Russell's 1903 - 1905 Anticipation of the Lambda Calculus

History and Philosophy of Logic 24 (1):15-37 (2003)

Authors
Kevin Klement
University of Massachusetts, Amherst
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 Interestingly, earlier unpublished manuscripts written by Russell between 1903 and 1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the Lambda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.
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DOI 10.1080/0144534031000076237
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References found in this work BETA

Philosophical and Mathematical Correspondence.Gottlob Frege, Gottfried Gabriel, Brian Mcguinness & Hans Kaal - 1982 - Revue Philosophique de la France Et de l'Etranger 172 (1):64-64.
Function and Concept.Gottlob Frege - 1997 - In D. H. Mellor & Alex Oliver (eds.), Properties. Oxford University Press. pp. 130-149.

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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.
Functions in Frege, Bolzano and Husserl.Stefania Centrone - 2010 - History and Philosophy of Logic 31 (4):315-336.
Abstraction in Fitch's Basic Logic.Eric Thomas Updike - 2012 - History and Philosophy of Logic 33 (3):215-243.

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