I just couldn't resist reposting some of a conversation I had on freeratio.org
A poster had asked how the problem of induction can be answered. I referred him to a post I wrote a while back and quoted it:
"I believe that it is more parsimonious (or simple) to postulate only one kind of cause for every kind of effect, and vice versa, and since simpler explanations are to be preferred (a view which I defend on a priori grounds in my book Atheism and Naturalism) then it follows it is reasonable to believe that the effects of the past that we observe today were created by causes that create similar effects in the present day. Think about it: If we observe Cause A creating Effect B, and we reason that it is simpler (and therefore more probable) to suppose that Effect B is only created by Cause A, then in cases where we observe Effect B without having the benefit of being around to witness Cause A occur, we can still be reasonably sure that Effect B was created by Cause A.
"And that isn't the only justification for induction. Here's another one: Induction can be likened to the sample-taking done by scientists. Scientists will often take a very large sample of something, and then reason that what is true of the sample is probably true of the whole (of whatever they are sampling). For example, if I interview 10,000 random people, and 90% of them inform me that they will re-elect Barack Obama, I can be reasonably sure that this is true of the entire population of voters. It is logically possible that somehow my sample wasn't representative of the entire population. Maybe, out of the entire population, only 10% want Obama re-elected. But it is extremely improbable that my sample would be that far off the mark.
"Likewise, when we reason inductively, we observe something so many times (equivalent to taking a sample) and we assume that that sample is probably representative of all cases of that kind of event."
Click here to read his response to this and my response to him. I spent a lot of time on the post, and if you're into philosophy then this should be intriguing.