2011-04-16, 12:12 AM
I don't think it's fair to say that it's "illogical", in any case. When really the only logical leap made is a relatively minor one: assuming that induction works in general, because it's never failed.
Personally, I think the law of large numbers is the most telling argument in favour of induction:
Just because you don't know something is true or false, does not mean the two are equally likely.
If I claim that I've flipped 10 coins, and the result was 10 heads, it's quite proper for you to be more skeptical than if I claim that it was 4 tails and 6 heads. Probabilistically speaking, of all the outcomes after flipping 10 coins, it takes a greater amount of "faith" to believe in the least likely proposition.
In order for the universe to suddenly change, and make induction invalid, it would have to go against every scientific test to this date - every attempt to predict the future that progressed successfully. The odds of that happening at the exact moment of your test, give that it has never happened before should be considered miniscule, and thus not cause for great concern.
If you like, you could break down the universe into smaller and smaller components of time, see that the same laws have governed each of these forward progressions - and the closer you get, the more it defies probability that in the next tiny unit of time, it'll go against all history and do something new. When you have 10^40 observations to the affirmative, and none to the negative, it's fair to say your next observation is more likely to also be affirmative.
Personally, I think the law of large numbers is the most telling argument in favour of induction:
Just because you don't know something is true or false, does not mean the two are equally likely.
If I claim that I've flipped 10 coins, and the result was 10 heads, it's quite proper for you to be more skeptical than if I claim that it was 4 tails and 6 heads. Probabilistically speaking, of all the outcomes after flipping 10 coins, it takes a greater amount of "faith" to believe in the least likely proposition.
In order for the universe to suddenly change, and make induction invalid, it would have to go against every scientific test to this date - every attempt to predict the future that progressed successfully. The odds of that happening at the exact moment of your test, give that it has never happened before should be considered miniscule, and thus not cause for great concern.
If you like, you could break down the universe into smaller and smaller components of time, see that the same laws have governed each of these forward progressions - and the closer you get, the more it defies probability that in the next tiny unit of time, it'll go against all history and do something new. When you have 10^40 observations to the affirmative, and none to the negative, it's fair to say your next observation is more likely to also be affirmative.