Abstract
If there is a doctrine shared by almost all analysts of the semantics of natural language in these days, it is the distinction between the different senses of “is”: the “is” of predication, the “is” of identity, and the “is” of existence. The “is” of predication is often called the copula. Some writers add an alleged “is” of class-inclusion as the fourth reading. The most forceful philosophical proponent of the ambiguity of “is” is undoubtedly Bertrand Russell. In The Principles of Mathematics 1 he writes:
The word is is terribly ambiguous, and great care is necessary in order not to confound its various meanings. We have (1) the sense in which it asserts Being, as in “A is”; (2) the sense of identity; (3) the sense of predication, in “A is human”; (4) the sense of “A is a-man” ... which is very like identity.2 In addition to these there are less common uses... where a relation of assertions is meant ... which ... gives rise to formal implication.
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Notes
The Principles of Mathematics (Cambridge University Press, London, 1903; reprinted, George Allen and Unwin, London, 1937); see p. 64, note.
Russell departs from the typical trichotomists and partially anticipates recent treatments of quantifies phrases. On the received view, Russell’s sense (4) has usually been assimilated to the “is” of predication. Fora discussion of some more recent views, see, e.g., Jaakko Hintikka,’Quantifiers in Logic and Quantifiers in Natural Languages’, in S. Körner, editor, Philosophy of Logic (Basil Blackwell, Oxford, 1976), pp. 208–232. A couple of years later Russell changed his mind on this point.
George Allen and Unwin, London, 1914, p. 50.
Frege’s achievement in creating the modern concept of a formal system — as well as his reasons for not discussing semantical matters systematically — are brought out very clearly by Jean van Heijenoort, ‘Logic as Language and Logic as Calculus’, Synthese, Vol. 17 (1967), pp. 324–330.
Cf. also Jean van Heijenoort, editor, From Frege to Gödel (Harvard University Press, Cambridge, Mass., 1967 ).
Frege discusses the different senses of verbs for being in ‘Ober Begriff and Gegenstand’, p. 194 of the original (pp. 43–44 of the Geach and Black translation).
None of these analysts of language has in so many words committed himself to first-order logic as his only canonical notation in semantics. In practice each one of them has nevertheless relied on first-order logic heavily and indeed well-nigh exclusively. The only one of these four scholars whose predilection for standard quantifications! logic is not conspicuous is Noam Chomsky. For evidence, I can now conveniently refer to his new book, Essays on Form and Intcrpremdon, North-Holland, Amsterdam 1977, especially his essay on “Conditions on Rules of Grammar” contained therein. For instance, on p. 197 Chomsky says that his analysis “is pretty much along the lines of standard logical analysis of the sentences of natural language”.
Donald Davidson’s allegiance to quantificational languages is motivated purely pragmatically, as shown by his note ‘Action and Reaction’, Inquiry, Vol. 13 (1970), pp. 140–148. There he points out that his position is even compatible with a relativity of logical form to the underlying logical theory. This point seems to anticipate some of the conclusions I will defend later in the present essay. The important but subtler differences between Davidson and myself in this respect need a longer discussion than I can launch here. (Cf. especially Section 12 below.)
Unsurprisingly, early Wittgenstein maintained the ambiguity of “is”; see Tractatus Logico-Phiosophicus, Kogan Paul, London, 1922, proposition 3.323.
See the papers collected in Esa Saarinen, editor, Game-Theoreticd Semantics (D. Reidel, Dordrecht, 1978), where further references to the literature are also provided. Cf. also Jon Barwise, ‘On Branching Quantifiers in English’, Journd of Philosophical Logic, Vol. 8 (1979), pp. 47–80.
