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  1. A new interpretation of russell's multiple-relation theory of judgment.Gregory Landini - 1991 - History and Philosophy of Logic 12 (1):37-69.
    This paper offers an interpretation of Russell's multiple-relation theory of judgment which characterizes it as direct application of the 1905 theory of definite descriptions. The paper maintains that it was by regarding propositional symbols (when occurring as subordinate clauses) as disguised descriptions of complexes, that Russell generated the philosophical explanation of the hierarchy of orders and the ramified theory of types of _Principia mathematica (1910). The interpretation provides a new understanding of Russell's abandoned book _Theory of Knowledge (1913), the 'direction (...)
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  • Russell's theory of types, 1901–1910: its complex origins in the unpublished manuscripts.Francisco A. Rodriguez Consuegra - 1989 - History and Philosophy of Logic 10 (2):131-164.
    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 (...)
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  • Russell, Presupposition, and the Vicious-Circle Principle.Darryl Jung - 1999 - Notre Dame Journal of Formal Logic 40 (1):55-80.
    Prompted by Poincaré, Russell put forward his celebrated vicious-circle principle (vcp) as the solution to the modern paradoxes. Ramsey, Gödel, and Quine, among others, have raised two salient objections against Russell's vcp. First, Gödel has claimed that Russell's various renderings of the vcp really express distinct principles and thus, distinct solutions to the paradoxes, a claim that gainsays one of Russell's positions on the nature of the solution to the paradoxes, namely, that such a solution be uniform. Secondly, Ramsey, Gödel, (...)
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  • On russell’s arguments for restricting modes of specification and domains of quantification.Bernhard Weiss - 1994 - History and Philosophy of Logic 15 (2):173-188.
    Russell takes his paper ?On denoting? to have achieved the repudiation of the theory of denoting concepts and Frege?s theory of sense, and the invention of the notion of incomplete symbols.This means that Russell attempts to solve the set theoretic and semantic paradoxes without making use of a theory of sense.Instead, his strategy is to revise his logical ontology by arguing that certain symbols should be treated as incomplete.In constructing such arguments Russell, at various points, makes use of epistemological and (...)
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