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Sunday, July 30, 2006

Embedded Belief Operators Again

The following sort of sentence is fun to think about:

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

I suggested in an earlier post that (1) 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. Mike suggested that there are readings where the time the belief is about is later than the time of speech but earlier than the time of believing. Here is his example: "Bush won't believe it when Hillary is president (i.e., say, in 2010), but he will believe it later."

So, it seems that (1) must have 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), Et'(t' < t & (t* < t' or t* = t') & Hillary is president is true at (w,t'))

But there is still something left to explain. How do we account for the availability of the two readings if temporalism is true? Well, it is easy to account for the different readings given something like Kent Bach's account of belief reports. On Kent's account, the very same proposition may describe different beliefs depending on which standards for belief description are salient in the context. If the proposition expressed by the operand sentence 'George Bush believes that Hillary Clinton is president' in (1) is a description of what is believed rather than the thing believed, it may pick out different beliefs in different contexts.

5 comments:

Mike said...

"If the proposition expressed by the operand sentence 'George Bush believes that Hillary Clinton is president' in (1) is a description of what is believed rather than the thing believed, it may pick out different beliefs in different contexts."

Brit, I'm probably being lazy, but how (given Bach) do you get the two interpretations you note "easily"?

Brit Brogaard said...

Hi Mike,
Well, if the 'that' clause can describe different belief contents in different contexts, even though it expresses the same temporal proposition in all contexts, then at least we can explain how it is possible for there to be more than one reading (given temporalism).

Brit Brogaard said...

I should add that Bach's account doesn't give us the two readings. It merely allows for the possibility that embedded 'that'-clauses may pick out different belief contents in different contexts.

Mike said...

Pretty complicated. You have these truth-conditions for (1):

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* < t' or t* = t') & Hillary is president is true at (w,t'))

So you have two cases for time of speech. Case one is when the assertion occurs before Hillary is president (say, just as she is being sworn in). This could mean that the time the assertion *begins* is prior to the beginning of the interval during which she is sworn in. But this is consistent with saying that the time the assertion is completed is *after* she is sworn in. So the speech time and presidency time overlap. Or, more simply, the entire assertion is complete before the beginning of her swearing in.
Case two is when the assertion occurs (in some sense) contemporaneously with her presidency. But I'm sure how to read the '=' sign here. You might use the identity sign for assertions that occur during the time she is president or for assertions that begin during her presidency and finish after. Lots of possibilities. Ideally you might want intervals rather than instants in your truth-conditions. Incredible how quickly the formulation gets complicated.

Brit Brogaard said...

Thanks, Mike! Yes, ideally one would use intervals in the meta-linguistic truth-conditions and span operators in the logical form.

Maybe "is identical to" should be "overlaps".