A Generic Russellian Elimination of Abstract Objects

Philosophia Mathematica 25 (1):91-115 (2017)
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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.

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Kevin Klement
University of Massachusetts, Amherst

Citations of this work

Numbers, Empiricism and the A Priori.Olga Ramírez Calle - 2020 - Logos and Episteme 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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References found in this work

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 - New York: Clarendon Press.

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