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- Benacerraf's_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.".
- Benacerraf's_identification_problem wikiPageExternalLink Benacerraf's%20Dilemma.pdf.
- Benacerraf's_identification_problem wikiPageID "42148664".
- Benacerraf's_identification_problem wikiPageRevisionID "602117890".
- Benacerraf's_identification_problem subject Category:Articles_created_via_the_Article_Wizard.
- Benacerraf's_identification_problem subject Category:Philosophical_problems.
- Benacerraf's_identification_problem subject Category:Philosophy_of_mathematics.
- Benacerraf's_identification_problem subject Category:Set_theory.
- Benacerraf's_identification_problem subject Category:Structuralism_(philosophy_of_mathematics).
- Benacerraf's_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.".
- Benacerraf's_identification_problem label "Benacerraf's identification problem".
- Benacerraf's_identification_problem sameAs m.0102dnfl.
- Benacerraf's_identification_problem sameAs Q17004819.
- Benacerraf's_identification_problem sameAs Q17004819.
- Benacerraf's_identification_problem wasDerivedFrom Benacerraf's_identification_problem?oldid=602117890.
- Benacerraf's_identification_problem isPrimaryTopicOf Benacerraf's_identification_problem.