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Sunday, July 23, 2006

Lewis' Tense Operators

In "Index, Context and Content" Lewis argues that we should take compositional semantic values to be functions from context and index to extensions. That way we can determine truth-values at one fell swoop. Here is how it works. Take:

(1) It will be the case that Hillary Clinton is president.

The prefix is a tense operator that shifts the time feature of the index from present to future. (1) is true iff 'Hillary Clinton is president' is true at the context of use and the shifted index.

Simple and elegant. But I think Lewis' approach runs into difficulties. The folllowing assumption is plausible:

Non-Redundancy: Tense operators are not typically semantically redundant.

Now consider:

(2) It will be the case tomorrow that Hillary Clinton is president

Lewis cannot say that 'tomorrow' is part of a prefix that functions as a temporal operator. For context is required to interpret 'tomorrow'. Yet context enters the picture only later. Otherwise it wouldn't be a one-step method for determining truth-values. So, Lewis must take (2) to have the form 'it will be the case that (Hillary Clinton is president tomorrow)'. But the tense operator is now semantically redundant.

4 comments:

adam_taylor said...

I am a little confused here. Why can't "tommorow" in this case be taken as a constraint on the scope of the tense operator. In other words, why not treat it as exactifying the operator by, limiting it's extension. It will not be the case if 40 years that HC will be president. But if I say,

"it will be the case that HC will be president"

I leave open the reading that it could be the case that HC will be president in 40 years.

If I say it will be the case tommorow, I narow the scope of the operator.

This way "tommorow" serves a non-redundant role.

Brit Brogaard said...

Thanks for your comment, Patrick! That's how it ought to be understood. Normally we'd apply context first to get a semantic value (in the standard sense), then we'd shift the index and then we'd apply the (shifted) index to get a truth-value. But Lewis suggests that context and index enter the picture all at once. He could say that we interpret 'tomorrow' first and then shift the index, but then we no longer have a one-step procedure for calculating truth-value. Perhaps he could say that the index-shifting and calculation of truth-value somehow take place all at once. But at least it is not obvious (to me anyway) how this is supposed to work.

Jason Stanley said...

Brit,

This post is a bit confusing, because your sentence (2) raises a problem for any straightforward operator treatment of tenses. In (2) (as essentially the first commentator points out) the only available reading is that Hillary Clinton is president at a time t that is both in the future and tomorrow. So in some sense, the future tense operator is redundant -- at least, it doesn't shift the time of evaluation to a time subsequent to tomorrow.

One way of treating this, as the first commentator also points out, is by not treating 'tomorrow' as an operator, but rather as a restrictor on the future tense operator. Be that as it may, there is a general problem posed by (2) for approaches that treat temporal expressions uniformly as operators; the two tense operators don't iterate -- (2) doesn't have a reading in which it asserts that in the future of tomorrow, Hillary will be president. So it's tricky focusing on the additional problem you want to raise for Lewis, given that (2) raises a more general problem for a class of approaches, of which Lewis's is just an (unorthodox) instance.

Brit Brogaard said...

Thanks for the clarifications, Jason! I should have been much more clear. I was assuming that any minimally adequate account of the tenses as sentential operators would take 'tomorrow' to be a restrictor, as Patrick (=Adam) and I have been talking about over the last two months.

Salmon is an advocate this view, and I am too. But since Salmon's view has appeared in print and mine hasn't yet, let us focus on his view. Roughly, on his view, 'tomorrow' can be seen as completing the basic tense operator. So, we have one complex tense operator rather than two independent ones. Now the problem for Lewis (I think) is that he takes the tense operator to shift the index first. The sentence is true iff the embedded sentence is true at the context and the shifted index. But I think Lewis's strategy encounters trouble in this case (where 'tomorrow' completes the basic operator) because that case seems to require context to interpret 'tomorrow'. If Lewis accepts Salmon's view, then context must be applied first and later as well. So we would have a two-step account, not a one-step account.

I think this is very interesting, because if I am right, then there is indeed a difference between the one-step and the two-step approaches (it is usually assumed that there is no difference, because the proposition can be defined) So, I think that if I am right, then that would actually lend support to the view you're defending, Jason (or alternatively to the view I am usually defending :-).