1 The primary source is “The logical Form of Action Sentences,” in Rescher, N. (ed) The Logic of Decision and Action (U. of Pittsburgh Press, Pittsburgh, 1968).Google Scholar

2 See Montague, R., “English as a Formal language,” reprinted in Formal Philosophy (Yale U. P., New Haven, 1974);Google Scholar also Parsons, T., “Some Problems Concerning the logic of Grammatical Modifiers,” in Davidson, D. and Harman, G. (eds), Semantics of Natural Language (Reidel, Dordrecht, 1972).Google Scholar

3 Davidson (op. cit.) took this to show that the intended analysis does not apply to adverbs like ‘intentionally'.

4 Davidson's original proposal was not subject to this particular objection since, when a verb has a direct object, he used a single three-place predicate in place of the three that I have used. E.g. he would have written Flipping(e, s, me) for ‘e is a flipping of s by me'. This, however, is subject to various objections. First, in some languages the roles of subject and direct object are treated on a par with the roles of certain prepositional objects (i.e. what we would write in English using prepositions); instead of using sentence position and/or prepositions to tell what a noun phrase is doing, the words have case engings which indicate this. Second, Davidson's original analysis cannot be extended as indicated in foot· note 21 below. And third, John Wallace has shown that similar difficulties arise even with prepositions. E.g. if I hit the eight-ball into the corner pocket, and, ‘in one and the same action’ hit the seven-ball into the side pocket, then, if there is really only one action involved, we can infer (from Davidson's symbolization) that I hit the eight-ball into the side pocket and the seven-ball into the corner pocket U. Wallace, “On What's Happening,” dittograph). I will suggest below that we keep the analysis while giving up the view that the two hittings are identical.

5 See Davidson, op. cit. p. 84.

6 The problem cannot be avoided by symbolizing the sentence with the operators in the opposite order, i.e. as In (p) (Y(W))j, for now we are not able to infer ln(p) (W) J with the rules already at hand. We could perhaps introduce a general principle of permutation for standard operators, which would allow us to switch their order and then utilize the rule that lets us drop intitial standard operators, but I think it is clear that we would Just be trying to encode the fact that we actually have underlying conjunctions, as in the event approach.

7 I am interested here in the de re reading of the sentence.

8 Lambda conversion is the principle that takes you from a formula of the form ƛxØ(a) to whatever you get by replacing free occurrences of x in Ø by a. There is a good introduction to the use of lambda abstracts in D. Dowty, A Guide to Montague's PTQ (Indiana University Linguistics Club).

9 Applying the operators in the opposite order would yield a logically equivalent analysis.

10 With certain auxiliary hypotheses this proposal will have certain consequences for the individuation of events. Suppose that phrases like ‘Mary's arriving late’ or 'John's whipping (of) the cream’ name events, and suppose that at the relevent time or times that Mary only arrived once and John only whipped the cream once. Then consider the following auxiliary hypothesis: the predicate of events that appears in the symbolization of nonintensional adverbials is the same as the predicate of events that appears in the symbolization of the etymologically related predicative adjectives. For example, ‘slow’ and ‘slowly’ contribute the same predicate of events to their translations, and so do ‘in the park’ (used adverbially) and ‘in the park’ (used adjectivally). The assumptions will then yield useful equivalences, such as:

11 In R. Montague, “The Proper Treatment of Quantification in Ordinary English,“ in Formal Philosophy, op. cit. Hereafter this work will be referred to as “Montague (PTQ)”.

12 Throughout this section I am indebted to E. Bach, Topics in English Metaphysics, 1979 draft. The word ‘eventuality’ is due to Bach. The ontological assumptions discussed in this section need much more development than they are given here; this is impossible here because of lack of space. I think something is to be gained, however, by linking up such an ontology with language, as I do below, for we can then exploit our understanding of English to see what the ontology would have to be like in order for it to provide the framework for a theory of the sort I am proposing. I have omitted facts and propositions from the ontology only because I am concentrating on aspects of language that do not require reference to them.

13 In particular, the occurence·time of an eventuality will (in simple cases) be the time at which a present·tense sentence which ‘reports’ the eventuality becomes true, and the time after which the correlated past-tense sentence becomes true. When I discuss present-tense sentences I always have in mind the ‘narrative present’ usage (what Barbara Partee calls the ‘sports announcer usage’), in which the speaker reports on what is happening at the time of utterance. The English present tense is more often used in other ways (e.g. to ascribe dispositions); I will not discuss these other uses at all.

14 There is quite a literature based on the idea that the truth (at a time) of a progressive sentence (e.g. ‘Agatha is building a house’) ought to be definable in terms of the truth (at some times or other) of the correlated nonprogressive sentence ('Agatha builds a house’). This idea seems inconsistent with the fact that it can be true that Agatha was building a house when she died, yet never true that she built a house. (Cf. Bennett, M. and Partee, B., Toward the Logic of Tense and Aspect in English (Indiana University Linguistics Club, 1978.Google Scholar) I think that the relation is rather this: events have two ‘parts', the development and the occurrence part, and the latter may be absent without the event failing to exist. (This involves distinguishing the existence of an event from its ‘occurrence'.) The progressive form of a verb reports the development part of the event, which is a state (or perhaps a process, I'm not sure) which can occur even if the event itself does not occur.

