¹ This work was supported in part by the U. S. Army Signal Corps, the Air Force Office of Scientific Research, and the Office of Naval Research; and in part by the National Science Foundation (Grant G-13903).

² There are exceptions, such as sentences with technical words that the speaker does not know and sentences too long for the speaker to scan in his lifetime. But these exceptions are of no systematic importance. Analogously, a person's mastery of an algorithm for propositional calculus can be said to exhibit itself in his ability to decide mechanically whether any well-formed formula of propositional calculus is a tautology, even though some well-formed formulae are too long for human processing, etc.

³ A solution to the projection problem is certainly less than a full theory of speech. In particular, it does not provide a theory of speech production (or recognition). The difference between a description of a language and a theory of speech production is the difference between asking for a characterization of the rules of language which a speaker knows and asking for an account of how he actually applies those rules in speaking. Some things left out by the first theory but not by the second are considerations of the psychological parameters of speech production (e.g. limitations of immediate memory, level of motivation), and developmental accounts of the way the child becomes a fluent speaker (by conditioning? by the exploitation of innate mechanisms? by some combination of innate endowment and learning?). Though such problems concerning speech production lie outside the scope of a theory of a language, such a theory is essential to a theory of speech production. It is first necessary to know what is acquired and used before it is sensible to ask how it is acquired and used.

⁴ This conception of grammar is due to Chomsky. Cf. Syntactic structures² ('s-Gravenhage, 1962); 'Three models for the description of language', I.R.E. transactions on information theory: Vol. IT-2, Proceedings of the Symposium on Information Theory (Sept. 1956). For a bibliography on transformational grammar, see Chomsky, ‘On the notion “rule of grammar” ‘, Structure of language and its mathematical aspects: Proceedings of symposia in applied mathematics 12.16 fn. 24 (1961).

⁵ Moreover, sentences that receive the same structural description may differ in that one is semantically ambiguous or anomalous but the other is not. Compare The bill is large, The paint is silent, and The street is wide, all of which receive the same structural description from the grammar.

⁶ Cf. Syntactic structures, Appendix II, for the transformations which relate these sentences.

⁷ Semantic type oddity is precluded by the assumption that IS contains at least one reading.

⁸ In the case where a sentence has exactly one reading in IS, i.e. is unambiguous, that reading must by the theory be assigned to the sentence in each and every normal setting.

⁹ Take the following example. Let m be a one-to-one mapping of the set of English sentences onto itself such that the image of each sentence is a sentence which differs from it in meaning. Then the sentence The sentence S which immediately follows this sentence is to be understood as m(S). is a setting such that the meaning of a sentence occurring in it is not one of the meanings of that sentence in isolation.

¹⁰ We express our gratitude to David Bellugi for referring us to My little golden book of jokes (New York, 1961), from which these examples are drawn.

¹¹ We have convinced ourselves of the truth of this claim by making it the basis of a party game. One person supplies a fact, however obscure, and the others try to construct a sentence which that fact disambiguates. The game is not remarkably amusing, but it is surprisingly convincing.

¹² For examples of studies toward a theory of this kind, cf. Z. S. Harris, ‘Discourse analysis’, Lg. 26.1–30 (1952); H. Herzberger, Contextual analysis (Princeton University dissertation 1957).

¹³ The qualification ‘mechanically’ is important: it precluded the employment of linguistic skills not represented by the grammar or the dictionary. It is precisely the possession of such skills that distinguishes the fluent speaker from the nonspeaker equipped with a grammar and a dictionary. Hence, the degree to which the nonspeaker is permitted access to such skills is the degree to which we obscure what must be accounted for. Conversely, by prohibiting their employment, as we do by the qualification ‘mechanically’, we bring into clear relief the skills that a semantic theory of a natural language must account for.

¹⁴ The distinction between the dictionary and the rules for its application corresponds, in psychological terms, to a difference between mental processes. The dictionary is something that the speaker learns item by item, more or less by rote, and is constantly learning more of. Knowledge of the rules for applying the dictionary, on the other hand, is gained early and in toto, and comes into play whenever a speaker uses his language. Correspondingly, the use of what is learned in learning a dictionary depends on recalling relatively independent bits of information. The rules involve the exercise of a faculty for coding and decoding linguistic information; they organize whatever systematic, nongrammatical information the speaker has about his language and are thus, in the strongest sense, essential to a knowledge of the language. To know a natural language one must know these rules, but one need not know more than a small fraction of its vocabulary.

