Polyadic Quantification via Denoting Concepts

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 ', `every ', and `any ' on the one hand, and `some ' and `a ' 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. What accounts for the expressive power of first-order polyadic quantification theory compared to its relatively impoverished monadic kin? The standard answer is that the former permits inter...

• Type: Journal
• Year: 2010
• Where: NDJFL
• Authors: Ori Simchen
• Keywords: Computer Networks, Expressive Power, First-order Polyadic Quantification, NDJFL 2010, Quantification Theory