Game-theoretical semantics is accordingly truth-conditional, as I believe every satisfactory semantics must be. Our game rules correspond to the recursive clauses of a Tarskl-type truth-definition. In both, the notions of truth and falsity are largely taken for granted in so far u they apply to atomic sentences, and the main problem is to extend them to other sentences. But the way this extension is accomplished is different in the two cases. In Tarski-type semantics, the recursive clauses which effect the extension apply from the inside out, whereas in game-theoretical semantics the rules have to be applied from the outside in. This has several important consequences, including the ability of game-theoretical semantics to cope with failures of compo-sitionality (also known as the Frege Principle). For such applications, see Jaakko Hintikka’s contribution to Philosophy and Grammar, edited by Stig Ranger and Sven Öhman (D. Reidel, Dordrecht, 1980 ). Also, Tarskl-type truth-definitions assume u it were the pobility of surveying the whole domain D at a glance (in effect, of quanti-fication over D), whereas in game-theoretical semantics we analyze further the specific process that connects the language in question with the reality it can be used to describe.
This fragment is not characterized here explicitly, for it does not matter for the theoretical conclusions of this paper precisely what is and is not included in it. For this theory, cf., e.g., R. Duncan Luce and Howard Raiffa, Games and Decisions ( John Wiley, New York, 1957 ).
This is a much taller order than might first appear. Sentences which are “semantic-ally atomic” in the sense-that their truth-values are determined by the interpretation of the nonlogical words they contain can be far from simple structurally. Unless some-thing more is said, we must for instance allow some “semantically atomic” sentences to be in the passive voice. It seems to me that the perfect complement to game-theoretical semantics as applied to English is Joan Bresnan’s recent theory of certain aspects of the lexical component of English grammar. (Most of it is unpublished; for a partial anticipation, see Joan Bresnan, ‘A Realistic Transformational Grammar’, in Morris Halle et aL, editors, Linguistic Theory and Psychological Reality, M.I.T. Press, Cambridge, Mass., 1978, pp. 1–59.) For Bresnan’s theory provides us with an account of the connections between different semantically atomic sentences which enables us to formulate their precise truth-conditions.
It is important to realize that these are not problems that absolutely have to be solved in order for game-theoretical semantics to be viable. For there is nothing intrinsically meaningless or unsatisfactory about infinite games. However, the psycho-linguistic plausibility of our semantical games would undoubtedly suffer if they could be infinitely long.
In the game rules, “X”, “Y”,… are linguistic rather than logical symbols, referring to linguistic expressions and at the same time acting as placeholders for them, as linguists are wont to expect their symbols to behave.
We also need ordering principles to tell the players in what order the several game rules have to be applied.
In Esa Saarinen, editor, op. cit. (note 6 above), and also in Avishai Margalit, editor, Meaning and Use (D. Reidel, Dordrecht, 1978 ).
See Peter Geach, ‘Good and Evil’, Analysis, VoL 17 (1956), pp. 33–42, and cf. George Curme, English Grammar (1947).
See note 14 above.
Cf., e.g., Edward S. Klima, ‘Negation in English’, in J. J. Katz and Jerry Fodor, editors, The Structure of Language (Prentice-Hall, Englewood Cliffs, N.J., 1964), pp. 246–323 (See especially p. 279 and the references given there in note 12) and Robert P. Stockwell, Paul Schachter, and Barbara Partee, The Major Syntactical Structures of English (Holt, Rinehart and Winston, New York, 1973 ), Chapter 5. “ See note 14 above.
A translation of this kind is part of the program of generative semanticists; cf. George Lakoff, ‘Generative Semantics’, in Danny D. Steinberg and Leon A. Jakobovits, editors, Semantics: An Interdisciplinary Reader (Cambridge U.P., Cambridge, 1971), pp. 232–296. Their theories cannot be considered satisfactory, however. Among other failures, they cannot explain any exceptions to the general ordering principles mentioned in Jaakko Hintikka’s earlier papers.
See Charles Kahn, The Verb “Be” in Ancient Greek (D. Reidel, Dordrecht, 1973); cf. also G. E. L. Owen, ‘Aristotle in the Snares of Ontology’, in R. Bambrough, editor, New Essays on Plato and Aristotle ( Routledge and Regan Paul, London, 1965 ), pp. 69–95.
