History and Philosophy of Logic 24 (1):15-37 (2003)
Authors |
|
Abstract |
Philosophy Dept, Univ. of Massachusetts, 352 Bartlett Hall, 130 Hicks Way, Amherst, MA 01003, USA Received 22 July 2002 It is well known that the circumflex notation used by Russell and Whitehead to form complex function names in Principia Mathematica played a role in inspiring Alonzo Church’s ‘Lambda Calculus’ for functional logic developed in the 1920s and 1930s. Interestingly, earlier unpublished manuscripts written by Russell between 1903 and 1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the Lambda Calculus. Russell also anticipated Scho¨nfinkel’s Combinatory Logic approach of treating multiargument functions as functions having other functions as value. Russell’s work in this regard seems to have been largely inspired by Frege’s theory of functions and ‘value-ranges’. This system was discarded by Russell due to his abandonment of propositional functions as genuine entities as part of a new tack for solving Russell’s paradox. In this article, I explore the genesis and demise of Russell’s early anticipation of the Lambda Calculus.
|
Keywords | No keywords specified (fix it) |
Categories | (categorize this paper) |
DOI | 10.1080/0144534031000076237 |
Options |
![]() ![]() ![]() ![]() |
Download options
References found in this work BETA
View all 42 references / Add more references
Citations of this work BETA
The Functions of Russell’s No Class Theory.Kevin C. Klement - 2010 - Review of Symbolic Logic 3 (4):633-664.
Russell, His Paradoxes, and Cantor's Theorem: Part II.Kevin C. Klement - 2010 - Philosophy Compass 5 (1):29-41.
The Paradoxes and Russell’s Theory of Incomplete Symbols.Kevin C. Klement - 2014 - Philosophical Studies 169 (2):183-207.
Functions in Frege, Bolzano and Husserl.Stefania Centrone - 2010 - History and Philosophy of Logic 31 (4):315-336.
Russell's Ontological Development Reconsidered.Graham Stevens - 2010 - British Journal for the History of Philosophy 18 (1):113-137.
View all 8 citations / Add more citations
Similar books and articles
Introduction to Combinators and (Lambda) Calculus.J. Roger Hindley - 1986 - Cambridge University Press.
A Modern Elaboration of the Ramified Theory of Types.Twan Laan & Rob Nederpelt - 1996 - Studia Logica 57 (2-3):243 - 278.
Recursion Theory and the Lambda-Calculus.Robert E. Byerly - 1982 - Journal of Symbolic Logic 47 (1):67-83.
Putting Form Before Function: Logical Grammar in Frege, Russell, and Wittgenstein.Kevin C. Klement - 2004 - Philosophers' Imprint 4:1-47.
Topological Representation of the Lambda-Calculus.Steve Awodey - 2000 - Mathematical Structures in Computer Science 10 (1):81-96.
Analytics
Added to PP index
2009-01-28
Total views
67 ( #148,735 of 2,410,259 )
Recent downloads (6 months)
2 ( #346,720 of 2,410,259 )
2009-01-28
Total views
67 ( #148,735 of 2,410,259 )
Recent downloads (6 months)
2 ( #346,720 of 2,410,259 )
How can I increase my downloads?
Downloads