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Tuesday, August 01, 2006

Double Access Readings

So-called double-access sentences, such as,

(1) John said that Mary is pregnant

pose a challenge for most theories of tense. The problem posed by double-access sentences is that they can be true only if the time the embedded content is about overlaps the time of utterance. So for (1) to be true, John must have said 'Mary is pregnant', and the time of Mary's alleged pregnancy must overlap the time at which the sentence is uttered. If we treat the tenses as quantifiers, (1) should come out as (t* is the time of utterance):

(1a) Et(t < t* & at t John says that Mary is pregnant at t)

But (1a) does not require for its truth that Mary's alleged pregnancy overlap the time of utterance. What about the following alternative analysis (based on a suggestion made by Higginbotham)?

(1b) Et(t < t* & at t John says that (Mary is pregnant at (t, t*)))

This seems fine. But if (1), upon analysis, cashes out to (1b), then we get the wrong result in cases like the following:

John said that Mary is pregnant
Peter believes everything John said
Hence, Peter believes that Mary is pregnant

On the double access reading of the first premise, its truth requires that John said that Mary's pregnancy overlaps his time of speech and the time the sentence is uttered. If we read the conclusion in a similar way, then the argument is valid, but the truth of the conclusion requires Peter to believe that Mary's alleged pregnancy overlaps the time of John's past speech. But surely the conclusion does not have such a reading. So, the argument cannot be valid if the first premise is given a double access reading.


Alan White said...

Very interesting case!

Pushing a possible de dicto, de re equivocation of what Peter believes aside, and focusing only on a de re reading, my reaction is that the argument demands further explication for the second premise. Why that is so might be revealed in the following exchange between three people Px:

P1: John said that Mary is pregnant
P2: Peter believes everything John said
P1: Hence, Peter believes that Mary is pregnant

But then followed with:

P3: Oh no--Peter doesn't know that John said that.

That's because while it's given (even among all of P1-P3) that Peter believes everything John has said in the past, only P3 is privileged to know that Peter could not infer anything about this matter because even though John said it, Peter did not know about this particular utterance. So the best universal cash value of the second premise lifted from this particular context is:

P2* Peter believes at any t everything John said that Peter knows/believes that John said up to and including t.

At least that's what I see here.

Brit Brogaard said...

Thanks, Alan. But couldn't the second premise just be read as follows (t* is the time of speech):

(p)(if there is a past time t such that at t John says that p, then at t* Peter believes that p)

Adam Arico said...

It seems practical to limit the scope of Peter's beliefs to those statements that he has heard John utter, but then the story can be similarly altered to preserve the problem posed by double-access readings:
P1: John said to Peter that Mary is pregnant.
P2: Peter believes everything that John (ever?) said to him
P3: Therefore, Peter believes that Mary is pregnant

Brit’s solution works just as well, if not better, but this is just another way of keeping the problem afloat.

Again, I'm afraid I don't see the problem. Yes, if we accept the premises, and if we also give the sentences double-access readings, then we are left to conclude that Peter has a potentially absurd belief (the belief is perfectly reasonable if Peter just talked to John an hour ago, yet perfectly absurd if it has been twenty years). But that's okay. If P2 (which, I think, is the source of potential absurdity) is true, then why wouldn't we be entitled to a double-access reading of the conclusion? Even though it seems counter-intuitive to grant Peter the belief when the utterance and the sentence are temporally distant, it logically follows from the premises. Unless we throw some sort of temporal limiter into P2 (e.g., P2*: Peter believes,for a reasonable/relevant duration, everything that John says), the logical consequence of P1 and P2 is that Peter will always believe that Mary is pregnant. Silly, yes; but valid nonetheless.

Brit Brogaard said...

Hi Adam. Here is the problem, as I imagined it (setting aside potential replies). We have an ordinary-language argument, viz "John said Mary is pregnant. Peter believes everything John said. So Peter believes Mary is pregnant" that appear to be valid. By 'appear to be valid' I mean that if you were to ask untutored "informants" (to use a term from linguistics) whether the inference is o.k., most would say that it is. We then use the theory we want to test to translate the premises and the conclusion. The theory should either give us the same result as our informants or explain why we do not get this result. Assuming that the tenses-as-quantifiers theory is the theory we want to test, then the conclusion does not have the reading you suggest. So, on a double-access reading of the first premise, the theory predicts that the argument is invalid.

Here is an analogy. According to Mark Richard, the following argument appears to be invalid:

Mary believed that Nixon was president.
Mary believes everything she believed.
So, Mary believes Nixon is president.

But temporalism makes the wrong predictions here, because it takes the proposition Mary once believed to be a temporal proposition, viz. the proposition that Nixon is president. Now, the temporalist cannot just reply that the argument is valid, unless she can explain why we tend to think it is not.

In other words, if a semantic theory makes predictions that deviate from the predictions made by untutored informants, then it has some explaining to do.