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

Authors
Ken Akiba
Virginia Commonwealth University
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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DOI 10.1093/philmat/8.1.26
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References found in this work BETA

Naming and Necessity.S. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.
Naming and Necessity.Saul A. Kripke - 1985 - 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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Citations of this work BETA

Vagueness in the World.Ken Akiba - 2004 - Noûs 38 (3):407–429.
Plural Metaphysical Supervaluationism.Robert Michels, Cristian Mariani & Giuliano Torrengo - 2021 - Inquiry: An Interdisciplinary Journal of Philosophy.
Mathematical Existence.Penelope Maddy - 2005 - Bulletin of Symbolic Logic 11 (3):351-376.
Mathematics and Fiction II: Analogy.Robert Thomas - 2002 - Logique Et Analyse 45:185-228.

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