Comment on Infinite Certainty

Sun, 27 May 2012 03:46:11 GMT

A string of nines as long as the Bible is really, really long.

But if we aren't willing to assign probabilities over some arbitrary limit (other than 1 itself), we've got some very serious problems in our epistemology. I would assign a probability to the Modern Synthesis somewhere around 0.99999999999999 myself.

If proposition An is the proposition "the nth person gets struck by lightning tomorrow", then consider the following conjunction, n going of course from 1 to 7 billion: P(A1 & A2 & ... & A7e9) Now consider the negation of this conjunction: P(~(A1 & ~A2 & ... A7e9))

I had damn well better be able to assign a probability greater than 0.9999 to the negation, or else I couldn't assign a probability lower than 0.0001 to the original conjunction. And then I'm estimating a 1/10000 chance of everyone on Earth getting struck by lightning on any given day, which means it should have happened several times in the last century. Also, I can't assign a probability of any one person being struck as less than 1/10000, because obviously that person must get struck if everyone is to be struck.

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