The only truth I have to announce is that I'm puzzled by something. Here is a familiar case.
Smith buys a ticket in a lottery with an enormous payoff. The odds are vanishingly small that Smith's ticket is a winner. Smith knows both the odds and that the payoff is enormous. If her ticket is a loser, it's a piece of trash. Smith realizes this, so she's considering recycling it. As a matter of fact, the ticket *is* a loser, and Smith believes that it is. Smith's only evidence that it's a loser, however, is her knowledge of the odds.
One of the following must be true, but which one? (In case it isn't obvious that one of these must be true, see "PROOF" below.)
(1) Smith doesn't know that the odds are vanishingly small that the ticket is a winner.
(2) She does know that the odds are vanishingly small that the ticket is a winner, yet she's not justified in proportioning her confidence to the odds.
(3) She's justified in proportioning her confidence to the odds (and thus being virtually certain) that the ticket won't win, yet she's not justified in believing that the ticket won't win.
(4) She's justified in believing that the ticket won't win, yet she doesn’t know that the ticket won't win.
(5) She does know that the ticket won't win, yet it's not acceptable for her to reason that, since the ticket won't win, she should recycle it.
(6) It's acceptable for her to reason that, since the ticket won't win, she should recycle it, yet it's not the case that she should recycle it.
(7) She should recycle it.
As I noted above, one of (1) through (7) must be true. But they are all hard to stomach. Very quickly, (1) through (7) have (at least) the following problems.
The scenario stipulates that (1) isn't the case, so, without reason to think the scenario is incoherent, we can't accept (1). Given that Smith wants to win the lottery, given that she paid good money for the ticket, and given that it's very little trouble for her to keep the ticket, it seems clear that (7) is false. If Smith had overriding reasons for not recycling the ticket, then (6) would seem true. But we can stipulate that she doesn't, in which case (6) looks false. And the same considerations apply to (5). It looks true if additional factors prevent Smith from reasoning that way, but we can just stipulate that they don't. Of course, Hawthorne and others would accept (4). But (4) seems unstable. Ex hypothesi, the ticket won't win and Smith isn't Gettiered with respect to her belief that it won't win. Thus, our grounds for denying that Smith knows seem to equal our grounds for denying that Smith is justified. (And speaking for myself, insofar as it's intuitive that Smith doesn't know, it's also intuitive that she's not justified.) So, it looks like anyone who wants to deny that Smith knows is pushed toward (2) or (3). But (2) seems false. Why on earth shouldn't Smith proportion her confidence to the odds? After all, ex hypothesi, she knows the odds and the odds exhaust her evidence. This leaves us with (3), which is also hard to swallow. Perhaps justified belief equals justified certainty. But then, which of our beliefs *is* justified? If we accept (3) and maintain that justified belief equals justified certainty, it will be a trick to avoid skepticism. Perhaps justified belief equals justified confidence above some threshold *below* certainty. But then, how can (3) be true while we have a significant stock of justified beliefs? Again, given that we accept (3), it will be tricky to avoid skepticism. Perhaps justified belief cannot be identified with any level of justified confidence, then. In this case, what does belief amount to, how is it related to confidence, and what explains how Smith could be justified in being virtually certain that the ticket won't win, yet not justified in *believing* that the ticket won't win?
I'm not sure what to say about these options, except that none of them looks particularly good. What do people think? If forced to pick among them, which should we pick?
Blake
PROOF: Here’s the proof I promised above.
Let 'p' through 'u' name the propositions in (1) through (7) as follows.
p = Smith knows that the odds are vanishingly small that the ticket is a winner.
q = Smith is justified in proportioning her confidence to the odds.
r = Smith is justified in believing that the ticket won't win.
s = Smith knows that the ticket won't win.
t = It's acceptable for Smith to reason that, since the ticket won't win, she should recycle it.
u = Smith should recycle the ticket.
Now consider the following presentation of (1) through (7).
(1) ~p
(2) p & ~q
(3) q & ~r
(4) r & ~s
(5) s & ~t
(6) t & ~u
(7) u
Either p is true or it's false. Suppose the latter. Then (1) is true. Suppose the former. Then either (2) is true or q is. Suppose q is. Then either (3) is true or r is. Suppose r is. Then either (4) is true or s is. So suppose s is true. Then either (5) is true or t is true. Suppose it’s t. Then either (6) is true or u is. But if u is true, then so is (7). So, one of (1) through (7) must be true.
