Fregean Extensions of First‐Order Theories

Mathematical Logic Quarterly 40 (1):27-30 (1994)
  Copy   BIBTEX

Abstract

It is shown by Parsons [2] that the first-order fragment of Frege's logical system in the Grundgesetze der Arithmetic is consistent. In this note we formulate and prove a stronger version of this result for arbitrary first-order theories. We also show that a natural attempt to further strengthen our result runs afoul of Tarski's theorem on the undefinability of truth

Categories

Keywords

Reprint years

DOI

10.1002/malq.19940400104

Other Versions

No versions found

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 100,774

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

The Finitistic Consistency of Heck’s Predicative Fregean System.Luís Cruz-Filipe & Fernando Ferreira - 2015 - Notre Dame Journal of Formal Logic 56 (1):61-79.
On a Consistent Subsystem of Frege's Grundgesetze.John P. Burgess - 1998 - Notre Dame Journal of Formal Logic 39 (2):274-278.
The Strength of Abstraction with Predicative Comprehension.Sean Walsh - 2016 - Bulletin of Symbolic Logic 22 (1):105–120.
Completeness and categoricity: Frege, gödel and model theory.Stephen Read - 1997 - History and Philosophy of Logic 18 (2):79-93.
Zigzag and Fregean Arithmetic.Fernando Ferreira - 2018 - In Hassan Tahiri (ed.), The Philosophers and Mathematics: Festschrift for Roshdi Rashed. Cham: Springer Verlag. pp. 81-100.
The Consistency of predicative fragments of frege's grundgesetze der arithmetik.Richard Heck Jnr - 1996 - History and Philosophy of Logic 17 (1 & 2):209-220.
Amending Frege’s Grundgesetze der Arithmetik.Fernando Ferreira - 2005 - Synthese 147 (1):3-19.
On first-order theories with provability operator.Sergei Artëmov & Franco Montagna - 1994 - Journal of Symbolic Logic 59 (4):1139-1153.
Fregean logics.J. Czelakowski & D. Pigozzi - 2004 - Annals of Pure and Applied Logic 127 (1-3):17-76.
Plural Grundgesetze.Francesca Boccuni - 2010 - Studia Logica 96 (2):315-330.

Analytics

Added to PP
2013-12-01

Downloads
26 (#835,533)

6 months
2 (#1,735,400)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

John L. Bell
University of Western Ontario

Citations of this work

What is neologicism?Bernard Linsky & Edward N. Zalta - 2006 - Bulletin of Symbolic Logic 12 (1):60-99.
Frege, Boolos, and logical objects.David J. Anderson & Edward N. Zalta - 2004 - Journal of Philosophical Logic 33 (1):1-26.
Tarski on “essentially richer” metalanguages.David DeVidi & Graham Solomon - 1999 - Journal of Philosophical Logic 28 (1):1-28.

Add more citations

References found in this work

Frege structures and the notions of truth and proposition.P. Aczel - 1980 - In Stephen Cole Kleene, Jon Barwise, H. Jerome Keisler & Kenneth Kunen (eds.), The Kleene Symposium: proceedings of the symposium held June 18-24, 1978 at Madison, Wisconsin, U.S.A. New York: sole distributors for the U.S.A. and Canada, Elsevier North-Holland.

Add more references