Logic and Plurals

Abstract

Many natural languages contain plural vocabulary such as ‘we’, ‘those’, ‘the philosophers’, ‘cooperate’, and ‘gathered’. What is the correct logical analysis of sentences involving such vocabulary? Before we can attempt to answer the question, we need to comment briefly on how we understand logical analysis. Logical analysis generally proceeds by paraphrasing sentences of natural language in a way that provides a more perspicuous representation of logically relevant features of those sentences. Often, the paraphrase is given in a formal language that is equipped with a deductive system and a model-theoretic semantics. However, as Quine observed, “to paraphrase a sentence of ordinary language into logical symbols is virtually to paraphrase it into a special part still of ordinary or semi-ordinary language [...].” (Quine 1960: 159) This is because, in many important cases, the sentences of the formal language are obvious counterparts of particular sentences of natural language (or natural language augmented with some mathematical locutions). The process of paraphrase into a more logically perspicuous fragment of natural language is known as regimentation. [...] This is an Accepted Manuscript of a book chapter published by Routledge/CRC Press in The Routledge Handbook of Collective Intentionality. © 2017 Routledge