Smith buys a ticket in a lottery with an enormous payoff. The odds are vanishingly small that Smith's ticket is a winner. Smith knows both the odds and that the payoff is enormous. If her ticket is a loser, it's a piece of trash. Smith realizes this, so she's considering recycling it. As a matter of fact, the ticket *is* a loser, and Smith believes that it is. Smith's only evidence that it's a loser, however, is her knowledge of the odds.
One of the following must be true, but which one? (In case it isn't obvious that one of these must be true, see "PROOF" below.)
(1) Smith doesn't know that the odds are vanishingly small that the ticket is a winner.
(2) She does know that the odds are vanishingly small that the ticket is a winner, yet she's not justified in proportioning her confidence to the odds.
(3) She's justified in proportioning her confidence to the odds (and thus being virtually certain) that the ticket won't win, yet she's not justified in believing that the ticket won't win.
(4) She's justified in believing that the ticket won't win, yet she doesn’t know that the ticket won't win.
(5) She does know that the ticket won't win, yet it's not acceptable for her to reason that, since the ticket won't win, she should recycle it.
(6) It's acceptable for her to reason that, since the ticket won't win, she should recycle it, yet it's not the case that she should recycle it.
(7) She should recycle it.
As I noted above, one of (1) through (7) must be true. But they are all hard to stomach. Very quickly, (1) through (7) have (at least) the following problems.
The scenario stipulates that (1) isn't the case, so, without reason to think the scenario is incoherent, we can't accept (1). Given that Smith wants to win the lottery, given that she paid good money for the ticket, and given that it's very little trouble for her to keep the ticket, it seems clear that (7) is false. If Smith had overriding reasons for not recycling the ticket, then (6) would seem true. But we can stipulate that she doesn't, in which case (6) looks false. And the same considerations apply to (5). It looks true if additional factors prevent Smith from reasoning that way, but we can just stipulate that they don't. Of course, Hawthorne and others would accept (4). But (4) seems unstable. Ex hypothesi, the ticket won't win and Smith isn't Gettiered with respect to her belief that it won't win. Thus, our grounds for denying that Smith knows seem to equal our grounds for denying that Smith is justified. (And speaking for myself, insofar as it's intuitive that Smith doesn't know, it's also intuitive that she's not justified.) So, it looks like anyone who wants to deny that Smith knows is pushed toward (2) or (3). But (2) seems false. Why on earth shouldn't Smith proportion her confidence to the odds? After all, ex hypothesi, she knows the odds and the odds exhaust her evidence. This leaves us with (3), which is also hard to swallow. Perhaps justified belief equals justified certainty. But then, which of our beliefs *is* justified? If we accept (3) and maintain that justified belief equals justified certainty, it will be a trick to avoid skepticism. Perhaps justified belief equals justified confidence above some threshold *below* certainty. But then, how can (3) be true while we have a significant stock of justified beliefs? Again, given that we accept (3), it will be tricky to avoid skepticism. Perhaps justified belief cannot be identified with any level of justified confidence, then. In this case, what does belief amount to, how is it related to confidence, and what explains how Smith could be justified in being virtually certain that the ticket won't win, yet not justified in *believing* that the ticket won't win?
I'm not sure what to say about these options, except that none of them looks particularly good. What do people think? If forced to pick among them, which should we pick?
Blake
PROOF: Here’s the proof I promised above.
Let 'p' through 'u' name the propositions in (1) through (7) as follows.
p = Smith knows that the odds are vanishingly small that the ticket is a winner.
q = Smith is justified in proportioning her confidence to the odds.
r = Smith is justified in believing that the ticket won't win.
s = Smith knows that the ticket won't win.
t = It's acceptable for Smith to reason that, since the ticket won't win, she should recycle it.
u = Smith should recycle the ticket.
Now consider the following presentation of (1) through (7).
(1) ~p
(2) p & ~q
(3) q & ~r
(4) r & ~s
(5) s & ~t
(6) t & ~u
(7) u
Either p is true or it's false. Suppose the latter. Then (1) is true. Suppose the former. Then either (2) is true or q is. Suppose q is. Then either (3) is true or r is. Suppose r is. Then either (4) is true or s is. So suppose s is true. Then either (5) is true or t is true. Suppose it’s t. Then either (6) is true or u is. But if u is true, then so is (7). So, one of (1) through (7) must be true.
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