15 Thus ‘While everyone was leaving Agatha was cleaning up’ does not require that there was ever a time at which each person was leaving (see note 14 regarding the progressive).

16 The canonical symbolism should be rich enough to contain lambda abstraction plus some means of referring to ‘intensions'. For definiteness the reader may assume that the canonical symbolism consists of the language IL of Montague (PTQ), supplemented to contain variables which range over eventualities and over times.

17 Actually, the translations should all contain reference to intensions; they would be ‘extensionalized’ by the adverbs whose translations contain lambda abstracts, along the lines of Montague's treatment of intensional and extensional transitive verbs in Montague (PTQJ.

18 In an extended version of this fragment we would allow adverbs to combine with sentences as well as with VP's; this would be necessary to account for the scope ambiguity of, e.g., Mary intentionally insulted everybody. This will cause no logical problems since (nonclosed) sentences are of the same logical type as VP's (see rules R4·R6 below).

19 There is not a general consensus concerning Just how adverbials appear in sentences, or concerning how their position in the sentence is correlated with the semantic role of the adverbial. Cf. Jackendoff, R., Semantic Interpretation in Generative Grammar. (MIT Press, Cambridge, 1972), Chapter 3.Google Scholar

20 Hereafter I will presume that lambda abstracts are always eliminated from translations, whenever possible, by lambda conversion. Also, I will indicate the translation of a phrase by writing the phrase itself followed by a prime.

21 In this fragment every subject translates using the primitive Agent, and every direct object using the primitive Obj. In a more detailed analysis I would follow recent work in linguistics and use different primitives along with a more flexible translation procedure (Cf. Jackendoff, op. cit., and Gruber, J., Lexical Structures in Syntax and Semantics (North-Holland, Amsterdam, 1976).Google Scholar For example, my notion of Agent seems to combine the notion of Provoker (linguists’ agent), as in John stood up, with that of Undergoer (linguists’ theme), as in John was sleeping. In certain cases these might be assigned to different parts of the sentence. For example, in John opened the door the subject is the provoker and the direct object is the undergoer, whereas in The door opened the subject is the undergoer and there is no direct object. We could exploit this more refined analysis by translating open in exactly the same way in each sentence (in spite of the fact that it appears as a transitive verb in the former and an intransitive verb in the latter) and translate the sentences as:

22 The rule is stated here in somewhat oversimplified form, and also needs some additional spelling out. (1) The rule requires the qualification that it must not be applied to any sentence which contains within it a head verb which is already in the past tense and which is not in a that-clause; (2) the rule presumes that will and has (or have) are in the present tense, and that the past tense of will is would; (3) the rule requires a precise definition of ‘head’ and of ‘main'; (4) there should be an additional qualification on Fut (a) to the effect that will has converts automatically to will have. Barbara Partee has pointed out (“Some Structural Analogies between Tenses and Pronouns in English,” Journal of Philosophy, 70 (1973), 601-09) that tenses appear to have something of a deictic aspect. E.g. if I ask ‘Did you shut off the gas?’ the answer is not ‘Yes’ merely because at some time in the past you shut off the gas; the question typically asks about some fairly specific interval of time. I think that this is right, and that it should be handled much the same as a related phenomenon dealing with quantifiers: namely, if I ask ‘Did you set every place?’ the answer is not ‘No’ merely because there are places in other parts of the world that you did not set; the question typically asks about some fairly specific set of places. In either case there should be a pragmatically determined implicit restriction of the range of some quantifier; the one related to ‘every’ in the second sentence, and the one that appears in the translation of the past tense morpheme in the former sentence.

23 This is somewhat sloppily stated, because of the wording ‘translates as a .. .'The point is that a given string of English words has associated with it two translations; a provisional one, utilized in buidling up sentences, and a ‘final’ one. This could be made precise either by explicitly relativizing translation to the parameters 'tensed’ and ‘closed', or by artificially altering the syntactic form of the sentence when converting it from a tensed sentence to a closed one.

24 In certain cases (e.g. probably in the case of former itself) the operators corresponding to nonpredicative adjectives could be further analysed; but in others (e.g. fake) this is probably not possible.

25 We have two options for how to treat measure adjectives, such as small. One is to treat them as nonpredicative adjectives, as with the operator approach discussed in section 3; the other is to treat them as predicative adjectives whose extensions vary with context. For arguments in favor of the latter treatment see Siegel, M., “Measure Adjectives in Montague Grammar,” in Davis, S. and Mithun, M. (eds) Linguistics, Philosophy, and Montague Grammar (U. of Texas Press, Austin, 1979),Google Scholar and Kamp, H., “Two Theories About Adjectives,” in Keenan, E. (ed) Formal Semantics of Natural Language, Cambridge U. P., Cambridge, 1975).Google Scholar

26 The present fragment would then improve on the treatment of tenses in PTQ. In addition to ignoring certain constructions (e.g. the simple past tense). PTQ treats incorrectly certain constructions that it includes. E.g. the fragment of PTQ allows the generation of A man who will date Mary has run with a translation which makes the sentence true if at sometime in the past a man ran, and at a later time in the past he dated Mary. (This is the translation which results from the direct combination of a man who will date Mary with run by rule S14; the translation requires that the dating postdate the running, but it does not require it to be in the future of the time of utterance.) This ignores the sequence of tense conventions of English which require that the operation of the perfect tense on a sentence convert will to would (see rule R5 above).