Thursday, May 29, 2014

In what sense are miracles improbable?

Atheists typically classify miracles as inherently improbable. And even some Christian philosophers assign a very low (but surmountable) prior probability to miracles. Low in what sense?

Consider two examples to illustrate my question.

Richard Feyman once said: 

You know, the most amazing thing happened to me tonight. I was coming here, on the way to the lecture, and I came in through the parking lot. And you won't believe what happened. I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!

In what sense is that improbable? 

i) Perhaps he meant, what are the odds that a license plate would have that combination of letters and numbers. Those exact letters and numbers in that exact sequence.

Let's pick a figure out of the air. Suppose the odds are one in 20 million that a license plate would have that number. 

If, however, there were 20 million license plates, then it's a dead certainty that one plate will have that number.

So even though it's astronomically unlikely that any given plate will have that number, it's certain that some plate will have that number.

ii) But maybe what he meant was not the improbability of the license plate, but the conjunction of two independent events. What are the odds that a car with that particular license in that particular lot would be there at the same time he happened to be there? 

However, as a good physicist, wouldn't he say it that conjunction was bound to happen given the antecedent conditions? That there was a causal chain of events leading up to that conjunction? It seems (to me at least) counterintuitive to say something inevitable is astronomically improbable.

But perhaps we need to distinguish between what's metaphysically improbable and what's epistemically improbable.

iii) To take another comparison, what are the odds of having B- blood type? I think the answer depends on the reference group. It's 2% for Caucasians, but 0.4% for Asians. 

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