See De sopkisticis elentchis 166b28–37, 168a34—b10; 169b4–6; 179a33–37.
David Hilbert and Paul Bemays, Grundlagen der Mathematik I—II (Springer, Berlin, 1934–39).
Richmond Thomason, editor, Formal Philosophy: Selected Papers of Richard Montague (Yale U.P., New Haven, 1974), especially Chapter 8.
Cf. SÖren Stenlund, Combinators, X-Terms and Proof Theory (D. Reidel, Dordrecht, 1972), and the references given there.
See Jerry Fodor, The Language of Thought (Thomas Y. Crowell, New York, 1975); and cf. Peter Geach, Mental Acts ( Routledge and Kegan Paul, London, 1957 ).
J. J. Katz, Semantic Theory ( Harper and Row, New York, 1972 ), pp. 3–7.
See Jean van Heijenoort, ‘Logic as Language and Logic as Calculus’, Synthese, Vol. 17 (1967), pp. 324–330.
See Joseph E. Stoy, Denotation! Semantics (MIT Press, Cambridge, Mass., 1977), and references given there to Scott’s work.
Cf., e.g., Jeffrey Pelletier, editor, Mass Terms (D. Reidel, Dordrecht, forthcoming) with a bibliography.
Cf., e.g., Renate Bartsch, Adverbialsemantik (Athenäum, Frankfurt am Main, 1972 ), Chapter 14; Renate Bartsch and Theo Venneman, Semantic Structures ( Athenäum, Frankfurt am Main, 1972 ), Chapter 2.
See Veikko Rantala, ‘Urn Models: A New Kind of Non-Standard Model For First-Order Logic’, Journd of Philosophical Logic, Vol. 4 (1975), pp. 455–474.
See note 6 above.
Acta Philosophcca Fennica, Vol. 28, No. 4 ( North-Holland, Amsterdam, 1976 ).
See, e.g., Knowledge and Belief ( Cornell U.P., Ithaca, N.Y., 1962 ).
See Hintikka (note 33 above), pp. 76–79.
Op. cit., pp. 72–74.
This follows from one of the conversational postulates discussed by Paul Grice, viz. from the one which enjoins a speaker not to make a weaker statement when he is in a position to make a stronger (and. relevant) statement. Hence the main phenomenon adduced by Lauri Karttunen as a reason for preferring his theory of questions, presented in Henry Hiz, editor, Questions (D. Reidel, Dordrecht, 1978), pp. 165–210, receives a most natural explanation on Hintíkka’s theory, too.
Op. cit., Chapters 6, 8–9.
This is not to say that speakers who have been brainwashed into relying on the framework of epistemic logic might not claim that English wh-questions are ambiguous, at least multiple ones. All that they would prove, however, is how easily affected and therefore frequently misleading our so-called intuitions are.
For the theoretical issues involved here, cf. op. cit., Chapters’ and II.
This example seems to originate from Emmon Bach’s unpublished note ‘Anti-pronominalization’ (Department of Linguistics, The University of Texas, January 15, 1969 ).
See The Semantics of Questions (note 33 above), pp. 115–119 and 147–149.
See C. L. Baker, ‘Notes on the Description of English Questions’, Foundations of Language, Vol. 6 (1970), pp. 197–219, for tests that can be used to distinguish free relative clauses from indirect questions, and for references to the linguistic literature relating to the distinction.
Emmon Bach, ’In Defense of Passive’ (unpublished).
Op. Cat. (note 33 above).
Charles Kahn, ‘Questions and Categories’, in Henry Hiz, editor, Questions (D. Reidel, Dordrecht, 1978 ), pp. 227–278.
This last section owes much to Steve Weis!et’s criticisms and comments. (One thing it does not owe to him are whatever mistakes it contains.)
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Hintikka, J. (1998). ‘Is’, Semantical Games, and Semantical Relativity. In: Paradigms for Language Theory and Other Essays. Jaakko Hintikka Selected Papers, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2531-6_4
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