philosophy discussion
Valerielee
8/28/2015
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Phil 2: Puzzles and Paradoxes
Prof. Sven Bernecker
University of California, Irvine
Lecture 14.2
Lottery Puzzle
Lottery Puzzle
• There are knowledge versions of the lottery paradox (I refer to them
as Lottery Puzzles to distinguish them from the Lottery Paradox)
that are not about actual lotteries. These lottery puzzles operate with
the principle of closure under known implications (instead of the
conjunction principle) and with fallibilism (instead of the probability
principle).
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“Recently … there has been a flurry of debates on the epistemic status
of lottery statements [i.e., lottery propositions], in the course of which
examples have been produced that may have significance for the
paradox and for closure” (Olin, A Case Against Closure, p. 242).
Two Epistemic Principles
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Fallibilism: If it is both highly probable and true that p, then (ceteris
paribus) S knows that p.
Closure under known implication: If S knows that p and if S
knows that p implies q, then S knows that q.
Fallibilism
• A subject can know something even though it could have been
false. This is not the same as saying that the subject can know
something that is false. Only truths can be known. (see lecture
11.3, slide #4).
• Fallibilism claims that a belief held on the basis of some evidence
can be knowledge even though the subject could have held that
belief on the basis of the same evidence in circumstances where
the belief is false. So the evidence that is sufficient for knowledge
in certain circumstances need not preclude the possibility of
error.
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Closure
Example: Sally knows that she is petting a dog. She also knows that
“being a dog implies being a mammal". Sally knows that she is petting a
mammal.
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Closure under known implication: If S knows that p and if S knows
that p implies q, then S knows that q.
The intuitive appeal of closure lies in the sense that in a valid argument,
the epistemic status of the premises extends to the conclusion” (Olin, A
Case Against Closure, p. 236)
Closure under known implication is weaker than:
Closure under implication: If S knows that p and if p implies q,
then S knows that q.
Closure under implication is implausible because it requires S to be
logically omniscient.
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Closure under known implication: If S knows that p and if S knows
that p implies q, then S knows that q.
• Note that the closure principle leaves it open how S knows
that q. That’s why the closure principle is different from this
principle:
– Transmission of knowledge: If S knows that p, and
knows that p implies q, then S knows q on the basis of p.
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Closure under known implication: If S knows that p and if S knows
that p implies q, then S knows that q.
Counterexample to Transmission of Knowledge (Olin, p. 237-8):
• Suppose I know
p: Cynthia will watch TV the entire evening on Wednesday
• based on her announced intention to do so. It is clear to me that p
implies:
q: There will not be a power failure on Wednesday evening.
• Transmission fails because my evidence that Cynthia will watch TV
on Wednesday evening -- her announced intention -- is clearly not
evidence that there will not be a power failure on Wednesday
evening. Since the evidence for p is not evidence for q I cannot
come to know q on the basis of knowing p.
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Examples of Lottery Puzzle
1) S knows that S won’t have enough money to go on a safari this year.
2) If S knows that S won’t have enough money to go on a safari this
year, then S is in a position to know that S will not win a major prize in
a lottery this year.
C) Therefore, S is in a position to know that S will not win a major prize in
a lottery this year.
Intuitively (1) and (2) are true, but in spite of the fact that (C) follows from
(1) and (2), intuitively (C) is not true.
Closure principle:
1) If S knows that p and
2) S knows that p implies q
C) Then, S knows that q 9
Another example:
1)I know that my car is now parked in Mesa Parking Structure
2)If I know that my car is now parked in the Mesa Parking Structure,
then I am in a position to know that my car has not been stolen in the
last few minutes.
C) Therefore, I am in a position to know that my car has not been
stolen in the last few minutes.
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My epistemic situation with respect to
parking my car is like my epistemic situation
with respect to a lottery. When I park my car
in an area with an appreciable rate of auto
theft, I enter a lottery in which cars are
picked, essentially at random, to be stolen
and driven away. Having my car stolen is the
unfortunate counterpart to winning the lottery.
Structure of Lottery Puzzle
Closure under known implications: If S knows that p and if S knows that p
implies q, then S knows that q.
p = ordinary proposition
q = lottery proposition
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“There is ... an ordinary proposition, a proposition of the sort that we ordinarily
take ourselves to know. There is, on the other hand, a lottery proposition, a
proposition of the sort that, while highly likely, is a proposition that we would be
intuitively disinclined to take ourselves to know. And ... the ordinary proposition
entails the lottery proposition” (Hawthorne, Knowledge and Lotteries, p. 5).
• Why ordinary propositions but not lottery propositions are knowable?
• Many philosophers define knowledge by means of this necessary
condition:
• If “p“ stands for an ordinary proposition, this knolwedge condition is
satisfied; but if “p“ stands for a lottery proposition it is not satisfied.
– If my car were stolen, I would still believe that it is not.
– If my ticket were going to win, I would still believe that it‘s a losing
ticket.
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S knows that p only if: if p were false, S would not believe that p
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Solutions to Lottery Puzzle
• Denial of knowledge of ordinary propositions (skepticism)
• Acceptance of the conclusion
• Denial of closure under known implications
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