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- Benacerrafs_identification_problem abstract "Benacerraf's identification problem is a philosophical argument, developed by Paul Benacerraf, against set-theoretic Platonism. In 1965, Benacerraf published a paradigm changing article entitled "What Numbers Could Not Be". Historically, the work became a significant catalyst in motivating the development of structuralism in the philosophy of mathematics.The identification problem argues that there exists a fundamental problem in reducing natural numbers to pure sets. Since there exists an infinite number of ways of identifying the natural numbers with pure sets, no particular set-theoretic method can be determined as the "true" reduction. Benacerraf infers that any attempt to make such a choice of reduction immediately results in generating a meta-level, set-theoretic falsehood, namely in relation to other elementarily-equivalent set-theories not identical to the one chosen. The identification problem argues that this creates a fundamental problem for Platonism, which maintains that mathematical objects have a real, abstract existence. Benacerraf's dilemma to Platonic set-theory is arguing that the Platonic attempt to identify the "true" reduction of natural numbers to pure sets, as revealing the intrinsic properties of these abstract mathematical objects, is impossible. As a result, the identification problem ultimately argues that the relation of set theory to natural numbers cannot have an ontologically Platonic nature.".
- Benacerrafs_identification_problem wikiPageExternalLink Benacerrafs%20Dilemma.pdf.
- Benacerrafs_identification_problem wikiPageID "42148664".
- Benacerrafs_identification_problem wikiPageLength "7120".
- Benacerrafs_identification_problem wikiPageOutDegree "36".
- Benacerrafs_identification_problem wikiPageRevisionID "639483898".
- Benacerrafs_identification_problem wikiPageWikiLink Abstract_and_concrete.
- Benacerrafs_identification_problem wikiPageWikiLink Abstract_objects.
- Benacerrafs_identification_problem wikiPageWikiLink Argument.
- Benacerrafs_identification_problem wikiPageWikiLink Binary_relation.
- Benacerrafs_identification_problem wikiPageWikiLink Category:Articles_created_via_the_Article_Wizard.
- Benacerrafs_identification_problem wikiPageWikiLink Category:Philosophical_problems.
- Benacerrafs_identification_problem wikiPageWikiLink Category:Philosophy_of_mathematics.
- Benacerrafs_identification_problem wikiPageWikiLink Category:Set_theory.
- Benacerrafs_identification_problem wikiPageWikiLink Category:Structuralism_(philosophy_of_mathematics).
- Benacerrafs_identification_problem wikiPageWikiLink Elementarily_equivalent.
- Benacerrafs_identification_problem wikiPageWikiLink Elementary_equivalence.
- Benacerrafs_identification_problem wikiPageWikiLink Formalism_(mathematics).
- Benacerrafs_identification_problem wikiPageWikiLink Function_(mathematics).
- Benacerrafs_identification_problem wikiPageWikiLink Functions_(mathematics).
- Benacerrafs_identification_problem wikiPageWikiLink Identity_(philosophy).
- Benacerrafs_identification_problem wikiPageWikiLink Impredicativity.
- Benacerrafs_identification_problem wikiPageWikiLink Infinity.
- Benacerrafs_identification_problem wikiPageWikiLink Intrinsic_and_extrinsic_properties.
- Benacerrafs_identification_problem wikiPageWikiLink Intrinsic_properties.
- Benacerrafs_identification_problem wikiPageWikiLink Intuitionism.
- Benacerrafs_identification_problem wikiPageWikiLink Isomorphic.
- Benacerrafs_identification_problem wikiPageWikiLink Isomorphism.
- Benacerrafs_identification_problem wikiPageWikiLink Law_of_identity.
- Benacerrafs_identification_problem wikiPageWikiLink Medieval_philosophy.
- Benacerrafs_identification_problem wikiPageWikiLink Natural_number.
- Benacerrafs_identification_problem wikiPageWikiLink Natural_numbers.
- Benacerrafs_identification_problem wikiPageWikiLink Nominalism.
- Benacerrafs_identification_problem wikiPageWikiLink Ontology.
- Benacerrafs_identification_problem wikiPageWikiLink Paradigm_shift.
- Benacerrafs_identification_problem wikiPageWikiLink Paul_Benacerraf.
- Benacerrafs_identification_problem wikiPageWikiLink Philosophical_argument.
- Benacerrafs_identification_problem wikiPageWikiLink Philosophy_of_mathematics.
- Benacerrafs_identification_problem wikiPageWikiLink Platonism.
- Benacerrafs_identification_problem wikiPageWikiLink Predicativism.
- Benacerrafs_identification_problem wikiPageWikiLink Pure_sets.
- Benacerrafs_identification_problem wikiPageWikiLink Real_number.
- Benacerrafs_identification_problem wikiPageWikiLink Real_numbers.
- Benacerrafs_identification_problem wikiPageWikiLink Reductionism.
- Benacerrafs_identification_problem wikiPageWikiLink Relation_(mathematics).
- Benacerrafs_identification_problem wikiPageWikiLink Set-theoretic.
- Benacerrafs_identification_problem wikiPageWikiLink Set_theory.
- Benacerrafs_identification_problem wikiPageWikiLink Structuralism_(philosophy_of_mathematics).
- Benacerrafs_identification_problem wikiPageWikiLink System.
- Benacerrafs_identification_problem wikiPageWikiLink Systems.
- Benacerrafs_identification_problem wikiPageWikiLink Transitivity_of_identity.
- Benacerrafs_identification_problem wikiPageWikiLinkText "Benacerraf's identification problem".
- Benacerrafs_identification_problem hasPhotoCollection Benacerrafs_identification_problem.
- Benacerrafs_identification_problem wikiPageUsesTemplate Template:Mset.
- Benacerrafs_identification_problem wikiPageUsesTemplate Template:Reflist.
- Benacerrafs_identification_problem subject Category:Articles_created_via_the_Article_Wizard.
- Benacerrafs_identification_problem subject Category:Philosophical_problems.
- Benacerrafs_identification_problem subject Category:Philosophy_of_mathematics.
- Benacerrafs_identification_problem subject Category:Set_theory.
- Benacerrafs_identification_problem subject Category:Structuralism_(philosophy_of_mathematics).
- Benacerrafs_identification_problem hypernym Argument.
- Benacerrafs_identification_problem comment "Benacerraf's identification problem is a philosophical argument, developed by Paul Benacerraf, against set-theoretic Platonism. In 1965, Benacerraf published a paradigm changing article entitled "What Numbers Could Not Be". Historically, the work became a significant catalyst in motivating the development of structuralism in the philosophy of mathematics.The identification problem argues that there exists a fundamental problem in reducing natural numbers to pure sets.".
- Benacerrafs_identification_problem label "Benacerraf's identification problem".
- Benacerrafs_identification_problem sameAs m.0102dnfl.
- Benacerrafs_identification_problem sameAs Q17004819.
- Benacerrafs_identification_problem sameAs Q17004819.
- Benacerrafs_identification_problem wasDerivedFrom Benacerrafs_identification_problemoldid=639483898.
- Benacerrafs_identification_problem isPrimaryTopicOf Benacerrafs_identification_problem.