Strategies for a Logic of Plurals

• Published in: The Philosophical quarterly Vol. 51; no. 204; pp. 289 - 306
• Main Authors: Oliver, Alex, Smiley, Timothy
• Format: Journal Article
• Language: English
• Published: Oxford, UK and Boston, USA Blackwell Publishers 01.07.2001; Blackwell Publishers Ltd; Blackwell; Oxford University Press
• Subjects: Abstract objects; Grammar; Mathematical logic; Mathematical relations; Mathematical set theory; Mathematical sets; Mathematics; Numbers; Philosophical analysis; Philosophical logics. Philosophy of language; Philosophical object; Philosophy; Predicates; Semantics; Singular terms; Singular; Russell (B.); Frege (G.); Whitehead (A. N.); Abstract; Combination; Reference; Collection; Logics; Predicate Calculus; Concrete; Identity
• ISSN: 0031-8094; 1467-9213
• DOI: 10.1111/j.0031-8094.2001.00231.x

English has plural terms (e.g., ‘Oliver and Smiley’, ‘the co‐authors of this paper’) as well as singular terms. But our standard formal languages, e.g., the predicate calculus, feature only singular terms. How can the plural idiom be formalized?‘Changing the subject’ is by far the most common plurals strategy among both philosophers and linguists: a plural term is replaced by a singular term standing for some complex object (a set or an aggregate) that ‘contains’ the individuals to which the plural term alludes. For example, one might simply replace ‘A, B imply C’ with ‘{A, B} implies [singular] C’. We uncover a surprising variety of ways to change the subject, of ever‐increasing complexity and ingenuity. Our question is whether any can made to work.