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Primary: Montague, R. (R. Thomason, ed.) (1974) Formal Philosophy, New Haven: Yale University Press. Kaplan, D. (1977) ‘Demonstratives’, in Almog/Perry/Wettstein (1989) Themes from Kaplan, Oxford: OUP, pp. 481-563.
Secondary: Lycan, W. G. (2000) Philosophy of Language, London; Routledge.
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The Relevance of Context
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One of the problems for Davidson’s truth conditional theory of meaning which I did not list is the problem of deictic terms. These are terms whose interpretations are pretty obviously contextually dependent. Statements like
(H) I am happy today
are not true or false regardless of the context in which they are spoken. When I say it now and here, it is true; but when you say it tomorrow at the dentist’s it will be false. If we have a theory of meaning for a language that generates T-sentences as the theorems about the sentences of the language then we can be sure that the T-sentence that will satisfactorily describe the truth conditions for that sentence will not be something like
‘I am happy today’ is true iff I am happy today
because the RHS doesn’t give us the sort of eternally true condition that will allow us to grasp the meaning (supposing that’s what the RHSs of T-sentences are intended for) in whatever context the statement occurs.
Suppose, for example that I left this OHP running and this sentence (H) on the screen when our class had finished. The students from the class which follows will observe the sentence and will understand what it means, but will have no idea what the truth value of the statement is because they will realise that in order to understand it they need more information. In fact even if the students knew all that there was to know about the world as it existed at the time they read the sentence they will still not know whether the sentence is true or not. But how can that be if the sentence is saying something about the world? How very different from the situation that ensues if I leave the sentence
Bob Zachariah Dobalina is happy on 12th October 2004.
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Accounting for Context Effects
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Inspired by such observations, Davidson proposes that the T-sentences that an adequate theory of meaning generates actually instantiate the schema
(TR) ‘S’ is true at time t when spoken by person p iff M
where ‘S’ is the label of a sentence in the object language, and M is that sentence, with deictic references to the speaker replaced by occurrences of p and deictic references to the time of utterance replaced by occurrences of t, if the metalanguage and the object language are identical, or a translation of that sentence if the metalanguage is different from the object language. For example, the T-sentence that is yielded for the sentence (H) would be something like
‘I am happy today’ is true at time t when spoken by person p iff p is happy at t.
In effect the truth of the sentence containing deictic elements is relativised to the time of utterance and the person uttering.
a. Indices
Using this sort of solution to the problem of contextually sensitive sentences requires modifications also to be made to the method by which a Tarskian semantics is provided for the natural language. I won’t go into this in any depth, but the trick basically is to use the same sorts of collections of possible worlds as are used to solve so many of the other problems for the basic Tarskian scheme. Again, we don’t have to worry about what possible worlds are really supposed to be, since we’re just talking about stipulating sets of objects for the extensions of predicates, and sets of sets of objects for their intensions. The interpretation of a predicate in the ‘actual world’ is a set of objects, and the interpretation of a predicate in any possible world is just another such set of objects. The ‘intension’ of the predicate is all the possible worlds in its interpretation. In fact a standard way of looking at intensions is as functions from worlds to extensions. Given a particular world, and given a particular sentence/predicate/function/constant, the intension will yield the particular extension desired (supposing that truth values are the extensions of sentences). Anyway, this will become a little clearer with an example. So, consider the sentence
Bob is happy
An appropriate interpretation for this sentence defines a reference for ‘Bob’ and an interpretation for ‘is happy’, thus:
v (‘Bob’) = Bob v (‘is happy’) = {Angela, Bob, Cleopatra, …}
and following the rules that we established before we find that
v(‘Bob is happy’) = 1 iff v(‘Bob’) is in v(‘is happy’)
and it’s clear that it is.
In the new system of relativised interpretation (and let us only consider relativisation to time) for the moment we get an appropriate interpretation thus:
v(‘Bob’) = Bob v(‘is happy’) = { {t1, {Angela, Bob, Cleopatra, …}}, {t2, {Angela, Barry, Charmaine, …}}, … }
in which the sets labelled by the time indices can be thought of as the extension of the predicate in the possible world labelled by that index – which, of course, is supposed to be the actual world at the labelled time, but that’s neither here nor there. We can also speak of the relativised interpretation as
v(‘is happy’, t2) = {Angela, Barry, Charmaine, …},
and following the obvious sorts of rules that I have no intention of explicitly stating Bob is happy at time t2 gets interpreted as
v(‘Bob is happy’, t2) = 1 iff v(‘Bob’) is in v(‘is happy’, t2)
and it’s clear that it isn’t.
The extension of this process to the relativisation by the person doing the uttering is also pretty easy.
