Trying to Explain Epistemic Probability With a Dice Bag

Before we get too far, here is the video that I am responding to. I am going to be referring to parts of it throughout this post, so I suggest watching it to get the necessary context. In it, Tracie Harris is using regular six-sided dice and an opaque dice bag to explain, with the help of Matt Dillahunty, the idea that one cannot just say that something is possible, even if one does not know that such a thing is impossible. While I think that this example is very insightful and good, I think that it can be improved with the help of some more nuance, namely around the idea of possibility.

How to make the idea of possibility more nuanced? We can do this by distinguishing between two kinds of possibility: ontological possibility and epistemic possibility. For instance, in the dice bag example in the video it is either ontologically possible for an 18 to be rolled, or ontologically impossible for an 18 to be rolled. The number of dice in the bag will determine whether it is ontologically possible for an 18 to be rolled.

Epistemic possibility is a little trickier to explain. Think of it this way: if I say that both the ontological possibility of rolling an 18, and the ontological impossibility of rolling an 18 are possible in the dice bag example, I am speaking of epistemic possibility. That is, from where we are sitting, in ignorance of the ontological possibility or impossibility of rolling an 18 with the contents of that dice bag, we can still say that for all we know either case is possible. Or in saying, “it may be ontologically possible to roll an 18″, the ‘it may be‘ part is not redundant with the latter part of the statement, but rather a statement of epistemic possibility in regards to the latter part of the statement.

Now, before this gets dismissed as supporting the idea that someone could rightly say that the supernatural is possible(the kind of claim that the video was arguing against), I want to clarify that if the statement “the supernatural is possible” is using ontological possibility, it is clearly unfounded. But, if the statement “the supernatural is possible” is meant to convey the idea that “for all I know, the ontological possibility or ontological impossibility of the supernatural could be the case” then it is not so wrong-headed, or at least not wrong in the same way as the first meaning.

To concisely sum up the above, I have tried to show that the statement, “it may be possible that X” is not redundant, in that, ‘it may be‘ is speaking of a different kind of possibility than the rest of the sentence. It seems clear that to say “it is possible that X” is different than “it may be possible that X”  Now I want to take this a little further and show why this distinction is important.

The reason why this is important, separate from the fact that more nuance is generally a good thing, is that it allows us to truly proportion our beliefs to the available evidence. Let’s keep going with the dice bag example for this. It seemed that in the base example in that video, Matt is given little to no evidence to move him to justify the claim that the dice in the bag can possibly roll an 18 or the claim that it is impossible to do so. That said, we can imagine taking this dice bag example a little further and provide some information about the bag or its contents that can serve as evidence. This evidence can then move us to think that either the claim that it is possible to roll an 18 is more likely to be true than the claim that it is impossible to roll an 18, or vice-versa.

For instance, if Tracie(who knows exactly how many dice are in the bag) decided to just say that there are three dice in the bag, we could evaluate whether her statement serves as evidence for either claim. Perhaps she sounds serious when she says this, and doesn’t appear to be bluffing, and suppose that we know that she is generally trustworthy, well then we might then think that her statement is strong evidence for the claim that it is possible for the dice to roll an 18. Of course, she could be misremembering, or she could in fact be bluffing, so the statement of her’s might not be the strongest evidence for the claim that it is possible to roll an 18, but one could say that given the tone, and her track record, it seems much more likely that she is telling the truth, and thus it seems much more likely that it is possible to roll an 18. This evidence does not conclusively prove whether it is possible or impossible, but it can sway us closer to one of those sides.

We could imagine more kinds of evidence, like perhaps the bag just looks really full, or really empty, or making lots of clanging sounds as it is moved(indicating many dice) or little to no sounds(indicating 1 die). There are many observations that we can make that can serve as evidence for either claim, and ideally, we would consider all the available evidence and proportion our belief in either the claim that it is possible, or the claim that it is impossible, based on the weight of the total evidence.

Proportioning one’s beliefs based on the available evidence is not merely trying to hold more true beliefs than false ones, but rather trying to believe claims in proportion to the evidence supporting them.

Anyway, thoughts?