Recent work on morphology – Lieber, 1981; Williams, 1981; Kiparsky, 1982; and Selkirk, 1982, in particular – has extended the notion of HEAD from syntax into new areas in morphology. In particular, these writers propose that in forms with derivational affixes, like English happiness, the affix is the head of the combination; for instance, Kiparsky assumes (following Lieber) ‘that all word formation is endocentric’, meaning by this ‘that the category of a derived word is always non-distinct from the category of its head, in English usually the rightmost constituent (cf. Williams, 1981)’ (133).

Extending Montague's (1974) framework, Barwise and Cooper (1981) argue that some generalized expressions (which I shall call vague quantifying expressions), such as most, many ana few, correspond not to quantifiers, but to determiners within noun phrases. They argue that we need not determine the meanings of these expressions by logic; rather, we may draw upon an idea similar to the one we employ when interpreting the meaning of the quantifier Qxø(x), that is, we may appeal to an underlying topology for their interpretation (1981: 161). Similarly, they invoke one of the ‘simplifying assumptions often made in model theory’; namely,… that one has a fixed context which determines the meaning of the basic expressions. We can think of this context as providing an interpretation for non-logical determiners… We shall assume… that there is a rich context held fixed that determines the PRECISE MEANING [my emphasis here] for the basic expressions, even those like ‘most’, ‘many’ and ‘few’. We refer to this as the fixed context assumption…

The fixed context assumption is our way of finessing the vagueness of non-logical determiners. We think that a theory of vagueness like that given by Kamp (1975) for other kinds of basic expressions could be superimposed on our theory (1981: 163).

In this paper I want to present a practical descriptive approach to the semantics of grammatical categories, especially of the binary type involving two forms only. In doing so, I hope to be able to attract the attention of linguists concerned with the structure of a comprehensive semantic theory of human language. Substitutional relations of a grammatical kind (as opposed to syntactic and lexical relations) are too often neglected in textbooks on modern semantics. For example, in Ruth Kempson's otherwise excellent introduction to semantic theory (Kempson, 1977), there is no mention of the semantics of grammatical categories at all. In my view, not only must such Substitutional relations be accommodated within a total theory of semantics – even on a narrow definition of the discipline – but they may provide important insights into the nature of meaning which will affect some of the current suppositions in semantic theory. In particular I shall attempt to shed light on the role of ‘subjectivity’ – a notion which is becoming increasingly difficult to ignore and which challenges the very common restriction among semanticists of the scope of semantics to just a truth-conditional component.

The debate over determinism and free choice in linguistics is not likely to be settled in this or the next century. All we can do is try to shed some light on the issue from time to time, and perhaps define areas that are best described deterministically, and others where freedom reigns, in majesty if not supreme. Nowhere has the debate been more lively than in descriptions of English stress and accent. The latest – to which this essay is a response (and which can be consulted for chronological developments – there is no need to repeat them here) is Gussenhoven (1983), ‘Focus, mode and the nucleus’. It is a forthright endorsement of a deterministic view, with the high merit of a rich assortment of examples – many attested and all perfectly idiomatic. The case that Gussenhoven builds is a solid one, and as it is directed in part against a view that I have espoused for a long time and still believe to be correct, it requires an answer.

Bolinger (1972) argued against the notion that the occurrence of sentence accents can be explained on the basis of syntactic structure, a position taken by, among others, Chomsky & Halle (1968) and Bresnan (1971, 1972), at least with regard to a (putative) corpus of sentences with ‘normal intonation’. Bolinger's chief argument against this ‘syntactic’ position was his richly supported observation that sentence accents function independently as markers of information content, and that therefore an approach that derives them from anything other than the intention of the speaker is misguided. In my own approach to the description of the position of sentence accents the view that sentence accents are the expression of the speaker's communicative intentions is fully endorsed. The issue in ‘Two views of accent’ (above, pp. 79–123) is no longer whether sentence accents are derived from syntax, but to what extent the particular word that a sentence accent is placed on is the unit on which these communicative intentions focus. For Bolinger the relation is direct: ‘accents mark individual words focused for their informativeness’, where ‘informativeness’ is subordinate to ‘interest’, which in turn shares with ‘power’ the assignment of accent. In his article, Bolinger criticises an alternative approach exemplified in Gussenhoven (1983) in which the relation is indirect.1 In this approach, which builds on work by Schmerling (1976), Ladd (1980) and others, the speaker is assumed to translate his communicative intensions into choices from a number of linguistic options, most importantly into a focus marking of the semantic constituents in his sentence (fragment). Sentence accent assignment rules translate these choices (again, mainly the focus marking) into sentence accents on particular words. I will adopt the term ‘highlighting’ for the former approach, and will refer to the latter as the ‘focus-to-accent’ approach.

Atomic Phonology is a theory constraining phonological rules and phonological components of grammars which has been developed largely by Daniel Dinnsen in a number of papers since 1978. The basic principles of Atomic Phonology are set out in the following quotation:

(1) The theory of atomic phonology maintains that all linguistic variation requiring distinctly varied formulations of phonological rules is predictable from a set of atomic rules and universal principles of grammar… Atomic rules are entirely independent rules of grammar which are presumed to be the most basic, most specific rules that can be motivated on empirical grounds… Atomic rules thus specify all the necessary initial conditions from which any correct variation on that process for any natural language can be predicted by universal principles. Non-atomic rules are dependent on atomic rules. The dependence on atomic rules derives from the requirement that non-atomic rules are all and only those rules which are complements of atomic rules or complements of their complements. The complement relation may be defined as follows: Two rules are complements… if just those commonly shared (identical) features in the structural descriptions of the two rules are sufficient to define precisely the same set of input relations defined by the two rules jointly (Dinnsen; 1979: 31).

But it would only be fair to add that there is still an essential difference between the hope that never dies and the hope that it was all wrong. (Van der Laan, 1929: 28)