It's metaphysical and epistemological implications and criticism by Dummett and others.
• ConsistencyOfHumesPrinciple
• FregesTheorem - Papers on the result that the Peano Postulates are interpretable within Frege Arithmetic (HP and 2nd order logic)
• ImplicitDefinitions - Whether implicit definitions can be regarded as grounding a priori knowledge.
• NeoFregeanAnalysis - A Neo-Fregean treatment of the Reals and the Complex Numbers
• NeoFregeanSets - A Neo-Fregean treatment of Set Theory
• RecarvingContent - The idea that Abstraction Principles can be regareded as carving up the content in a different way.
• ReductionistObjection - Worries concerning a reductive reading of Abstracion Principles.
• RejectionistObjection - Rejecting for various reasons the method of Abstraction per se.
• Second-order logic - Issues concerning the status of Second-order logic on a Neo-Fregean framwork.
• ReviewsOfNeoFregeanProgramme - a list of reviews and critical notices of Hale and Wright
• AlternativeNeoFregeanProgrammes - Alternative programmes that seek to develop the insight of Frege's central claims.
• NeoFregeanMetaontology - some references for the very recent debate concerning metaontology and neo-Fregeanism

SecondOrderLogic

• SecondOrderConsequence
• SOLogicOntology
• SOLogicHistory
• SOLogicNaturalLanguage
• SOLogicProofTheory
• SOLogicModelTheory
• SOLogicCategoricity
• SchemaLogic
• RamifiedSOL
• PredicativeSOL
• see also:
  • TypeTheory
  • NeoFregeanSecondOrderLogic
  • MathPlurals - plural-talk in the philosophy of mathematics and second-order logic
    • PluralsLegitimacy - can plural-talk be legitimately interpreted as a non-first-order resource?
    • PluralsApplications - philosophical applications for plural-talk

MathematicalReference

• ReferenceToAbstractObjects - General issues about referring to abstract entities
• InscrutabilityArguments - Inscrutability arguments, resolutions and the mathematical case
• Reference and Realism in Mathematics
  • DeflationismMinimalismReference - 'Thin' theories of reference
  • ReferenceUnderlyingTruth - Arguments for a substantive (often physicalistic) theory of reference
• ContextPrinciple - Neo-Fregean 'thin' account of reference (neo-Fregean research topic)
• CaesarProblem - Cross-category identity statements 1 (neo-Fregean research topic)
• CounterCaesarProblem - Cross-category identity statements 2 (neo-Fregean research topic)

MathIntuitionism

This is a selection of major topics concerning the Intuitionistic view of mathematics

• IntuitKant
• IntuitBrouwer
• IntuitHeyting
• IntuitDummett
• IntuitModelTheory
• IntuitTranslations
• IntuitMeaning
• IntuitProofTheory
• IntuitNegation
• IntuitCommunicationProblem
• IntuitMathematics

MathPlurals

Philosophical issues surrounding English plurals.

• PluralsLegitimacy - Can plural-talk be legitimately interpreted as a non-first order resource?
• PluralsApplications - Philosophical applications for plural-talk.

UnrestrictedQuantification

Philosophical issues surrounding quantification over absolutely everything.

• UnrestrictedDomain - Is there such a thing as an unrestricted domain?
• UnrestrictedIndeterminacy - Can one determinately quantify over everything there is?
• UnrestrictedApplications - Applications of absolutely unrestricted quantification.

Miscellaneous Topics

• ComplexNumbers
• TypeTheory

-- RobertWilliams - 28 Jul 2003

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