Philosophical Problems in Logic pp 1-19 | Cite as

# Meaning Relations, Possible Objects, and Possible Worlds

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## Abstract

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).

## Keywords

Modal Logic Singular Term Modal Qualifier Virtual Object Definite Description
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## References

- C. I. Lewis and C. H. Langford,
*Symbolic Logic*, (Dover ed.) New York 1959, pp.66–70.Google Scholar - 2.H. S. Leonard ‘Essences, Attributes and Predicates’,
*Proceedings and Addresses of the American Philosophical Association***37**(1964) 25–51.CrossRefGoogle Scholar - So the conceptions of Kant’s
*Inaugural Dissertation*and Wittgenstein’s*Tractatus*relate to the former; Sellars’ ‘extra-conceptual’ possibilities to the latter.Google Scholar - 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.Google Scholar
- 5.Cf. R. Meyer and K. Lambert ‘Universally Free Logic and Standard Quantification Theory’
*The Journal of Symbolic Logic***33**(1968) 8–26.CrossRefGoogle Scholar - 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).Google Scholar - 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.CrossRefGoogle Scholar - 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.Google Scholar
- 9.S. A. Kripke, ‘A Completeness Theorem in Modal Logic’,
*Journal of Symbolic Logic***24**(1959), 1–14.CrossRefGoogle Scholar - See reference 7. This discussion concerns the kind of statements which provides the central examples in the debate about essentialism.Google Scholar
- 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.Google Scholar - See the paper cited in reference 11 and references therein.Google Scholar
- 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.Google Scholar - 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.CrossRefGoogle Scholar - H. Leonard, ‘Essences, Attributes, and Predicates’,
*Proc. Amer. Philos. Assoc*. (1964).Google Scholar - 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.Google Scholar

## Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1970