Facets of Infinity: A Theory of Finitistic Truth

Dissertation, Princeton University (1992)

Zlatan Damnjanovic
University of Southern California
The thesis critically examines the question of the philosophical coherence of finitism, the view which seeks to interpret mathematics without postulating an actual infinity of mathematical objects. It is argued that a widely accepted characterization of finitism, most recently expounded by Tait, is inadequate, and a new characterization based on the notion of elementary abstraction is proposed. It is further argued that the notion of elementary abstraction better explains the bearing of Godel's incompleteness theorems on the issue of the coherence of finitism. By abstraction is meant a procedure by which one recognizes or establishes that some infinite process exhibits a distinctive uniformity. If the procedure does not require one to conceive of the integers in any other way than as the result of simple iterations, we call such abstraction elementary. Some six different formal models exploring a variety of different ways in which this notion can be made precise are proposed as possible formal characterizations of finitistic truth. It is proved that all these different models are equivalent with respect to finitistically meaningful sentences. This is taken as strong evidence that the notion of elementary abstraction is determinate enough to provide a basis for a coherent philosophical formulation of finitism
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,775
External links

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.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

On the Concept of Finitism.Luca Incurvati - 2015 - Synthese 192 (8):2413-2436.
Varieties of Finitism.Manuel Bremer - 2007 - Metaphysica 8 (2):131-148.
Two (or Three) Notions of Finitism.Mihai Ganea - 2010 - Review of Symbolic Logic 3 (1):119-144.
Gödel on Intuition and on Hilbert's Finitism.W. W. Tait - 2010 - In Kurt Gödel, Solomon Feferman, Charles Parsons & Stephen G. Simpson (eds.), Kurt Gödel: Essays for His Centennial. Association for Symbolic Logic.
Strict Finitism and the Happy Sorites.Ofra Magidor - 2012 - Journal of Philosophical Logic 41 (2):471-491.
Elementary Realizability.Zlatan Damnjanovic - 1997 - Journal of Philosophical Logic 26 (3):311-339.
Undefinability Vs. Definability of Satisfaction and Truth.Roman Murawski - 1999 - Vienna Circle Institute Yearbook 6:203-215.
Interpreting Formal Logic.Jaroslav Peregrin - 1994 - Erkenntnis 40 (1):5 - 20.
Iteration One More Time.Roy T. Cook - 2003 - Notre Dame Journal of Formal Logic 44 (2):63--92.
Reals by Abstraction.Bob Hale - 2000 - Philosophia Mathematica 8 (2):100--123.


Added to PP index

Total views

Recent downloads (6 months)

How can I increase my downloads?


Sorry, there are not enough data points to plot this chart.

My notes