philosophy paper 3
Valerielee
12.3SolutionstothePredictionParadoxII.pdf
8/27/2015
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Phil 2: Puzzles and Paradoxes
Prof. Sven Bernecker
University of California, Irvine
Lecture 12.3
Solutions to the
Prediction Paradox II
Proposed Solutions
• Reinterpreting the teacher‘s announcement (Olin, “Believing in
Surprises“, pp. 42-3)
• Disallowing reasoning backwards in time (Olin, “Believing in Surprises,“
pp. 41-2)
• Denying knowledge of future contingents
• Rejecting the KK-thesis (Olin, “Believing in Surprises,“ pp. 46-51)
• Denying knowledge of the teacher‘s announcement (Olin, “Believing in
Surprises,“ pp. 51-7)
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Prop. Solution: Denying Knowledge
of Announcement
• Proposal: for the student to reason the way she does, it has to be
assumed that the teacher’s announcement is true and that the
student knows that it is true. But the student cannot know the
truth of the announcement. This solves the paradox: surprise
exams are possible, but the stduents cannot know that there will
be a surprise exam.
• Why is it not possible for the student to know that the teacher’s
announcement is true?
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The first stage of the student’s argument:
But for the student to know on Thursday evening that an exam will be given on
Friday she also needs to know (remember) that the teacher is reliable and said:
The student also needs to know (remember) that the teacher who is reliable,
said:
Thesis: the student cannot know (A) on Thursday evening.
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(B) If an exam is held on day D then you will not know this before that day.
(A) There will be an exam on exactly one of the days Monday to Friday
If the only exam of the week is held on Friday, then on Thursday evening
the student will know that an exam will be held on Friday.
8/27/2015
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Why can the student not know (A) on Thursday evening?
There is no epistemically relevant difference for the student between (A)
and (B). The student has exactly the same evidence for each: the fact
that the teacher said it. But if the student knows both (A) and (B), then,
realizing that it is now Thursday evening and no exam has yet been
held, she also knows this statement:
Statement (C) is the knowledge version of Moore’s paradox (see lecture
11.3):
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(C) There will be an exam on Friday and I don’t know that there will be an
exam on Friday.
p, but I don’t know that p
• In lecture 11.3 we saw that a statement of the form “p, but I don’t
know that p” cannot be sincerely asserted without absurdity.
• Here the issue is that the student cannot know the statement “p but I
don’t know that p.” For if the student knew
• then she would know that she does not know that there will be an
exam on Friday. But if she knows that she does not know that there
will be an exam on Friday, then she does not know that there will be
an exam on Friday. So the student cannot know (C).
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(C) There will be an exam on Friday and I don’t know that there will be
an exam on Friday.
• Given that the student cannot know (C), she cannot know (A).
• Even though on Thursday evening the student has evidence that
confirms (A), she does not know (A). To know (A) she would have
to know “p, but I don’t know that p.” But that’s impossible.
• And if the student cannot know (A), then she cannot know that the
teacher’s announcement is true. So on Thursday evening, given
no prior exam, the student cannot know the teacher’s
announcement.
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(A) There will be an exam on exactly one of the days Monday to Friday.
• The prediction paradox is a problem about knowledge.
• Surprise exams are possible and they can be sincerely
announced. At the time the teacher announces the surprise
exam the student can also know there will be a surprise exam
sometime next week.
• But at various later junctures (e.g., on Thursday evening) the
students can no longer know that there will be a surprise exam.
They cannot know this because their knowing it is incompatible
with it being a surprise exam.
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