History and Philosophy of Logic 10 (2):131-164 (1989)

In this article I try to show the philosophical continuity of Russell's ideas from his paradox of classes to Principia mathematica. With this purpose, I display the main results (descriptions, substitutions and types) as moments of the same development, whose principal goal was (as in his The principles) to look for a set of primitive ideas and propositions giving an account of all mathematics in logical terms, but now avoiding paradoxes. The sole way to reconstruct this central period in Russell is to resort to unpublished manuscripts, which show the publications of these years to be the extremities of one same iceberg. Thus the logical problems (doubts about propositions, matrices and functions) are parallel to the ontological (the searching for genuine logical subjects) and methodological ones (the status of eliminative reduction). Paradoxes were the cause that the kind of (constructive) definition already applied by Russell, as an inheritance of Moorean analysis, obtained a new trait: ontological elimination, which, beginning with a ?no classes theory? and the theory of descriptions, led to a new theory of judgment (already present in manuscripts from 1906), ?incomplete symbols, and logical constructions
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DOI 10.1080/014453408908837147
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References found in this work BETA

Introduction to Metamathematics.Stephen Cole Kleene - 1952 - Princeton, NJ, USA: North Holland.
On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
Knowledge by Acquaintance and Knowledge by Description.Bertrand Russell - 1911 - Proceedings of the Aristotelian Society 11:108--28.
The Development of Logic.W. C. Kneale - 1962 - Oxford University Press.
Logic and Knowledge.BERTRAND RUSSELL - 1957 - Philosophical Quarterly 7 (29):374.

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