David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
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.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Stephen G. Simpson (1999). Subsystems of Second-Order Arithmetic. Springer-Verlag.
Neil Tennant (1987). Anti-Realism and Logic: Truth as Eternal. Oxford University Press.
Bob Hale (2000). Reals by Abstraction. Philosophia Mathematica 8 (2):100--123.
Ian Rumfitt (2003). Singular Terms and Arithmetical Logicism. Philosophical Books 44 (3):193--219.
Ian Rumfitt (1999). Logic and Existence: Ian Rumfitt. Aristotelian Society Supplementary Volume 73 (1):151–180.
Citations of this work BETA
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.
Florian Steinberger (2011). What Harmony Could and Could Not Be. Australasian Journal of Philosophy 89 (4):617 - 639.
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.
Similar books and articles
John F. Sowa (2006). Worlds, Models and Descriptions. Studia Logica 84 (2):323 - 360.
M. W. Bunder (2000). Expedited Broda-Damas Bracket Abstraction. Journal of Symbolic Logic 65 (4):1850-1857.
Demetris P. Portides (2005). A Theory of Scientific Model Construction: The Conceptual Process of Abstraction and Concretisation. [REVIEW] Foundations of Science 10 (1):67-88.
Cynthia A. Stark (2010). Abstraction and Justification in Moral Theory. Hypatia 25 (4):825-833.
Kit Fine (2002). The Limits of Abstraction. Oxford University Press.
Eric Thomas Updike (2012). Abstraction in Fitch's Basic Logic. History and Philosophy of Logic 33 (3):215-243.
Stephen Schiffer (2005). Russell's Theory of Definite Descriptions. Mind 114 (456):1135-1183.
Rafal Urbaniak (2010). Neologicist nominalism. Studia Logica 96 (2):149-173.
Matti Eklund (2009). Bad Company and Neo-Fregean Philosophy. Synthese 170 (3):393 - 414.
NeilTennant (2004). A General Theory of Abstraction Operators. Philosophical Quarterly 54 (214):105–133.
Added to index2009-01-28
Total downloads36 ( #109,417 of 1,792,039 )
Recent downloads (6 months)8 ( #102,466 of 1,792,039 )
How can I increase my downloads?