The Logic and Meaning of Plurals. Part II

Author: Yi, Byeong-uk

Source: Journal of Philosophical Logic, Volume 35, Number 3, June 2006 , pp. 239-288(50)

Publisher: Springer

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Abstract:

In this sequel to “The logic and meaning of plurals. Part I”, I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages.

Keywords: class; irreducibility of plurals; logic; model theory; natural language; non-axiomatizability of logic; plural; regimentation of plurals; second-order logic; semantics; set; singular; the many; the one