Assuming a lottery of n tickets, the premises are:
P1. Ticket 1 won't win
P2. Ticket 2 won't win
P3. Ticket 3 won't win
...
Pn. Ticket n won't win
From this we can deduce:
C1. No ticket will win
It's a valid inference. — Michael
Let's say that 100 people have each picked out a ball. Given the high odds, I am justified in believing that Person 1 doesn't have the black ball. — Michael
In Gettier's original example, a person called Smith is applying for a job. Another person, Jones, whom is known to have 10 coins in his pocket, is applying for the job as well, and Smith (for a justified reason) believes Jones will get the job. This is the belief a. The conclusion b is that the person who gets the job has 10 coins in his pocket. What happens is that Smith himself gets the job, but also, although he didn't know this, had 10 coins in his pocket. — BlueBanana
Uh... No. No. No.
Read the paper...
↪creativesoul Nitpicking, the case is practically the same. — BlueBanana
Uh, no it's not. The differences matter tremendously. — creativesoul
Because you cannot rule out the possibility that any of these people have the ball you are not justified in believing that any one of them doesn't have the ball. Until you rule out the possibility that X is the case you are not justified in believing X is not the case. The justified belief is X is probably not the case. Likewise, with the lottery, if one has a ticket, the belief that this person will not win is not justified. That's why people buy tickets, the belief "I will not win" is not justified despite the low odds. However, "I will probably not win is justified". — Metaphysician Undercover
It does. If for each ticket "this ticket won't win" is true then no ticket will win. — Michael
... it's not true that if you buy P1, P2, P3,...Pn that no ticket will win. That's like saying if I buy every possible ticket, no ticket will win, again it doesn't follow. — Sam26
That wasn't my argument, though. My argument was that if P1 won't win and if P2 won't win and if P3 won't win ... and if Pn won't win then no ticket will win. — Michael
The argument is:
P1. Ticket 1 won't win
P2. Ticket 2 won't win
P3. Ticket 3 won't win
P4. There are 3 tickets
C. No ticket will win
(Except with more than 3 tickets, obviously). — Michael
This argument I can agree with, but it's more complicated than that. Here we're talking about what's probably the case, and the inductive argument above is weak, so the conclusion that no ticket will win follows. However, if my argument is based on P1, P2, P3...P4 (P4 being the total number of tickets bought, viz., 1.2 x 10^8), out of a possible number of possibilities of 1.5 x 10^8, then what conclusion do you think follows? It certainly isn't that C. No ticket will win. It's then probable (based on my e.g.) that you have a winning ticket based on the number of tickets you've bought in relation to the total number of possible combinations. — Sam26
The argument is:
P1. Ticket 1 won't win
P2. Ticket 2 won't win
P3. Ticket 3 won't win
P4. There are 3 tickets
C. No ticket will win
(Except with more than 3 tickets, obviously). — Michael
All I'm saying is that the above argument follows, but the conclusion would change based on the number of tickets bought. Originally you included P4 as Pn, which would mean a range of possible numbers, and its this range which would change the conclusion. The conclusion that no ticket will win depends on the range of Pn, and if the range is high enough, then your conclusion would be false. It's true, given this e.g., but it may be false given your other example. If this doesn't relate to your point, then I'm not sure what you're saying. — Sam26
What about the chair I'm sitting in? Is there a vanishingly small but non-zero chance it will disappear as I sit here, or turn into pudding, or whatever? Maybe? — Srap Tasmaner
So while self-contradiction might rule out a possibility, contradicting some belief or beliefs of ours does not. — Srap Tasmaner
Then what makes the ID example different to the lottery ticket example? We're justified in believing that the ID isn't fake because the probability that it is is high, but we're not justified in believing that the lottery ticket won't win even though the probability that it will is high? — Michael
P1. Ticket 1 won't win
P2. Ticket 2 won't win
P3. Ticket 3 won't win
...
Pn. Ticket n won't win
From this we can deduce:
C1. No ticket will win — Michael
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