David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
The goal is to sketch a nominalist approach to mathematics which just like neologicism employs abstraction principles, but unlike neologicism is not committed to the idea that mathematical objects exist and does not insist that abstraction principles establish the reference of abstract terms. It is well-known that neologicism runs into certain philosophical problems and faces the technical difficulty of finding appropriate acceptability criteria for abstraction principles. I will argue that a modal and iterative nominalist approach to abstraction principles circumvents those difficulties while still being able to put abstraction principles to a foundational use.
|Keywords||neologicism nominalism set theory|
|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
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Kit Fine (2002). The Limits of Abstraction. Oxford University Press.
Rafal Urbaniak (2010). Neologicist nominalism. Studia Logica 96 (2):149-173.
Bernard Linsky & Edward N. Zalta (2006). What is Neologicism? Bulletin of Symbolic Logic 12 (1):60-99.
G. A. Antonelli (2010). Notions of Invariance for Abstraction Principles. Philosophia Mathematica 18 (3):276-292.
Otávio Bueno & Edward N. Zalta (2005). A Nominalist's Dilemma and its Solution. Philosophia Mathematica 13 (3):297-307.
Øystein Linnebo (2009). Bad Company Tamed. Synthese 170 (3):371 - 391.
Joseph Hill (2010). Is Buridan's Theory of Abstraction Incompatible with His Nominalist Semantics? An Evaluation of Klima's Charge Against Buridan. Proceedings of the American Catholic Philosophical Association 84:167-178.
Ornaith O'Dowd (2011). Care and Abstract Principles. Hypatia 27 (2):407-422.
Øystein Linnebo & Gabriel Uzquiano (2009). Which Abstraction Principles Are Acceptable? Some Limitative Results. British Journal for the Philosophy of Science 60 (2):239-252.
Matti Eklund (2009). Bad Company and Neo-Fregean Philosophy. Synthese 170 (3):393 - 414.
Added to index2010-08-17
Total downloads37 ( #87,809 of 1,724,892 )
Recent downloads (6 months)2 ( #268,597 of 1,724,892 )
How can I increase my downloads?