Indefiniteness of mathematical objects

Philosophia Mathematica 8 (1):26--46 (2000)
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Abstract

The view that mathematical objects are indefinite in nature is presented and defended, hi the first section, Field's argument for fictionalism, given in response to Benacerraf's problem of identification, is closely examined, and it is contended that platonists can solve the problem equally well if they take the view that mathematical objects are indefinite. In the second section, two general arguments against the intelligibility of objectual indefiniteness are shown erroneous, hi the final section, the view is compared to mathematical structuralism, and it is shown that a version of structuralism should be understood as embracing the same view

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Ken Akiba
Virginia Commonwealth University

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References found in this work

Naming and Necessity.S. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.
Naming and Necessity.Saul Kripke - 1980 - Critica 17 (49):69-71.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Vagueness, truth and logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.

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