David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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Philosophical Quarterly 54 (214):105-133 (2004)
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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Citations of this work BETA
Bernard Linsky & Edward N. Zalta (2006). What is Neologicism? Bulletin of Symbolic Logic 12 (1):60-99.
Florian Steinberger (2011). What Harmony Could and Could Not Be. Australasian Journal of Philosophy 89 (4):617 - 639.
Neil Tennant (2014). Logic, Mathematics, and the A Priori, Part II: Core Logic as Analytic, and as the Basis for Natural Logicism. Philosophia Mathematica 22 (3):321-344.
Neil Tennant (2013). Parts, Classes and Parts of Classes : An Anti-Realist Reading of Lewisian Mereology. Synthese 190 (4):709-742.
Nissim Francez (2014). A Logic Inspired by Natural Language: Quantifiers As Subnectors. Journal of Philosophical Logic 43 (6):1153-1172.
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