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Thursday, July 27, 2006

Temporalism and Embedded Belief Operators

Thanks to Jason Stanley I have been reading up on the literature on embedded belief operators. While reading I suddenly started worrying about the following sentence:

(1) In 2030 it will be the case that George Bush believes that Hillary Clinton is president.

This time I worried on behalf of the temporalist. Even assuming 'in 2030' is a restrictor of 'it will be the case that', the sentence has two readings. On one reading, the time of believing is the same as the time the belief is about. On the other reading, the time the belief is about overlaps the time of speech, and the time of believing is later than the time of speech. The problem for the temporalist is that the temporalist takes the object of belief to be a temporal proposition. So how do we get both readings? I am not sure. But here is a suggestion. What about the following meta-linguistic truth-conditions (ignoring 'in 2030')? @ is the actual world, and t* is the time of speech.

There is a future time t such that, for all worlds w that are compatible with what George Bush believes at (@, t), Hillary Clinton is president is true at (w, t)

There is a future time t such that, for all worlds w that are compatible with what George Bush believes at (@, t), Hillary Clinton is president is true at (w, t*)

10 comments:

Mike said...

Brit,

This reading,

"There is a future time t such that, for all worlds w that are compatible with what George Bush believes at (@, t), Hillary Clinton is president is true at (w, t*)"

seems to express the proposition that at t in @ Bush has the belief that Hillary is president at (the time of utterance) t* in @.

But there is perhaps a reading that is not about the time of utterance. It might read that at t Bush has the belief that Hillary is president at some time or other earlier than t (not necessarily the time of utterance).
For instance, someone might say "Bush won't believe it when Hillary is president (i.e., say, in 2010), but he will believe it later." So the time of utterance is prior to the time of her assuming the presidency.

So maybe this?

There is a future time t such that, for all worlds w that are compatible with what George Bush believes at (@, t), (Et*)(t* < t, @) at which 'Hillary Clinton is president' is true.

Brit Brogaard said...

Yes, I like that. Thanks, Mike! But I would add that t* (in your truth-condition) must be later than the time of speech (and earlier than t). Or could t* be earlier than the time of speech?

Mike said...

Brit, I might be missing your point. Isn't the earlier-than-speech case the easier one? Hillary is already sworn in and then I utter "Bush is not going to believe that she is president". The later-than-speech case is unusual. Hillary is not yet president and you say "Bush is not going to believe that Hillary is president". But this case works too. Here's an example: Hillary is just about to be sworn in as president and you say "You know, Bush is not going to believe that Hillary is president". Interesting that you can say that truthfully before she techinically is president. But it seems to me perfectly grammatical. So t* can be after the time of speech.

Brit Brogaard said...

Hi Mike, Suppose Bush believes in 2020 that Hillary is president from 2000-2004, and suppose I assert the following in 2010:

(1) Bush will believe that Hillary is president.

Can my assertion be true in these circumstances? Suppose 'no'. Then doesn't your truth-condition need strengthening? For your truth-condition says:

"There is a future time t such that, for all worlds w that are compatible with what George Bush believes at (@, t), (Et*)(t* < t, @) at which 'Hillary Clinton is president' is true.

In other words, isn't it satisfied under the envisaged conditions? Either way, however, you're right that the restriction cannot simply be a requirement to the effect that t* is later than the time of speech.

Adam Arico said...

Okay, I think I'm missing something. The sentence is ambiguous (even in ordinary parlance), so whatever interpretation we give it (Temporalist or Eternalist) _should_ yield more than one possible reading. It seems that the sentence could be saying either "(In 2030) Bush does not believe that (in 2030) Hilary is President" or "(In 2030) Bush does not believe that (in, say, 2010) Hilary is President". Thus, it's a plus for temporalism that it _can_ yield either interpration. Why do you think it's a problem to have two readings? What am I missing?

Mike said...

"Suppose Bush believes in 2020 that Hillary is president from 2000-2004, and suppose I assert the following in 2010:

(1) Bush will believe that Hillary is president.

Can my assertion be true in these circumstances? Suppose 'no'"

Brit, that sounds right. The assertion of (1) after Hillary is president is true so long as she is president at the time of the assertion. Well, almost. It *can* be true even in the case you envisage. Suppose Bush will also believe (mistakenly) that Hillary is president in 2010. And suppose you're trying to convey in 2010 that W is going to (mistakenly) believe that Hillary is president then! In that case what you said in (1) is true. But bizarre examples aside, I think you're right.

Brit Brogaard said...

Mike: things are getting complicated. So I may be rambling but I still think some further restriction is required. So consider again:

(1) It will be that Bush believes that Hillary is president.

(1), of course, does not require for its truth that Hillary is ever president (it requires only that Bush will believe it). So, the following clever case:

"Suppose Bush will also believe (mistakenly) that Hillary is president in 2010. And suppose you're trying to convey in 2010 that W is going to (mistakenly) believe that Hillary is president then!"

will reduce to the case we looked at earlier where the time the belief is about overlaps the time of speech.

But if there is no case of (1) being true where the time the belief is about is, say, 10 years earlier than the time of speech, then we need to restrict the truth-condition you offered earlier.

I think the following will do (tu is the time of utterance):

There is a future time t such that, for all worlds w that are compatible with what George Bush believes at (@, t), (Et*)(t* < t & t* > tu, @) at which 'Hillary Clinton is president' is true.

I still think we can account for your case:
"Hillary is already sworn in and then I utter "Bush is not going to believe that she is president". ".

Does this seem right to you?

Brit Brogaard said...

Thanks for your comment, Adam! The problem I had in mind was that it might seem to some that the temporalist cannot account for both readings. If you do not do possible worlds semantics, and you're a temporalist, you can only account for one. The reading you offer is unaccceptable to the temporalist (even if acceptable to the eternalist).

Brit Brogaard said...

Mike: "t* > tu" should be "t* is later than or identical to tu".

Adam Arico said...

Thanks, Brit.