Strategies for a logic of plurals

Philosophical Quarterly

Volumn 51, Issue 204, 2001, Pages 289-306

  Oliver, Alex ^a   Smiley, Timothy ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746163553     PISSN: 00318094     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.0031-8094.2001.00231.x     Document Type: Article

References (46)

1. Popularly but wrongly attributed to Meinong. See T.J. Smiley, 'The Theory of Descriptions', Proceedings of the British Academy, 67 (1981), pp. 321-37, at pp. 324-5
2. See, e.g., Frege, Grundgesetze der Arithmetik, Vol. 1 (1893)
3. Frege, 'Logic in Mathematics' (1914), in his Posthumous Writings, ed. H. Hermes et al. (Oxford: Blackwell, 1979), pp. 203-50, at p. 227
4. See A. Morton, 'Complex Individuals and Multigrade Relations', Noûs, 9 (1975), pp. 309-18
5. M. Dummett, Frege: Philosophy of Mathematics (London: Duckworth, 1991), p. 93
6. See also J. Higginbotham and B. Schein, in 'Plurals', Proceedings of the North Eastern Linguistics Society, 19 (Univ. of Massachusetts, 1989), pp. 161-75, who argue that plural terms are predicative in nature and refer to concepts
7. Boolos' work on plurals can be found in 'To Be is to Be a Value of a Variable (or to Be Some Values of Some Variables)', Journal of Philosophy, 81 (1984), pp. 430-49
8. 'Nominalist Platonism', Philosophical Review, 94 (1985), pp. 327-44
9. and 'Reading the Begriffsschrift', Mind, 94 (1985), pp. 331-44
10. For some initial criticisms, see A. Oliver, 'Logic, Mathematics and Philosophy', British Journal for the Philosophy of Science, 51 (2000), pp. 857-73, §5
11. Frege, 'Logic in Mathematics', pp. 227-8
12. This was emphatically not some casual thought. He makes identical remarks about 'Bunsen and Kirchhoff laid the foundations of spectral analysis' in his letter to Russell of 28 July 1902: see his Philosophical and Mathematical Correspondence, ed. G. Gabriel et al. (Oxford: Blackwell, 1980), p. 140
13. For the true story, see A. Oliver, 'Frege and Dummett are Two', The Philosophical Quarterly, 44 (1994), pp. 74-82
14. See, e.g., G. Link, 'The Logical Analysis of Plurals and Mass Terms: a Lattice-Theoretical Approach', in R. Bäuerle, C. Schwarze and A. von Stechow (eds), Meaning, Use and Interpretation of Language (Berlin: De Gruyter, 1983), pp. 302-23
15. We owe the structure of this neat argument to P. Lasersohn, Plurality, Conjunction and Events (Dordrecht: Kluwer, 1995), pp. 96-104
16. Higginbotham, 'On Higher-Order Logic and Natural Language', in T.J. Smiley (ed.), Philosophical Logic (Oxford UP', 1998), pp. 1-27, at pp. 19-20
17. G. Massey, 'Tom, Dick and Harry, and All the King's Men', American Philosophical Quarterly, 13 (1976), pp. 89-107
18. Boolos, 'To Be is to Be a Value of a Variable', p. 448
19. For example, when sets imply sentences, implication ceases to be transitive and logical equivalence can no longer be defined as reciprocal implication. Even an author as astute as Hodges falls into this trap: see W. Hodges, Logic (Harmondsworth: Penguin, 1977), p. 128 (definition of |=), p. 133 (transitivity), and p. 136 (logical equivalence)
20. B. Bolzano, Paradoxes of the Infinite (1851), tr. D. Steele (London: Routledge & Kegan Paul, 1950), §3
21. D. Davidson, 'The Logical Form of Action Sentences', in N Rescher (ed.), The Logic of Decision and Action (Univ. of Pittsburgh Press, 1967), pp. 81-95
22. H.-N. Castañeda, 'Comments on Davidson's "The Logical Form of Action Sentences"', in Rescher (ed.), pp. 104-12
23. Davidson, 'Reply to Comments', in Rescher (ed.), pp. 115-20
24. Davidson, 'The Method of Truth in Metaphysics' (1977), repr. in his Inquiries into Truth and Interpretation (Oxford: Clarendon Press, 1984), pp. 199-214, at pp. 208-10
