Bernard Linsky
University of Alberta
This note presents a transcription of Russell's letter to Hawtrey of 22 January 1907 accompanied by some proposed emendations. In that letter Russell describes the paradox that he says "pilled" the "substitutional theory" developed just before he turned to the theory of types. A close paraphrase of the derivation of the paradox in a contemporary Lemmon-style natural deduction system shows which axioms the theory must assume to govern its characteristic notion of substituting individuals and propositions for each other in other propositions. Other discussions of this paradox in the literature are mentioned. I conclude with remarks about the significance of the paradox for Russell.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Reprint years 2002, 2003
DOI 10.15173/russell.v22i2.2026
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: 60,795
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

Why Ramify?Harold T. Hodes - 2015 - Notre Dame Journal of Formal Logic 56 (2):379-415.
The Functions of Russell’s No Class Theory.Kevin C. Klement - 2010 - Review of Symbolic Logic 3 (4):633-664.

Add more citations

Similar books and articles

Russell's Substitutional Theory of Classes and Relations.Gregory Landini - 1987 - History and Philosophy of Logic 8 (2):171-200.
Variable, Structure, and Restricted Generality.S. Gandon - 2013 - Philosophia Mathematica 21 (2):200-219.
The 1900 Turn in Bertrand Russell’s Logic, the Emergence of His Paradox, and the Way Out.Nikolay Milkov - 2017 - Siegener Beiträge Zur Geschichte Und Philosophie der Mathematik 7:29-50.
Zermelo and Russell's Paradox: Is There a Universal Set?G. Landini - 2013 - Philosophia Mathematica 21 (2):180-199.
On Russell's Vulnerability to Russell's Paradox.James Levine - 2001 - History and Philosophy of Logic 22 (4):207-231.
New Evidence Concerning Russell's Substitutional Theory of Classes.Gregory Landini - 1989 - Russell: The Journal of Bertrand Russell Studies 9 (1):26.
Intuition and Russell´s Paradox.Margaret Cuonzo - 2001 - Principia: Revista Internacional de Epistemologia 5 (1-2):73-85.
Relatives of the Russell Paradox.Kees Doets - 1999 - Mathematical Logic Quarterly 45 (1):73-83.
Russell's Way Out of the Paradox of Propositions.André Fuhrmann - 2002 - History and Philosophy of Logic 23 (3):197-213.


Added to PP index

Total views
7 ( #1,023,009 of 2,438,737 )

Recent downloads (6 months)
1 ( #436,491 of 2,438,737 )

How can I increase my downloads?


My notes