How small must the chance of error be before we accept something as true and certain?
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From: Dann Corbit on 3 Aug 2010 13:49 In article <pan.2010.08.03.17.39.18.115194(a)nowhere.com>, nobody(a)nowhere.com says... > > 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. How great a chance > > of error is to be allowed? One chance in ten? One chance in a million? > > It depends entirely on how severe are the consequences of being wrong. If > you are trying to remember what time a movie starts that you really want > to see, you may just show up at the theater when you think the movie > starts, and just hope you are correct. If, however, you are an airline > pilot, ready to take off with a plane full of people, and a gauge on the > panel indicates a problem, you will abort takeoff until the problem is > solved. > > > 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. > > Even better: the odds of the cards in a deck of 52 cards being in one > particular sequence is roughly 10^70. However, the odds that they are in > one of those available sequences is 100%. That is why Creationists are > wrong when they say that the odds of some particular thing > turning out the way that it did are so small that Divine Intervention is > necessary to explain it. It's the difference between prediction and > rationalization after the fact. It also depends upon what the definition actually says, and how it is to be used. Imagine a planet with grass, ducks and eagles and no other flora or fauna. Imagine that there are 10^12th ducks and all of them are white except one, which is brown. The statement: "All ducks are white" is false, from a mathematical standpoint, though pragmatically true most of the time. It may also be true that brown is dominant genetically and in 50 years time most ducks are brown. Can a tornado go through a junkyard and assemble a ready-to-fly 747 from the junkpile? The probability is not zero, but it is close enough that we would never worry about it happening. |