antishock8 wrote:You just proved my point, brother. Using your logic then it's up to the individual to decide whether or not whatever point, proved through induction, is worth accepting as fact. OR, because the conclusion is disheartening it can be disregarded because there's no way to prove it infallibly.
You can't prove anything via induction. That's the entire point. All you can really do is establish levels of probability.
If you don't believe me, go read the latest copy of
Nature or
Science and let me know how many times scientists use the word "prove" (or equivalent language) to describe the results of their research. Science depends almost exclusively on induction, but good scientists understand the limits of this form of reasoning (and, hopefully, have read their Popper).
Induction must assume that there is no "weirdness" present in the universe; or that natural laws are responsible for making everything behave similarly. There are numerous real-world examples, however, that illustrate that this is not the case. As a simple case, take the lottery: a sample of hundreds or even thousands of individuals who have played the lottery would very likely reveal no jackpot winner. This sample could be repeated many times and almost certainly reveal the same result. What would be a valid conclusion?
A. Those who play the lottery are extremely unlikely to win the jackpot. (And its corollary: It is unwise to play the lottery at all from a financial standpoint.)
B. Nobody wins the lottery.
A is valid. B is invalid. (Some A --> Every A is a basic logical fallacy in predicate calculus) Lottery winners exist, but they are a data point which sampling is unlikely to be able to measure, therefore they fall outside the ability of induction to analyze completely. At the same time, we cannot say that induction provides no relevant analysis: it is perfectly valid to base one's decision-making off of A, and one need not resort to the unwarranted certainty of B's declaration to do so.
"My name is Ozymandias, king of kings: Look on my works, ye Mighty, and despair!" Nothing beside remains.