Moore-belief: ``p, and I don't believe that p."
Surprise Exam: ``p, and you won't know that p." ((i)change `I' to `you,' then (ii) change `don't know' to `won't know.')
Surprise Exam-belief: ``p, and you won't believe that p."
From this point of view, it seems that the simplest case would be to ignore the effect of time. What about a synchronous surprise-exam sentence:
Surprise Exam Synchronous: ``p, and you don't know that p."
[Can I say this to God, who knows everything? No.]
Should you believe SES? Let's agree in advance that it's certainly possible that something of the form of SES be true: there are plenty of true things that we do not know or believe!
SES could either be true or false. Case 1: it is true. Then you don't know that p. But why not? You've just been told. Perhaps the speaker has undermined her credibility by questioning your conversational competence (ie, your ability to pick up on what is said to you.) So even though the speaker is speaking truly, you can't tell she is. So she is correct. But if she is correct, then you should believe SES...shouldn't you?
[Quine's solution seems to be: to assume that SES is true is not to assume that you believe it is true. (This is the point with the Fermat analogy.) That's right in general, but the content of SES is special, such that, if you assume it's true, you ARE making assumptions about whether you believe it's true. Namely, you are assuming you don't believe it's true. And that is odd. Suppose the mathematician assumed not only that Fermat's theorem was true, but that he, the mathematician, didn't believe it, and relied on the fact that he didn't believe it to prove it! ]
Case 2: SES is false. Then (->) either p is false or you do know that p. Case 2a: p is false. No contradictions here; p is contingent, after all. [Is this something you cannot conclude if e.g. God is giving the exam? p may be contingent, but God is infallible*.] Case 2b. You do know that p. Then p is true. But this conflicts with the assumption of Case 2. Contradiction.
(What's needed here is not merely God's infallibility. There's also something about assertions. If I assert `p and q', I have asserted `p' and I have asserted `q'.)
The data are: the argument that there can be no exam appears sound, but it can't be true. So, what is wrong with the argument? The ``Logical Approach" says that the argument is not actually sound, because it is circular or self-referential in some way. [Compare: the sorites appears sound, but it can't be true. So, what is wrong with the sorites argument?] An alternative Logical Approach might be: the argument is sound, but it doesn't show what we think it shows.
The ``Epistemological Approach," on the other hand, is interested in the idea that whether or not an exam is a surprise depends on what we justifiably believe. So it is really a puzzle about justification. This is the route according to which the paradox is importantly related to Moore's sentence.
Logical approach: suppose the announcement is correct, and there will be a surprise exam. Then there won't be a surprise exam (because it won't be a surprise.)
(The announcement can be incorrect in two ways: either there will be no exam, or there will be but it won't be a surprise.)
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