Tuesday, July 13, 2010

On believing newspaper reports of lottery victories

In my paper on miracles I presented a typical objection to Hume-style arguments from probability against the acceptance of miracle reports.

But when one attempts to develop this idea into mathematical probability theory, one must avoid untoward consequences, and Hume simply did not possess the mathematical sophistication to accomplish this. If the theory of probabilistic inference he himself presents in "Of Miracles" is taken literally, it has the consequence that if the Arizona Republic were to report that I won the lottery, you should disbelieve the report, because my chance of winning the lottery is less than the percentage of erroneous reports by the Republic. But surely this is implausible.

Or consider reports in the media of one-time events, such as the election of an African-American President, or a landing on the moon. Before those events occurred, we had uniform experience of their nonoccurrence. If you assign those events a probability zero, then that means that whatever evidence we have for their occurrence has to be trumped by their antecedent improbability. This sort of example was pointed out by Hume's 18th century critics, and it looks as if it was even pointed out to Hume when he was writing "Of Miracles," since his treatment of the Indian Prince case looks to me like a response to a critic of an earlier draft.


Steven Carr said...

But those events are not assigned a probability of zero.

It is Christians who claim that some events break the laws of physics and so need a god to do them.

Victor Reppert said...

On the assumption that you have an omnipotent God, and you have some idea of what that God is likely to do, you have to take that into consideration.

Obviously, laws of physics are absolute only if physics is closed. It begs the question to assume causal closure when assessing the probability of events.