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Meaning Relations, Possible Objects, and Possible Worlds

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Philosophical Problems in Logic

Part of the book series: Synthese Library ((SYLI,volume 29))


Our aims are threefold. First we shall present our philosophical approach to meaning and modality, and outline the formal semantics which it provides for modal logics (Sections I and II). Secondly, we shall show that for certain philosophical reasoning concerning truths ex vi terminorum, the logic of possible objects provides an explication where the logic of modal operators does not (Section III). Finally, we shall explore the extension of our theory to names and definite descriptions (Section IV).

The research for this paper was supported in part by NSF grant GS-1566. The first two parts of this paper comprise a brief presentation of the approach to meaning and modality developed in B. van Fraassen, ‘Meaning Relations Among Predicates’, Nous 1 (1967), 161–179 (henceforth MRP), and ‘Meaning Relations and Modalities’, presented at the APA (Eastern) Conference, Dec. 1968 (Nous 3 (1969), 155–167; henceforth MRM).

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  1. C. I. Lewis and C. H. Langford, Symbolic Logic, (Dover ed.) New York 1959, pp.66–70.

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  2. H. S. Leonard ‘Essences, Attributes and Predicates’, Proceedings and Addresses of the American Philosophical Association 37 (1964) 25–51.

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  3. So the conceptions of Kant’s Inaugural Dissertation and Wittgenstein’sTractatus relate to the former; Sellars’ ‘extra-conceptual’ possibilities to the latter.

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  4. See MRM. At the Irvine Colloquium we followed the exposition of MRM, and Dana Scott pointed out the elegance gained by not trying to represent natural modality at the same time. However, in the course of a philosophical retrenchment such as is attempted in MRM, due attention should be given to the peculiarities of natural modality.

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  5. Cf. R. Meyer and K. Lambert ‘Universally Free Logic and Standard Quantification Theory’ The Journal of Symbolic Logic 33 (1968) 8–26.

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  6. Cf. the discussion in R. H. Thomason, ‘Modal Logic and Metaphysics’ in The Logical Way of Doing Things (ed. by K. Lambert), New Haven (1969).

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  7. H. Putnam, ‘Reds, Greens, and Logical Analysis’, Philosophical Review 65 (1956) 206–217; A. Pap, ‘Once More: Colors and the Synthetic A Priori’, Philosophical Review 66 (1957), 94–99; H. Putnam, ‘Rejoinder to Arthur Pap’, Philosophical Review 66 (1957) 100–103.

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  8. This was suggested by Professor T. Drange, West Virginia University, to Profs. R. Meyer, Bryn Mawr College, and K. Lambert, who subsequently constructed the counterexample which follows.

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  9. S. A. Kripke, ‘A Completeness Theorem in Modal Logic’, Journal of Symbolic Logic 24(1959), 1–14.

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  10. See reference 7. This discussion concerns the kind of statements which provides the central examples in the debate about essentialism.

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  11. For explicit consideration of such stronger description theories, see our ‘On Free Description Theory’, Zeitschrift für math. Logik und Grundl. der Math. 13 (1967) 225–240.

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  12. See the paper cited in reference 11 and references therein.

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  13. Note that x = n may be true when n is a name, in which case n is the name of a subsistent; if E!x&x = n is true, n names an existent, and if □ x = n is true then n is the name of a substance.

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  14. See especially J. M. Dunn and N. D. Belnap, Jr. ‘The Substitution Interpretation of the Quantifiers’, Nous 2 (1968) 177–185, and H. Leblanc ‘A simplified account of validity and implication for quantificational logic’, Journal of Symbolic Logic 33 (1968) 231–235.

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  15. H. Leonard, ‘Essences, Attributes, and Predicates’, Proc. Amer. Philos. Assoc. (1964).

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  16. See Thomason, op. cit and ‘Some Completeness Results for Modal Predicate Calculi’ in the present volume, pp. 56–76. In this appendix we follow the more general exposition of MRM.

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© 1970 D. Reidel Publishing Company, Dordrecht, Holland

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Lambert, K., Van Fraassen, B.C. (1970). Meaning Relations, Possible Objects, and Possible Worlds. In: Lambert, K. (eds) Philosophical Problems in Logic. Synthese Library, vol 29. Springer, Dordrecht.

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