Philosophical Quarterly 54 (214):105-133 (2004)

Neil Tennant
Ohio State University
I present a general theory of abstraction operators which treats them as variable-binding term- forming operators, and provides a reasonably uniform treatment for definite descriptions, set abstracts, natural number abstraction, and real number abstraction. This minimizing, extensional and relational theory reveals a striking similarity between definite descriptions and set abstracts, and provides a clear rationale for the claim that there is a logic of sets (which is ontologically non- committal). The theory also treats both natural and real numbers as answering to a two-fold process of abstraction. The first step, of conceptual abstraction, yields the object occupying a particular position within an ordering of a certain kind. The second step, of objectual abstraction, yields the number sui generis, as the position itself within any ordering of the kind in question.
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DOI 10.1111/j.0031-8094.2004.00344.x
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References found in this work BETA

Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.
Singular Terms and Arithmetical Logicism.Ian Rumfitt - 2003 - Philosophical Books 44 (3):193--219.
The Limits of Abstraction.Kit Fine - 1998 - In Matthias Schirn (ed.), The Philosophy of Mathematics Today. Clarendon Press.

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Citations of this work BETA

Abstract Objects.Gideon Rosen - 2008 - Stanford Encyclopedia of Philosophy.
What Harmony Could and Could Not Be.Florian Steinberger - 2011 - Australasian Journal of Philosophy 89 (4):617 - 639.
What is Neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.
Mathematical Abstraction, Conceptual Variation and Identity.Jean-Pierre Marquis - 2014 - In Peter Schroeder-Heister, Gerhard Heinzmann, Wilfred Hodges & Pierre Edouard Bour (eds.), Logic, Methodology and Philosophy of Science, Proceedings of the 14th International Congress. London, UK: pp. 299-322.

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