Paradox and Potential Infinity

Journal of Philosophical Logic 42 (1):195-219 (2013)
  Copy   BIBTEX

Abstract

We describe a variety of sets internal to models of intuitionistic set theory that (1) manifest some of the crucial behaviors of potentially infinite sets as described in the foundational literature going back to Aristotle, and (2) provide models for systems of predicative arithmetic. We close with a brief discussion of Church’s Thesis for predicative arithmetic.

Categories

Keywords

Reprint years

DOI

10.1007/s10992-011-9218-y

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,349

External links

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

Through your library

My notes

Similar books and articles

Aristotle on mathematical infinity.Theokritos Kouremenos - 1995 - Stuttgart: F. Steiner. Edited by Aristotle.
Actual versus Potential Infinity (BPhil manuscript.).Anne Newstead - 1997 - Dissertation, University of Oxford
Aristotelian Infinity.John Bowin - 2007 - Oxford Studies in Ancient Philosophy 32:233-250.
On interpretations of bounded arithmetic and bounded set theory.Richard Pettigrew - 2009 - Notre Dame Journal of Formal Logic 50 (2):141-152.
Infinity: the quest to think the unthinkable.Brian Clegg - 2003 - [Berkeley, Calif.]: Publishers Group West.
In defense of epistemic arithmetic.Leon Horsten - 1998 - Synthese 116 (1):1-25.
Ramified Frege Arithmetic.Richard G. Heck - 2011 - Journal of Philosophical Logic 40 (6):715-735.
Developing arithmetic in set theory without infinity: some historical remarks.Charles Parsons - 1987 - History and Philosophy of Logic 8 (2):201-213.
Varieties of Finitism.Manuel Bremer - 2007 - Metaphysica 8 (2):131-148.
The philosophy of strict finitism.Ernest J. Welti - 1987 - Theoria 2 (2):575-582.
Infinity in science and religion. The creative role of thinking about infinity.Wolfgang Achtner - 2005 - Neue Zeitschrift für Systematicsche Theologie Und Religionsphilosophie 47 (4):392-411.
Challenges to predicative foundations of arithmetic.Solomon Feferman - manuscript
Models of arithmetic and upper Bounds for arithmetic sets.Alistair H. Lachlan & Robert I. Soare - 1994 - Journal of Symbolic Logic 59 (3):977-983.
Predicative fragments of Frege arithmetic.Øystein Linnebo - 2004 - Bulletin of Symbolic Logic 10 (2):153-174.
Classical arithmetic as part of intuitionistic arithmetic.Michael Potter - 1998 - Grazer Philosophische Studien 55 (1):127-41.

Analytics

Added to PP
2011-12-23

Downloads
86 (#192,516)

6 months
8 (#352,434)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Add more citations

References found in this work

Elements of Intuitionism.Michael Dummett - 1977 - New York: Oxford University Press. Edited by Roberto Minio.
Elements of Intuitionism.Michael Dummett - 1980 - British Journal for the Philosophy of Science 31 (3):299-301.
Intuitionism.A. Heyting - 1956 - Amsterdam,: North-Holland Pub. Co..
Paradoxien des Unendlichen.Bernard Bolzano - 2012 - Hamburg: Felix Meiner Verlag. Edited by Christian Tapp.

View all 21 references / Add more references