How small must the chance of error be before we accept something as true and certain?
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From: Immortalist on 2 Aug 2010 20:15 Suppose, for the sake of argument, that a belief could be completely justified without all chance of error being excluded. How great a chance of error is to be allowed? One chance in ten? One chance in a million? It won't matter. If there is one chance n, whatever number n may be, we shall be led into contradiction. Imagine we say one chance in a million is acceptable. Now, suppose we set up a fair lottery with a million tickets numbered consecutively from 1, and that a ticket has been drawn but not inspected. Of course, there is only one chance in a million that the number 1 ticket has been drawn. So by the current proposal, we would be completely justified in believing that the number 1 ticket was not picked. There is only one chance in a million of error. Hence we would be completely justified in claiming to know that the number 1 ticket was not picked. Moreover, people really do speak this way about lotteries; they do say they know that the ticket they hold was not drawn because there is so little chance of it. However, a similar claim can be made concerning the number 2 ticket, for there is equally little chance that it was picked. So we can say that we know that the number 2 ticket was not picked. But then the same reasoning applies to each ticket in the lottery. Of each ticket in the lottery, we would be completely justified in believing, and, hence, in claiming to know, that the ticket has not been drawn. But the set of things we would thus claim to know is inconsistent. It is contradictory to claim that each of the tickets in a fair lottery with one winning ticket is not the winner. For if each is not the winner, then the lottery with one winning ticket has no winning ticket. Of course, requiring the chance of error to be less than one in a million will not help. However small the chance, we can find a large enough lottery to create the paradox. Since the assumption that a belief may be completely justified though there is some chance of error leads to contradiction, we must reject it. To analyze knowledge in terms of complete jusification that allows for some chance of error is to render knowledge logically inconsistent... Philosophical Problems and Arguments: An Introduction by James W. Cornman, Keith Lehrer, George Sotiros Pappas http://www.amazon.com/exec/obidos/tg/detail/-/0872201244/
From: Virgil on 2 Aug 2010 21:50 In article <fbb9b92d-178a-4e4a-9628-9b0a2eb37fb7(a)u38g2000prh.googlegroups.com>, Immortalist <reanimater_2000(a)yahoo.com> wrote: > Suppose, for the sake of argument, that a belief could be completely > justified without all chance of error being excluded. How great a > chance of error is to be allowed? Suppose not!
From: Cwatters on 3 Aug 2010 07:31 "Immortalist" <reanimater_2000(a)yahoo.com> wrote in message news:fbb9b92d-178a-4e4a-9628-9b0a2eb37fb7(a)u38g2000prh.googlegroups.com... > Suppose, for the sake of argument, that a belief could be completely > justified without all chance of error being excluded. How great a > chance of error is to be allowed? One chance in ten? One chance in a > million? It won't matter. If there is one chance n, whatever number n > may be, we shall be led into contradiction. Imagine we say one chance > in a million is acceptable. Now, suppose we set up a fair lottery with > a million tickets numbered consecutively from 1, and that a ticket has > been drawn but not inspected. Of course, there is only one chance in a > million that the number 1 ticket has been drawn. So by the current > proposal, we would be completely justified in believing that the > number 1 ticket was not picked. There is only one chance in a million > of error. Hence we would be completely justified in claiming to know > that the number 1 ticket was not picked. > > Moreover, people really do speak this way about lotteries; they do say > they know that the ticket they hold was not drawn because there is so > little chance of it. They say that not just because of the odds but also because of superstition (if I run around claiming to have a winning ticket I'm bound to jinx myself). There are also no negative consequences of being wrong, the worse that happens is they win the lottery. Would they feel so confident in asserting they didn't have the winning ticket if the consequences of "winning" was death?
From: Zerkon on 3 Aug 2010 09:43 On Mon, 02 Aug 2010 17:15:56 -0700, Immortalist wrote: > Suppose, for the sake of argument, that a belief could be completely > justified without all chance of error being excluded. This premise is so loaded with mixed innuendo. A coin tossed into the air might carry a belief but belief and chance becomes irrelevant when the coin lands. 'Justified' demands one who acts as judge. Odds demand odd makers. What or who grounds these terms? Suppose for the sake of more interesting argument, belief is not a spectator sport. Belief becomes conviction or principle with innate justification and a basis for action. A believer does things not just wait for things to be done.
From: John M on 3 Aug 2010 22:55
"Immortalist" <reanimater_2000(a)yahoo.com> wrote in message news:fbb9b92d-178a-4e4a-9628-9b0a2eb37fb7(a)u38g2000prh.googlegroups.com... > Suppose, for the sake of argument, that a belief could be completely > justified without all chance of error being excluded. How great a > chance of error is to be allowed? One chance in ten? One chance in a > million? It won't matter. If there is one chance n, whatever number n > may be, we shall be led into contradiction. Is it true if I claim you and I are both people? How can I prove being happy? So the belief must define it's own margin of error. Which is the primary problem with the concept of God, everyone seems to have their own definition of the word, so how can that concept be proven or disproved with sufficient 'accuracy'? But lets try another way. On the blackboard any level of precision can be generated, but in the /real world/ certainty is as illusive as the wind. What if I sell apples for a living? I wish to know, with mathematical precision (sufficient certainty) which aspect of an apple is more valuable to my customers, a nice red color or a nice round shape? Or which mix of the two, etc? How do we compare/quantify two entirely different things such as color and shape? "Fuzzy Multidimensional Logic" "No assertion is ever known with certainty... but that does not stop us making assertions." Carneades, 214-129 BCE Conclusion "The fuzzification of our ideas is not a new thing, our brains have been doing it for millions of years. What is new is the discarding of the dualist true/false dogma of traditional philosophy, which has created a world strewn with artificially forced boundaries, whether they be logical, scientific, religious or political - a justification for conflict that has been enthusiastically embraced by shallow thinkers everywhere." http://www.calresco.org/lucas/fuzzy.htm |