Thursday, September 25, 2014

Possibility, probability and propensity

I have defended at length the idea that metaphysical possibility is grounded in the causal powers of things. It just occurred to me that this view is very naturally connected to the view that objective probability is grounded in causal propensities. We can think of probability as a measure of the degree of possibility, and of possibility as an attenuated kind of probability. If we see things in this very natural way—and hopefully its naturalness isn't just due to alliteration—then we have a unified and mutually supporting story about probability and possibility. Both are grounded in causal powers, but differently. Possibility is grounded in the bare existence of causal powers. Probability is grounded in the propensities of causal powers. If we have reason to accept one view, that tends to give us reason to accept the other.

Clearly anything that's made possible by the causal powers account of possibility—let's call this "causally possible"—is possible. So the only question about the causal powers account of possibility is whether it captures all possibilities. Suppose some things are possible but not causally possible. Then we can ask about their probabilities. If probabilities are propensities, then we should say that such things have zero probability, since nothing has a propensity to produce them. And not just the kind of "numerical zero" that classical probability assigns to a sequence of infinitely many heads, but the deep kind of zero that is had by the probability that one equals two. It's plausible, though, that things with this deep zero probability just can't happen. So the propensity account of probability neatly suggests the causal powers account of possibility.

And the converse is also plausible. If all possibilities are causal possibilities, it is very natural to measure the degree of their possibility by the causal propensities.

Of course the above is very vague. It may be that particular details of how one works out a causal powers account of possibility don't sit well with the particular details of a propensity account of objective probability.


Heath White said...

I'm going to have to remember the phrase "the deep kind of zero".

Alexander R Pruss said...

I remember a paper where they distinguished between "0" and "0*" in this context. I don't remember for sure which was which.

William said...
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Michael Gonzalez said...

Pruss, have you ever considered the connection between Ockham's Razor and the PSR? If Ockham's Razor is stated as "do not multiply causes beyond necessity", then anyone who accepts that principle had better accept the PSR, or else they will never accept any causal explanation of anything. If contingent statements can hold without causes, then Ockham's Razor will always cut against any putative causes, won't it?

This was just a random rumination of mine, but you were the first person who came to mind when I thought of it.