¹⁵ Our sources for dictionary information throughout this paper have been The shorter Oxford English dictionary and Webster's new collegiate dictionary.

¹⁶ In the entries for some lexical items, there will be paths in which the lowest semantic marker dominates nothing, i.e. paths which do not terminate in distinguishes. Such lexical items have special theoretical significance: they are the natural language's representation of semantic categories. Cf. J. J. Katz and J. A. Fodor, ‘Categories’, unpublished.

¹⁷ For further specification of what semantic features of a sentence can be marked in terms of the output of a semantic theory cf. J. J. Katz, ‘Analyticity and contradiction in natural language’, to be published in 1963.

¹⁸ It can be argued on grammatical grounds that the phrase the colorful ball should be represented simply as :

i.e. without the internal syntactic structure it is given in Fig. 9. This representation does not include the information (required by the projection rules) that colorful is a modifier of the head ball. But the need for this sort of information does not commit us to the assumption that all branching in derived constituent structure trees is binary. For such information can be obtained by examining the transformational history of the sentence. This is a typical case of the way a projection rule can use information taken from the transformational history of the sentences to which it is applied.

¹⁹ It should be made clear that the rules we shall give are not intended as a contribution to a semantic theory of English but only as examples of the type of rules that such a theory would employ.

²⁰ The reason why Ω₁ appears in the output of (R₁) is that some heads are, in turn, modifiers of other heads; e.g. adjectives are heads for adverbs and also modifiers for nouns: (light (red)) ball. In these cases, the conditions in Ω₁ will be required for selection.

²¹ R. B. Lees, The grammar of English nominalizations xvii-xviii (UAL 26:3, 1960).

²² Cf. J. J. Katz, ‘Analyticity and contradiction in natural language’, to appear in Readings in the philosophy of language.

²³ In taking NP_c as part of the sequence of grammatical markers in the dictionary entry for the, we are not claiming that the is a concrete noun phrase, but only that it occurs as an element of a concrete noun phrase and that, when it does, it has the sense in P ₁. This constitutes an extension of the notion of a ‘part of speech’ classification, but a natural and necessary one.

²⁴ Here some explanation is called for. (Instancy) is assigned to verbs representing durationless events. Any sentence whose main verb is marked (Instancy) which is of the form Subject + Verb + ed + Object + for + numerical quantifier + measure of time will be understood to mean that the object was verbed more than once. Compare He hit the ball for three hours with He studied the book for three hours. Next, (Intensity) is assigned to verbs taking adverbs like hard, soft, gently. Finally, the marker (Improper Part) is assigned to lexical items that represent wholes which the language contrasts with their parts. The term ‘Improper Part’ is borrowed from James Thomson.

²⁵ For the background of this point cf. Fodor, ‘Projection and paraphrase in semantics’, Analysis 21:4. 73–7 (1961), and Katz, ‘A reply to “Projection and Paraphrase in Semantics” ‘ Analysis 22:2.36–41 (1961).

²⁶ In these instances too, if both active and passive have the same meaning because both are ambiguous.

²⁷ We can highlight the difference between theories containing only type 1 rules and theories containing rules of both type 1 and type 2 by contrasting the ways that they would deal with relative clause constructions. A theory containing only type 1 rules would determine from the transformational history of a sentence containing such a construction which nominal the relative suppresses, and would then treat the relative clause as an adjectival on that nominal, with amalgamation proceeding in the normal way. A theory containing both types of rules would first provide an interpretation for the matrix sentence and the embedded sentence which underlie the sentence containing the relative clause, and would then convert the semantic interpretations of the source sentences into a semantic interpretation of the sentence containing the relative.

²⁸ The conception of a metatheory for semantics which is sketched below is adapted from Chomsky's conception of a metatheory for grammar, which he refers to as ‘linguistic theory’. Cf. Syntactic structures, and The logical structure of linguistic theory (microfilm).

²⁹ It is not at all clear that the request for such a criterion is a reasonable one. Would one ask for an analogous criterion to distinguish the concepts of physics from those of chemistry?

³⁰ Lees, The grammar of English nominalizations 14.