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A General Theory of Abstraction Operators

Neil Tennant
The Philosophical Quarterly (1950-)
Vol. 54, No. 214 (Jan., 2004), pp. 105-133
Stable URL: http://www.jstor.org/stable/3543078
Page Count: 29
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A General Theory of Abstraction Operators
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Abstract

I present a general theory of abstraction operators which treats them as variable-binding termforming 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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