The paradoxes and Russell's theory of incomplete symbols

Philosophical Studies 169 (2):183-207 (2014)
Russell claims in his autobiography and elsewhere that he discovered his 1905 theory of descriptions while attempting to solve the logical and semantic paradoxes plaguing his work on the foundations of mathematics. In this paper, I hope to make the connection between his work on the paradoxes and the theory of descriptions and his theory of incomplete symbols generally clearer. In particular, I argue that the theory of descriptions arose from the realization that not only can a class not be thought of as a single thing, neither can the meaning/intension of any expression capable of singling out one collection (class) of things as opposed to another. If this is right, it shows that Russell’s method of solving the logical paradoxes is wholly incompatible with anything like a Fregean dualism between sense and reference or meaning and denotation. I also discuss how this realization lead to modifications in his understanding of propositions and propositional functions, and suggest that Russell’s confrontation with these issues may be instructive for ongoing research
Keywords Bertrand Russell  Paradox  Meaning  Class  Denoting  Language  Symbolism  Descriptions  Logic
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DOI 10.1007/s11098-013-0165-z
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References found in this work BETA
On Denoting.Bertrand Russell - 2005 - Mind 114 (456):873 - 887.
Basic Laws of Arithmetic.Gottlob Frege, Philip A. Ebert & Marcus Rossberg (eds.) - 2013 - Oxford University Press.
My Philosophical Development.Bertrand Russell - 1959 - London: Allen & Unwin.

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Reality is Not Structured.Jeremy Goodman - forthcoming - Analysis:anw002.

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