Florida Philosophical Review 12 (1):83-92 (2011)

Burkay Ozturk
Texas State University
This paper deploys a Cantor-style diagonal argument which indicates that there is more possible mathematical content than there are propositional functions in Russell and Whitehead's Principia Mathematica and similar formal systems. This technical result raises a historical question: "How did Russell, who was himself an expert in diagonal arguments, not see this coming?" It turns out that answering this question requires an appreciation of Russell's understanding of what logic is, and how he construed the relationship between logic and Principia Mathematica.
Keywords Principia Mathematica  expressive completeness  incompleteness  cantor  diagonalization  Godel  Russell  Whitehead
Categories (categorize this paper)
Reprint years 2012
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy

 PhilArchive page | Other versions
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

My Philosophical Development.B. RUSSELL - 1958 - Hibbert Journal 57:2.
My Philosophical Development.Morris Weitz & Bertrand Russell - 1961 - Philosophical Review 70 (1):112.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Russell's Completeness Proof.Peter Milne - 2008 - History and Philosophy of Logic 29 (1):31-62.
The Versatility of Universality in Principia Mathematica.Brice Halimi - 2011 - History and Philosophy of Logic 32 (3):241-264.
The Logic of "Principia Mathematica".Darryl Jung - 1995 - Dissertation, Massachusetts Institute of Technology
Proper Definition in "Principia Mathematica".C. G. Morgan - 1973 - International Logic Review 7:80.
Principia Mathematica Centenary.Ronny Desmet - 2010 - Process Studies 39 (2):225-263.
The Propositional Logic of "Principia Mathematica" and Some of its Forerunners.Daniel J. O' Leary - 1988 - Russell: The Journal of Bertrand Russell Studies 8 (1):92.
Quantification Theory in *9 of Principia Mathematica.Gregory Landini - 2000 - History and Philosophy of Logic 21 (1):57-77.
Principia Mathematica Vol. Iii.A. N. Whitehead & B. Russell - 1913 - Cambridge University Press.
Principia Mathematica Vol. Ii.A. N. Whitehead & B. Russell - 1912 - Cambridge University Press.


Added to PP index

Total views
157 ( #74,713 of 2,508,046 )

Recent downloads (6 months)
10 ( #72,416 of 2,508,046 )

How can I increase my downloads?


My notes