This paper presents a grammatical theory which has certain mathematical properties, and which produces the sentences of a language by means of two simple processes, word-entry and entry-reduction, with the meaning of each sentence being indicated directly by its construction. The reason for seeking a mathematical control on grammatical analysis lies partly in the inherent possibilities of such a connexion, and partly in the complex and somewhat haphazard nature of grammar, which makes one wonder if there is not something simpler and more principled involved. In the event, the system of grammatical analysis which is reached here is not an alternative to descriptions of grammatical patterns, but rather a complement to them; for in producing the sentences it locates and explicates those patterns as resultants of the two processes, but without cataloguing or arranging them.

It is a common experience in language study (and elsewhere) that a consideration of a few carefully chosen examples can allow us a neat, simple, even elegant solution; but that the more data we examine, the more complex the whole question becomes. In some such cases we are tempted to abandon discrete categories in favour of a ‘squish’ (Ross, 1972, 1975). English indirect object constructions seem to present this kind of problem.

Modern Romance - with the exception of Rumanian - has a class of causative+ infinitive constructions in which the infinitive subject surfaces as an agentive, as in (1) below, where the agentive phrase is italicized:(1) (a) Il s'est fait haïr par toils. (French) He himself is made hate by all.(b) Si fece odiare da tutti. (Italian) Himself he-made hate by all.(c) Se hizo odiar por todos. (Spanish) Himself he-made hate by all.(d) Fez-se odiar Por todos. (Portuguese) He-made+ himself hate by all.‘He made himself hated by everyone.’

1. One of the most influential articles on noun phrases that have been published in the field of transformational grammar is no doubt Emmon Bach's celebrated paper ‘Nouns and noun phrases’, which he published in 1968. According to Bach there is both syntactic and semantic evidence that typically predicative nouns such as idiot, dope, angel, etc. are introduced into English noun phrases by way of underlying relative clauses.

Huddleston (1977: 43), following some remarks by Poutsma (1926: 441–447), suggests that in (Huddleston's numbering)(1) I could have got the money easily enoughthere is past tense transportation (PTT), in that the CAN clause has ‘Unreal Mood (marked by the inflection on CAN) and underlying Past Tense’ and that the application of a transformational rule (PTT) allows ‘the Past Tense to be realized in the complement – by HAVE’. He proceeds to argue that the same is true of(5) (i) If he could have swum, [he would certainly have survived].

1. There seems still to be some controversy over the matter of whether or not the putative presence in English of obligatory anaphoric references to overtly missing antecedents is of any service in resolving the question of where, if anywhere, these overtly missing antecedents are covertly present.

2. The matter at hand was originally raised by Postal (1969), who asserted that if English permitted anaphors to recover missing antecedents from ‘within’ or ‘beneath’ their sentences' surface antecedents, then the (syntactic) derivations of those sentences had better include somewhere beneath the surface whatever it was that was recovered. Having said this, Postal concluded that English was (with trifling exceptions) unhappily devoid of such anaphoric recovery, since prime examples where such recovery would be required – for example, (1) – were plainly ungrammatical.