Denoting Concepts and Ontology in Russell's Principles of Mathematics

Journal for the History of Analytical Philosophy 10 (7) (2022)
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Abstract

Bertrand Russell’s _Principles of Mathematics_ (1903) gives rise to several interpretational challenges, especially concerning the theory of denoting concepts. Only relatively recently, for instance, has it been properly realised that Russell accepted denoting concepts that do not denote anything. Such empty denoting concepts are sometimes thought to enable Russell, whether he was aware of it or not, to avoid commitment to some of the problematic non-existent entities he seems to accept, such as the Homeric gods and chimeras. In this paper, I argue first that the theory of denoting concepts in _Principles of __Mathematics_ has been generally misunderstood. According to the interpretation I defend, if a denoting concept shifts what a proposition is about, then the aggregate of the denoted terms will also be a constituent of the proposition. I then show that Russell therefore could not have avoided commitment to the Homeric gods and chimeras by appealing to empty denoting concepts. Finally, I develop what I think is the best understanding of the ontology of _Principles of __Mathematics_ by interpreting some difficult passages.

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Wouter Cohen
University of Manchester

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References found in this work

On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
Principles of Mathematics.Bertrand Russell - 1903 - New York,: Routledge.
My philosophical development.Bertrand Russell - 1959 - London,: Allen & Unwin.
The nature of judgment.G. E. Moore - 1899 - Mind 8 (2):176-193.

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