The number of lines in Frege proofs with substitution

Archive for Mathematical Logic 37 (1):15-19 (1997)
  Copy   BIBTEX

Abstract

. We prove that for sufficiently large \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $n$\end{document}, there are tautologies of size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $O$\end{document} that require proofs containing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $\Omega$\end{document} lines in axiomatic systems of propositional logic based on the rules of substitution and detachment.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,400

External links

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

Through your library

Similar books and articles

Frege on definitions.Sanford Shieh - 2008 - Philosophy Compass 3 (5):992-1012.
Frege's new science.G. Aldo Antonelli & Robert C. May - 2000 - Notre Dame Journal of Formal Logic 41 (3):242-270.
Remarks on Independence Proofs and Indirect Reference.Günther Eder - 2013 - History and Philosophy of Logic 34 (1):68-78.
Number: From the nyāya to Frege-Russell.J. L. Shaw - 1982 - Studia Logica 41 (2-3):283 - 291.
Identity, individuality, and unity.E. J. Lowe - 2003 - Philosophy 78 (3):321-336.
The Depth of Resolution Proofs.Alasdair Urquhart - 2011 - Studia Logica 99 (1-3):349-364.
Frege-Russell numbers: Analysis or explication?Erich Reck - 2007 - In The Analytic Turn. London: Routledge. pp. 33-50.

Analytics

Added to PP
2013-10-30

Downloads
16 (#670,075)

6 months
1 (#452,962)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Alasdair Urquhart
University of Toronto, St. George Campus

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references