The first problem you might have with something like this is that there may well be very many more required relativisations than the two that Davidson has picked out. You are right to make this observation Well done. In fact, very early on authors like Montague (attempt to read him at your peril!) thought that they could explain all possible contextual sensitivities by the use of just 8 indices. They were,
I = (a possible world, a time, a place, a speaker, an audience, a sequence of objects pointed at, a discourse fragment, a sequence of assignments)
You can imagine how complicated an interpretative system would become if all these indices had to be kept track of. We’re going to have to have to have a schema that goes like
(TI) ‘S’ is true relative to indices (a, b, c, d, e, f, g, h, i) iff M
where ‘S’ is the label of a sentence in the object language, and M is that sentence, with deictic references replaced by occurrences of a, b, c, d, e, f, g, h, i, as appropriate, if the metalanguage and the object language are identical, or a translation of that sentence if the metalanguage is different from the object language.
but the practical application of such a thing is of no concern to us. We’re interested in whether it can even in principle do the things that it has to do. And the conclusion would have to be that it really can’t. How would that index be able to cope with a sentence like
Bob came to the lecture
The interpretation of ‘came’ in this sentence seems to rely upon the vantage point of the speaker. It depends upon the speaker attending the lecture. Furthermore, the vantage point is not the vantage point of the speaker at the moment that the sentence is uttered, because the vantage point in question is unaltered if the speaker is speaking the day after the lecture, and at the time of uttering the sentence is sitting in a bus. The index in question here is some sort of reference time. It is only necessary to note that the index proposed by Montague does not include either vantage point or reference time, and that there doesn’t look to be any reasonable way to treat either of those indices as functions of his 8 proposed indices. Given that that is the case, the Montague index is shown to be unsatisfactory.
I suppose it’s possible that Montague’s index + these two might be satisfactory, but just a little thought – a cursory scanning of almost any piece of literature – will suggest that there are an unlimited number of indices. Just from the example above we can see that there are also going to be indices for reference places, maybe reference persons, etc. And that’s just by analogizing. In any case, the general consensus amongst right-thinking natural language intensional semanticists is that the indexing system is a dead end solution. It won’t work.
b. Functions
A ‘better’ way of accounting for the contextual effects is one suggested by Harman. Instead of having an indeterminate and probably indetermin-able set of indices for each aspect of the context that is identified as relevant to the truth-evaluation/meaning of a sentence as uttered, simply declare that each deictic element that occurs in a sentence is to be interpreted by relativising with respect to the total context in the appropriate way. To make this more concrete, we suppose that there is a function, a, that operates upon deictic elements and the context in which they occur, C, in such a way that the T-sentence that the theory generates properly accounts for the effect of the context on that deictic element. For example,
Bob is happy now
is a sentence of the language for which the deictic element ‘now’ really needs to be interpreted so as to indicate that the time in question is the time at which the utterance occurs. The T-sentence that a theory of meaning for the language will generate, given that such an a function is possible, will be something like
(Ta) ‘Bob is happy now’ is true in the context C iff Bob is happy a(‘now’, C)
and a(‘now’, C) is a function that yields the appropriate time at which to interpret Bob as being happy, i.e. at the time of utterance.
You’ll recollect that I mentioned just a moment ago that a standard way of looking at intensions is as functions from worlds to extensions; well, something similar applies here with the function a and all other such rules and functions. They can be considered as functions from contexts to intensions. Given a particular context, and given a particular sentence/predicate/function/constant, the function will yield the particular intension desired. Kaplan, in his underground masterpiece on demonstratives,[1] defines the content of a sentence to be what we’ve been calling its intension, which turns out, as you might expect, to be equivalent to the proposition expressed by the sentence (recall the possible world view of propositions.) And he calls the rules like a the character of the sentence. Content, on this story, is not fixed in sentences with deictic elements (like demonstratives); what fixes this content is the ‘character’ of the sentence operating upon the context in which the sentence occurs. Thus: Character on context gives content.
All that is left for the intensional semanticist now is to discover how to define a. Unfortunately this turns out to be non-trivial. What sort of function will allow the proper interpretation of ‘now’ when it occurs in the following sentences in the following contexts?
i. ‘Now that I’ve finished’ said at the end of the lecture. But you will also read it at the end of the lecture notes; in which case I don’t intend anything temporal. It’s more like a processual indicator.
ii. ‘Stephen can’t come to the phone now’ said by my answering machine to you when you call. It’s true enough when you hear it. But it certainly wasn’t true when I said it – because I was on the phone when I was saying it. The paradoxicalness of it all! (I once spent two hours discussing the semantics of phone messages with a very long-suffering lecturer. Don’t you try it.)
iii. ‘Now, I have already spoken about such and such’. Spoken at any time during this lecture. There’s no intended reference to any particular time there at all. It’s more like. ‘Stop, think, remember, consider the consequences of the following.’
iv. Suppose I’m giving directions to someone who wants to get to New Farm. ‘Head out of town. You will go along Coronation Drive till you get to the Regatta. Now turn left.’ Not now, but then. Or there.
And so on. You can play this game for hours in your own time, trying to come up with new ways in which the element ‘now’ doesn’t operate in the way we first suggested. Poor a. [1] Kaplan (1977)
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Prospects
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There are actually ongoing research projects which have the aim of explaining how something like a can be made to work, but we’re not going to talk about this any further now. At this point I simply want to remark that the approach to pragmatics that we’ve been looking at in this section is a natural development of the truth-conditional view of the philosophy of language. It’s a type of pragmatics that might be called semantic pragmatics. It’s not the only approach to pragmatics however, and in the final two lectures we’ll look more closely at some other approaches which have had some success.
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