The big problem with producing theory by induction is that you can’t use it to extrapolate to unobserved cases: The “prediction” is only viable within the range of cases in which it was developed. We have no epistemological reason to believe that what happened today will happen tomorrow. A child who moves to Alaska during the winter – a six-month period of perpetual darkness – may believe that the sun has died or will never appear again. Just because the first few months of the child’s stay in Alaska are dark, however, does not mean that the darkness will persist forever. It was a valid inference within the period in which it was developed, but no matter what the child thinks, we have no logically valid reason to believe that the theory will hold tomorrow, or four weeks from now, or a year from now.
Just like all those investment agency ads note in the fine print, past performance is not a guarantee of future performance. Take, for example, Bertrand Russell’s famous story of the inductivist turkey:
The turkey found that, on his first morning at the turkey farm, that he was fed at 9 a.m. Being a good inductivist turkey he did not jump to conclusions. He waited until he collected a large number of observations that he was fed at 9 a.m. and made these observations under a wide range of circumstances, on Wednesdays, on Thursdays, on cold days, on warm days. Each day he added another observation statement to his list. Finally he was satisfied that he had collected a number of observation statements to inductively infer that `I am always fed at 9 a.m.’. However on the morning of Christmas eve he was not fed but instead had his throat cut.[1]
Or, as famed physicist Richard Feynman noted in his commentary on the Challenger disaster report, “When playing Russian roulette the fact that the first shot got off safely is of little comfort for the next.”[2]
More precisely speaking, we can fit an infinite number of lines through a set of points and still obtain the same squared correlation coefficient (R2, or amount of variation explained). This means that the problem of induction is not, “is my theory correct,” but is instead “which theory is correct?” And unfortunately, without being able to make predictions outside of the sample, we have no way to test the theories to determine which is correct.
[1] Quoted from http://www.network54.com/Forum/44103/message/984939488/Russell%27s+Inductivist+Turkey
[2] Quoted from http://thephilosophyofscience.wordpress.com/2011/06/15/the-unexpected/