Philosophia Mathematica:nkv031 (2015)

Authors
Kevin Klement
University of Massachusetts, Amherst
Abstract
In this paper I explore a position on which it is possible to eliminate the need for postulating abstract objects through abstraction principles by treating terms for abstracta as ‘incomplete symbols’, using Russell's no-classes theory as a template from which to generalize. I defend views of this stripe against objections, most notably Richard Heck's charge that syntactic forms of nominalism cannot correctly deal with non-first-orderizable quantifcation over apparent abstracta. I further discuss how number theory may be developed in a system treating apparent terms for numbers using these definitions.
Keywords abstract objects  Russell, Bertrand  abstraction principles  abstraction  incomplete symbols
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DOI 10.1093/philmat/nkv031
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References found in this work BETA

Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
What Numbers Could Not Be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
The Principles of Mathematics.Bertrand Russell - 1903 - Revue de Métaphysique et de Morale 11 (4):11-12.
Frege’s Conception of Numbers as Objects.Crispin Wright - 1983 - Critical Philosophy 1 (1):97.
Frege's Theorem.Richard G. Heck - 2011 - Oxford, England: Clarendon Press.

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Citations of this work BETA

Numbers, Empiricism and the A Priori.Olga Ramirez Calle - 2020 - Logos and Episteme: An International Journal of Epistemology 11 (2):149-177.
Russell and the Neo-Logicists.Sébastien Gandon - 2017 - Annals of the Japan Association for Philosophy of Science 25:1-21.

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