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

Kevin Klement
University of Massachusetts, Amherst
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 Interestingly, earlier unpublished manuscripts written by Russell between 1903 and 1905—surely unknown to Church—contain a more extensive anticipation of the essential details of the Lambda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

Principia Mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.

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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.
Russell's Ontological Development Reconsidered.Graham Stevens - 2010 - British Journal for the History of Philosophy 18 (1):113-137.

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