Nominalist Neologicism

Abstract

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.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,221

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

  • Only published works are available at libraries.

Similar books and articles

The limits of abstraction.Kit Fine - 2002 - New York: Oxford University Press. Edited by Matthias Schirn.
Which abstraction principles are acceptable? Some limitative results.Øystein Linnebo & Gabriel Uzquiano - 2009 - British Journal for the Philosophy of Science 60 (2):239-252.
Care and Abstract Principles.Ornaith O'Dowd - 2012 - Hypatia 27 (2):407-422.
Bad company tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.
Notions of Invariance for Abstraction Principles.G. A. Antonelli - 2010 - Philosophia Mathematica 18 (3):276-292.
What is neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.

Analytics

Added to PP
2010-08-17

Downloads
92 (#170,147)

6 months
5 (#244,526)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Rafal Urbaniak
University of Gdansk

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references