Let's have turkey!
Every day for a thousand days, the farmer feeds a turkey. At the start of all of this, the turkey is unsure of his environment. As the farmer starts feeding him, he sees the pattern: this farmer guys has his best interest at heart! He provides a shelter for him. He gives him food. Takes care of him when he is sick. Every day, the turkey's confidence in this belief grows - corroborating evidence, he says! Until day one thousand and one, Thanksgiving.
The above example was lifted from a book a friend recommended to me that I am currently reading: The Black Swan. It is also an example that I have used most of my life in a different form to show why I do not believe in inductive reasoning. Low probability events with high impact are ignored by humans - we are not really wired for it, and yet those types of events are what make our world what it is. We live in denial.
People make predictions based on the past, thinking that each new piece of corroborating evidence makes their predictions more valid, and yet that is provably false. If A then B. Not B. Therefore Not A. "All swans are white" and all swans you ever see are white, seeing more white swans does nothing to prove that all swans are white. The correct version of this sentence, based on the stated logic is:
If Swan, then White.
Not White.
Therefore not Swan.
So, any non-white object that you see would be proof that there are no black swans, even though black swans do exist. A red car therefore proves all swans are white. This is the Black Swan theory. Induction and corroboration fail in the real world. It is events on the edge, events that can not be predicted based on the past that wreck the models we have. Just like day one thousand and one for the turkey - he will have no way of knowing he future or the real reason for events in his life up to that day. But someone with a different vantage point might... like The Farmer.
The Edward