Notre Dame Journal of Formal Logic

Polyadic Quantification via Denoting Concepts

Ori Simchen


The question of the origin of polyadic expressivity is explored and the results are brought to bear on Bertrand Russell's 1903 theory of denoting concepts, which is the main object of criticism in his 1905 "On Denoting." It is shown that, appearances to the contrary notwithstanding, the background ontology of the earlier theory of denoting enables the full-blown expressive power of first-order polyadic quantification theory without any syntactic accommodation of scopal differences among denoting phrases such as 'all φ', 'every φ', and 'any φ' on the one hand, and 'some φ' and 'a φ' on the other. The case provides an especially vivid illustration of the general point that structural (or ideological) austerity can be paid for in the coin of ontological extravagance.

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Notre Dame J. Formal Logic Volume 51, Number 3 (2010), 373-381.

First available in Project Euclid: 18 August 2010

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Zentralblatt MATH identifier

Primary: 01A60: 20th century 03B10: Classical first-order logic

polyadic quantification Russell denoting


Simchen, Ori. Polyadic Quantification via Denoting Concepts. Notre Dame J. Formal Logic 51 (2010), no. 3, 373--381. doi:10.1215/00294527-2010-023.

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