316 The subjectivity of utterance

formalize (11) and (12) respectively (provided that Past is itself given the appropriate definition):

(11a) Past (p)

and

(12a) Past (Past (p)).

As to the precise interpretation of (1 la) and (12a), this will of course depend upon the way in which the tense-operators are defined in the particular system of tense-logic that is used for the formalization.

One way of interpreting tense-operators is by using them as indices to possible worlds (see 7.6). For example, (lla) can be seen as meaning that p is true in (or of) some possible world which is past in relation to (i.e., which has preceded) the world indexed by the cognitive or locutionary temporal zero-point (t₀ — "now"), and (12a) as meaning that p is true in (or of) some world which is past in relation to the world which is past in rela­tion to the world indexed by t₀. Clearly, present-tense and future-tense operators (and, in principle, proximate-tense and remote-tense operators) can be defined in terms of deictic tem­porality and can be used similarly as indices to possible worlds. It is also clear that, from a theoretical point of view, there is no problem about constructing an indefinitely large number of complex multi-level tense-systems by combining a small number of tense-operators in a variety of ways and by allowing tense-operators to be combined with one another and with other prep­ositional operators (of negation, modality, etc.) without limit.

But (lla) and (12a), interpreted in this way, do not satisfac­torily represent the meaning of (11) and (12). As the adverbials in the brackets, 'last week' and 'the previous week', make clear, the simple past tense and the pluperfect tense have definite refer­ence, at least in utterances of these sentences in contexts in which the reference of these adverbials is either explicit or impli­cit. The adverbials merely make explicit what otherwise would probably be implicit in the context of utterance. In this respect, (11) and (12) are typical of most, if not all, tensed sentences (or clauses) in English and other natural languages. As many

10.3 The grammatical category of tense 317

grammarians have observed, tense is comparable, semantically, with the definite article or demonstrative pronouns and adverbs. Like them, it is basically deictic and definite, but, also like them, it may be anaphoric or may combine deixis with anaphora. The fact that this is so means that any system of tense-logic which treats natural-language tenses as being comparable with the existential quantifier ("There is some earlier/later world in which p is true") needs to be modified. In fact, it is well recognized by formal semanticists that current systems of tense-logic do not satisfactorily formalize even the purely temporal meaning of the most basic dichotomous or trichotomous tense-distinctions of natural languages.

Having said this, I must however go on to emphasize that this evident inadequacy of formal semantics (in its current state of development) does not imply that linguistic semantics has noth­ing to learn from recent and continuing attempts to bring the tense-systems of natural languages within its scope. This is a point I have been making throughout this book, and it is a point that I will make once again, with respect to the analysis of mood and modality, in the following section. There is no doubt that the notion of possible worlds, indexed for deictic temporal reference, is a powerful and intuitively attractive notion for the further development of linguistic semantics.

Standard definitions of tense usually fail to make explicit the fact that the reference of natural-language tenses, in contrast with that of the tense-operators of certain systems of tense-logic, is characteristically definite, rather than indefinite. They also fail to make explicit the further fact (although this is more obvious) that it is characteristically incidental. For example, in uttering (11) one would not normally be referring to some point of time in the past in order to say something about this point of time. The proposition expressed would not be a proposi­tion about time in the sense that the tenseless proposition "John's uncle die" is a proposition about the contextually determined referent of the expression 'John's uncle'. It is possible in some natural languages, if not all, to refer directly to points or inter­vals of time and to make statements about them: it is even poss­ible, arguably, to treat the events that occur at a particular