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On plural reference and elementary set theory

Helen Morris Cartwright

Synthese 96 (2):201 - 254 (1993)

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A note on plural pronouns.H. M. Cartwright - 2000 - Synthese 123 (2):227 - 246.details Gareth Evans'' proposal, as amended by Steven Neale –that a definite pronoun with a quantifiedantecedent that does not bind it has the sense ofa definite description – has been challenged inthe singular case by appeal to counter-examplesinvolving failure of the uniqueness condition forthe legitimacy of a singular description. Thischallenge is here extended to the plural.Counter-examples are provided by cases in which aplural description `the Fs'' does not denote,despite the propriety of the use of `they'' or`them'' it is to replace, because (...) Download Export citation Bookmark
Plural quantification and classes.Gabriel Uzquiano - 2003 - Philosophia Mathematica 11 (1):67-81.details When viewed as the most comprehensive theory of collections, set theory leaves no room for classes. But the vocabulary of classes, it is argued, provides us with compact and, sometimes, irreplaceable formulations of largecardinal hypotheses that are prominent in much very important and very interesting work in set theory. Fortunately, George Boolos has persuasively argued that plural quantification over the universe of all sets need not commit us to classes. This paper suggests that we retain the vocabulary of classes, but (...) Download Export citation Bookmark 36 citations
Reciprocity and Cumulative Predication.Wolfgang Sternefeld - 1998 - Natural Language Semantics 6 (3):303-337.details This paper investigates different readings of plural and reciprocal sentences and how they can be derived from syntactic surface structures in a systematic way. The main thesis is that these readings result from different ways of inserting logical operators at the level of Logical Form. The basic operator considered here is a cumulative mapping from predicates that apply to singularities onto the corresponding predicates that apply to pluralities. Given a theory which allows for free insertion of such operators, it can (...) Download Export citation Bookmark 36 citations
Mathematical determinacy and the transferability of aboutness.Stephen Pollard - 2007 - Synthese 159 (1):83-98.details Competent speakers of natural languages can borrow reference from one another. You can arrange for your utterances of ‘Kirksville’ to refer to the same thing as my utterances of ‘Kirksville’. We can then talk about the same thing when we discuss Kirksville. In cases like this, you borrow “ aboutness ” from me by borrowing reference. Now suppose I wish to initiate a line of reasoning applicable to any prime number. I might signal my intention by saying, “Let p be (...) Download Export citation Bookmark 3 citations
Plurals and complexes.Keith Hossack - 2000 - British Journal for the Philosophy of Science 51 (3):411-443.details Atomism denies that complexes exist. Common-sense metaphysics may posit masses, composite individuals and sets, but atomism says there are only simples. In a singularist logic, it is difficult to make a plausible case for atomism. But we should accept plural logic, and then atomism can paraphrase away apparent reference to complexes. The paraphrases require unfamiliar plural universals, but these are of independent interest; for example, we can identify numbers and sets with plural universals. The atomist paraphrases would fail if plurals (...) Download Export citation Bookmark 50 citations

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