1.3.5. Indexicality

We will give less direct attention indexicality than to implicature, but it would be hard to ignore the phenomenon. Although indexicality is most obvious in sentences with indexical words like I, that, here, and yesterday, there are other features of a sentence, most notably its tense, that can make the proposition it expresses vary with context in which it is asserted. The sentence It’s sunny is as bound to the time of assertion as is It’s sunny now. And, while not every sentence contains indexical terms, it is only very special sentences that are not indexical in virtue of tense.

If the propositions expressed by sentences vary with the context, it seems that the logical properties and relations of these sentences (which we trace to the propositions they express) may vary as well. Let’s look at one example. The proposition expressed by the sentence I am here will depend on the speaker, the speaker’s location, and the time of utterance. And this sentence may express the same proposition as the sentence You are there when the latter is used by a second speaker in an appropriately related context. There are also many contexts in which these sentences might be asserted where they would not express the same proposition. But sentences are supposed to be logically equivalent when they express the same proposition, so it seems these sentences would be equivalent when used in some contexts and not equivalent when used in others. And the same issue arises for deductive properties as well as relations; a sentence that is a tautology when used in one context might not be a tautology when used in a different context.

More broadly it may seem that we really should not speak of sentences as having deductive properties and standing in deductive relations. If a sentence expresses no fixed proposition independent of the context in which it is asserted, we can really only talk about the deductive properties and relations of sentences-in-context, of sentences each taken together with a context of use. The term statement has sometimes been used to speak of a particular use of a sentence. If we use this terminology, we can say that certain statements made using the sentences I am here and You are there are equivalent and that it statements rather than sentences have deductive properties and stand in deductive relations. Something like this approach would be required if we really were to study the phenomenon of indexicality. However, the logical forms on which we will focus do not include indexical elements, so it will be possible for us to ignore this aspect of meaning.

Even when indexical elements are present, we can set aside explicit reference to contexts of use when speaking only of logical properties and relations that do not vary from context to context. For such deductive properties and relations will hold of sentences in virtue of the specific ways the propositions they express vary with the context of use—i.e., in virtue of the “characters” of these sentences. For example, we can say that sentences are equivalent if their characters lead them to express the same proposition in any context of use, and we can say that a sentence is a tautology if its character leads it to express a tautologous proposition in every context of use. Again, although the propositions expressed by The package will arrive next Wednesday and The package will arrive next week will very depending on the time of utterance, the proposition expressed by the first sentence will always entail the one expressed by the second sentence. We will limit consideration to logical properties and relations of sentences that are independent of the context of use in this way. So, even though I am here and You are there may be used to make statements that are equivalent, we will not count these sentences as equivalent because it is not the case that, in each context, the propositions expressed by these sentences are the same. (Indeed, it is not easy to think of any single context with respect to which the two would express the same proposition since a single context would require that both be spoken by the same person.)

In fact, we can use this approach without explicitly considering the characters of sentences at all. In fact, this was done in the example in 1.2.3 that included the sentences The package will arrive next Wednesday and The package will arrive next week. There we simply took it for granted that sentences were being compared with respect to some one context, and we spoke freely of the propositions they expressed in that context without bothering to note that they expressed different propositions in other contexts. This procedure is legitimate if we not to assume anything special about the context of use. And it will be easy not to make special assumptions about the context of use because the deductive properties and relations we are interested in do not depend on this context. There is an analogy here to a typical use of variables in algebra. When numerical laws are used to manipulate algebraic formulas, it is assumed that variables appearing in those formulas have been assigned numerical values. But there is often no need to consider what those values are since the laws being used apply to all numbers.

Of course, there are things we will miss by ignoring character and context. The effects of shifting context in the course of a conversation are among the things we cannot deal with. The assertion I am here followed by the confirmation Oh, so that’s where you are is a simple example of this. Another phenomenon we will miss is the exploitation of some sort of dependence on context to convery information about the context. If I assert Today is Tuesday, the proposition expressed may be no more informative than is Tuesday is Tuesday since the first sentence, if true, merely tells us about Tuesday that it is Tuesday. But my assertion can still be helpful because someone who tries to accommodate it will need to take it to have been asserted on Tuesday, and will thus know what day it is. In short, even if the proposition expressed by Today is Tuesday in a given context is a tautology and conveys no information, the assumption that this sentence expresses a tautology (rather than an absurdity) in that context yields information about the context. And this way of deriving information can support a form of non-deductive inference.

On the other hand, our approach need blind us to all logical properties and relations that derive from indexical terms. We have seen this already in the case of next Wednesday and next week, but the role of the indexical terms can be less trivial than this. For example, the terms today and tomorrow are related in such a way that Tomorrow is the day after today is true in any context, so we can recognize it as a tautology. And we can also recognize that Today is Tuesday implies Tomorrow is Wednesday.

It would be too much to say, however, that our limited perspective will not blind us to any logical properties or relations that hold for all contexts of use. For there are relations between the meanings of indexical terms that hold in any context, but only with respect to the actual world of that context; and our approach will miss logical relations that derive from these aspects of meaning. For example, whoever is the speaker in a context will actually be speaking at the time of utterance, so the premise Today is Tuesday would justify the conclusion I am speaking on Tuesday. But this conclusion is not entailed by the premise—even given the contextually assigned meanings of the terms—since nothing about the day of the week of a given date logically necessitates someone speaking. To get a feel for the issue, it may help to look at a related example: although I am here now is true in the actual world of any context, it is not a tautology. That is, the proposition expressed by I am here now in a context of utterance is bound to be true in the actual world of that context, but this proposition will also be false in other possible worlds. And the fact that it is false in other worlds can be crucial for the meaning of sentences—such as I am here now but I almost didn’t make it—that speak of unactualized possibilities.