Russell's substitutional theory of classes and relations

History and Philosophy of Logic 8 (2):171-200 (1987)
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Abstract

This paper examines Russell's substitutional theory of classes and relations, and its influence on the development of the theory of logical types between the years 1906 and the publication of Principia Mathematica (volume I) in 1910. The substitutional theory proves to have been much more influential on Russell's writings than has been hitherto thought. After a brief introduction, the paper traces Russell's published works on type-theory up to Principia. Each is interpreted as presenting a version or modification of the substitutional theory. New motivations for Russell's 1908 axiom of infinity and axiom of reducibility are revealed

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Author's Profile

Gregory Landini
University of Iowa

References found in this work

Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
The Principles of Mathematics.Bertrand Russell - 1903 - Cambridge, England: Allen & Unwin.
Knowledge by acquaintance and knowledge by description.Bertrand Russell - 1911 - Proceedings of the Aristotelian Society 11:108--28.
Principia mathematica.A. N. Whitehead - 1926 - Mind 35 (137):130.

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