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-FALLACIESConfirmation
is key part of good reasoning, but it can be done badly. People sometimes use confirmation to convince themselves of things that really they should not believe.
i. -HIGH P(E|NOT-H)-
Forgetting about a Test’s False Positive Rate
Confirmation needs evidence for which P(E|Not-H) is lower than P(E|H). Ideally we want a zero false positive rate for any predicted evidence that supports an hypothesis. The most basic confirmation fallacy is simply to forget to consider P(E|Not-H): What’s the chance of this evidence if we’re wrong? If that probability is close to P(E|H), then the test is useless.
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Bob confirms that today is his girlfriend’s birthday:
Argument 12.1: If it’s my girlfriend’s birthday today
(which I forgot),…show more content… An ad hoc explanation is suggested just to “protect” an hypothesis from disconfirmation; but there is no other evidence for the explanation besides the false prediction.
Abby makes a precise prediction: Calvin’s house on 13th Ave. will burn down this year.
The year goes by, and Calvin’s house does not burn down.
The prediction was false. Abby should lower the probability of her hypothesis. But instead, she says: “Calvin’s house didn’t burn down, but I bet that’s only because the four-leaf clover that he keeps in his pocket is lucky, and it cancelled the bad luck of living on 13th Ave.”
We may assume that Abby does not have good evidence that four-leaf clovers have magic powers.
Her explanation of the false prediction looks ad hoc. She is just trying to protect her “13” hypothesis.
When is it rational to continue believing an hypothesis, and to try to think of another explanation after a false prediction? When is an explanation not ad hoc? The short answer is: when background beliefs support the hypothesis or the other explanation! That’s all we can say. The point here is that a