25. See J. McCawley, 'The Role of Semantics in a Grammar', in E. Bach and R. Harms (eds), Universals in Linguistic Theory (New York: Holt, Rinehart & Winston, 1968), pp. 124-69, at pp. 152-3
26. The idea also appeared independently in R. Bartsch, 'The Semantics and Syntax of Number and Numbers', in J. Kimball (ed.), Syntax and Semantics, Vol. 11 (New York: Seminar Press, 1973), pp. 55-93, at pp. 74-5. As it happens, both fail to include the 'No one else did' clause. We shall not press the opposite objection, that if 'The Fs φd', it need not be the case that every one of the Fs played a part in the φing (e.g., 'The Romans conquered Gaul')
27. Davidson, 'The Logical Form of Action Sentences', p. 93
28. Schein means to do this: 'All predicates are, first of all, about events' (Plurals and Events, p. 3)
29. And Higginbotham says that both he and Parsons had extended Davidson's analysis of action verbs to 'all predicates whatsoever': 'On Higher-Order Logic and Natural Language', p. 20
30. where he cites his 'On Semantics', Linguistic Inquiry, 16 (1985), pp. 547-93
31. and Parsons, Events in the Semantics of English (MIT Press, 1990). In fact, however, Parsons (p. 187) says that predicates involving common nouns 'probably do not pick out events or states'. And even for Schein, not all predicates are predicates of events. For he turns 'is one of into the converse of the predicative relation, and this has no new place for event terms
32. 'That it is meaningless (as Mr Bradley contends) to regard a class as being or not being a member of itself, must be assumed for the avoidance of a more mathematical contradiction; but I cannot see that this could be meaningless if there were such things as classes': Russell, 'Some Explanations in Reply to Mr Bradley', Mind, 19 (1910), pp. 373-8, at p. 376
33. E. Zermelo, 'Investigations in the Foundations of Set Theory, F (1908), tr. in J. van Heijenoort (ed.), From Frege to Gödel (Harvard UP, 1967), pp. 199-215, at p. 200
34. In his rejoinder to Oliver's 'The Logic of Plurals', presented at the Oxford Philosophy Society, May 1997
35. Various examples of 'collections': Parsons suggests an analysis of plural action sentences just like Castaneda's, except that he talks of groups instead of sets or sums. But he says next to nothing about the nature of them (Events in the Semantics of English, pp. 45-7)
36. McCawley, who, as we have observed, changes the subject to sets, explains that his sets are not the same as those of mathematics, since he has no empty set and ignores the difference between an individual and its singleton ('The Role of Semantics in a Grammar', p. 146)
37. Cresswell makes order count, for example, taking 'admire each other' to apply to ordered pairs: Semantical Essays: Possible Worlds and Their Rivals (Dordrecht: Kluwer, 1988), p. 138
38. David Lewis, who does, reformulates the argument using 'class-like thing' in place of 'set': Parts of Classes (Oxford: Blackwell, 1991), p. 68
39. D.M. Armstrong, Universals and Scientific Realism, I: Nominalism and Realism (Cambridge UP, 1978), p. 32
40. T. Burge, 'A Theory of Aggregates', Noûs, 11 (1977), pp. 97-117
41. F. Landman, 'Groups, I' and 'Groups, II', both in Linguistics and Philosophy, 12 (1989), pp. 559-605 and 723-44
42. J. Lønning, 'Collective Readings of Definite and Indefinite Noun Phrases', in P. Gärdenfors (ed.), Generalised Quantifiers (Dordrecht: Reidel, 1987), pp. 203-35
43. J.M.E. McTaggart, The Nature of Existence, Vol. 1 (Cambridge UP, 1921), ch. 15
44. R. Montague, unpublished notes quoted in R. Bartsch, 'The Semantics and Syntax of Number and Numbers', pp. 79-80
45. M. Resnik, 'Second-Order Logic Still Wild', Journal of Philosophy, 85 (1988), pp. 75-87
46. R. Schwarzschild, Pluralities (Dordrecht: Kluwer, 1996)