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 tense of It’s sunny binds it as closely to the time of its utterance as would use of the word now. And, while not every sentence contains indexical words, 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. And there are many cases of logical properties and relations that do not vary. Although the propositions expressed by The package will arrive next Wednesday and The package will arrive next week will vary depending on the time of utterance, the content of the first sentence will always include the content of the second, so a relation of implication will always hold between them.

Since we are studying formal logic, we are interested in generalizations about properties and relations that hold in virtue of certain forms of expression; and the particular forms of expression we will study do not change their significance from the context to context, so we will only be interested in logical properties and relations that are not context dependent. Although the propositions expressed by I put that here yesterday and I didn’t put that here yesterday vary significantly with the context, the function of the word not insures that in any given context, the two sentences will express contradictory propositions. And this invariable function of not is the sort of thing that we will study.

In fact, we can ignore the role of context entirely. When comparing The package will arrive next Wednesday and The package will arrive next week in 1.2.3 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. That is we treated the expressions next Wednesday and next week in the way we would treat references to specific dates or time periods—such as September 5, 2012 and the week of September 3, 2012. This procedure is legitimate if we are careful not to assume anything special about the context of use, and it will be easy not to make special assumptions about the context because the deductive properties and relations we are interested in do not depend on this context.