Abstract
Logical syntax and semantics constitute a very central part of modern logical theory. Syntax is concerned exclusively with the signs or expressions of a language and their interconnections. In semantics, on the other hand, we are interested not only in signs and their interconnections but also in the relationships between signs and the objects which they designate or denote or stand for in one way or another. Such a semantics is a denotational or designational semantics. A second branch of semantical theory is concerned not only with denotation but with the meaning or intension of expressions. Such a theory is sometimes called an intensional semantics. We know a good deal about denotational semantics, thanks to the work of Carnap, Kotarbiński, Tarski, and others. In a sense, denotational semantics may now be regarded as a completed body of theory. The study of intensions, however, is in its infancy, and indeed it can be said safely that at the present time we have no fully satisfactory semantical theory of intensions at all.
Supported by a grant from the National Science Foundation, Grant No G9737. This paper contains a preliminary version of some of the material in the author’s Intension and Decision, a Philosophical Study, Prentice-Hall, New York, to appear.
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References
Cf. Carl G. Hempel, Fundamentals of Concept Formation in Empirical Science (International Encyclopedia of Unified Science, Vol. II, No. 7), University of Chicago Press, Chicago, 1952, p. 14 and passim.
R. Carnap, Meaning and Necessity, 2nd ed., University of Chicago Press, Chicago, 1956; and A. Church, ‘A Formulation of the Logic of Sense and Denotation’ in Structure, Method, and Meaning, Essays in Honour of Henry M. Sheffer, Liberal Arts Press, New York, 1951, pp. 3–24 and The Need for Abstract Entities in Semantic Analysis,’ Proceedings of the American Academy of Arts and Sciences 80 (1951) 100–112.
Holt, New York, 1957, pp. 234–254.
Cf. the author’s Truth and Denotation, A Study in Semantical Theory, University of Chicago Press, Chicago; University of Toronto Press, Toronto and Routledge and Kegan Paul, London, 1958, pp. 151–159.
The notation “F(F Com G) ” reads: the class of all classes F such that Fis common to G. The circumflex, often used as the notation for class abstraction, omitted here and troughout.
Cf. DesR3, Truth and Denotation, p. 168.
The “H” in the so-called assertion sign applying to the symbolic context following it and indicating that that context is a theorem in the language at hand.
The Notion of Analytic Truth, University of Pennsylvania Press, Philadelphia and Oxford University Press, London, 1959; and Toward a Systematic Pragmatics (Studies in Logic and the Foundations of Mathematics), North-Holland Publishing Co., Amsterdam, 1959. On page 28 of the former, line 22, please insert“ ~ (Ed’)d’ Occb c” after the first “b”. Also please note that the first and third definitions on page 78 of the latter are slightly too broad but may easily be emended.
For a full discussion of structural descriptions and concatenation see Truth and Denotation, pp. 70–90 and pp. 156–157.
Note that the total strict intension of a in this sense would be essentially what is called the absolute quasi-intension of a, as defined in Toward a Systematic Pragmatics, p. 88.
It is to assure that “Mms” is analytic that descriptions are taken here as primitive.
Cf. B. Russell, An Inquiry into Meaning and Truth, Norton, New York, 1940, p. 209
R. Carnap, Meaning and Necessity, p. 152
W. V. Quine, ‘Notes on Existence and Necessity’, Journal of Philosophy 40 (1943) 120; and Toward a Systematic Pragmatics, pp. 91–92. Concerning virtual classes, see Truth and Denotation, pp. 49–52 and p. 106 f.
Cf. Truth and Denotation, pp. 278–281, for an analogous argument.
We shall utilize informally some suitable adaptation of Carnap’s theory of confirmation, as applied to the object-language at hand. See R. Carnap, Logical Foundations of Probability, University of Chicago Press, Chicago, 1950.
The notion of being a moment is definable within the underlying theory of time. SeeToward a Systematic Pragmatics, pp. 36–37. Cf. also J. H. Woodger, The Technique of Theory Construction (International Encyclopedia of Unified Science, Vol. II, No. 5), University of Chicago Press, Chicago, 1939, pp. 32–33 andThe Axiomatic Method in Biology, Cambridge University Press, London, 1937, p. 56 ff.
Cf. especially D. Davidson, J. C. C. Mckinsey, and P. Suppes, ‘Outlines of a Formal Theory of Value I’, Philosophy of Science 22 (1955) 140–160.
2nd ed., Princeton University Press, Princeton, 1947.
Cf. Davidson, etc., op. cit., p. 156. A sentence is LFls (logically false) if and only if its negation is analytic.
Pp 47–49.
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© 1964 D. Reidel Publishing Company/Dordrecht-Holland
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Martin, R.M. (1964). Toward A Logic of Intensions. In: Gregg, J.R., Harris, F.T.C. (eds) Form and Strategy in Science. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-3603-0_12
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