A researcher puts you into a room. On the table is a blue ball. Somebody put it there. It could have been Alice, Bob, or Charlie. Given only that information—and no more—who put it there? You have to pick one and only one.
If the choice seems arbitrary, it’s because it is. Whoever you pick has equal justification given only the information provided.
Instead of choosing, we can switch to probability. Given only the information provided, what is the probability Alice placed the ball? Same as for the other two: one-third (the proof of that is found in here).
We have learned three things. One, probability is conditional on only the information given or assumed. Two, decision (or choice) is not probability: decision uses probability, but it is a step beyond it. Three, there must have been a cause for the ball.
The probability is straightforward (but see this page if you want to learn more). The choice, decision, or act is less so. Given the probability, and given what you think will happen if you were to guess right or wrong, you make a choice, a decision, or you act. Two people can have the exact same precise duplicate identical information, and thus must necessarily come to the same probability, but they can easily come to different (even wildly different) decisions because they believe their choices will have different consequences—and their choices may very well have different consequences. And no matter what the (conditional) probability is, and no matter what we decide, there will still be a true cause.
Probability (epistemology), act (or will), and cause (metaphysics). All different steps which must be kept distinct when analyzing any problem.
The philosophical concept of inference to the best explanation can confuse and conflate these three steps or categories. Not systematically, so that we can apply a correction, but willy-nilly, depending on who is wielding the tool.
Inference to the best explanation (IBE) asks us to make a choice on a cause without examining—in any thorough sense—probability or the consequences of decision. This is not to say the technique does not and cannot come to correct probabilities, decisions, and understandings of cause. It can and very often does, especially in those areas in which we have expertise or extensive knowledge.
The reason IBE works, when it works, is that people are good at the individual steps without knowing or explicitly acknowledging they are using those steps. That will be obvious in a moment.
What happens when you see a ball and you really want to know the cause of it being there? You run through possibilities. I specified only three, and then said nothing more except that there were these three. There is no information about Alice’s motives, or her placement (where was she?), her personality, nothing. The information allowed was restricted in the extreme. Given only it, we could make a choice, but we recognized that choice’s arbitrariness. That arbitrariness informs the decision we would make, depending on how we view the consequences of making right or wrong decisions (which may well be different for each reader).
We also implicitly recognized one aspect of the cause: the efficient cause. We know a person placed it there, but we don’t know why. We do not know anything of the final cause, the reason the ball was put there. That we don’t know the motivation does not, obviously, mean we do not know the ball isn’t there. It is there. We also do not know the formal and material causes: we do not know the means the person used. Again, our ignorance of these does not mean the ball is not there.
That the IBE does not work here—there is no single best explanation and no identification of all aspects of the cause—is not the fault of the artificial nature of the problem: it is the fault of IBE. Any epistemological technique that claims to be an algorithm to discover the best guess of truth on given information (IBE does not claim to always find truth) has to work everywhere, or we have to look elsewhere for better algorithms. I claim we can’t find one: we’re stuck with probability, decision, and cause. Life and thinking isn’t so easy.
Now in real life you are not as restricted as in this artificial situation. You are free to guess or assume or measure other probative evidence that will modify the probability, change the decision, or lead to fuller understanding of the causes.
Didn’t I see Alice here earlier? I thought Bob said he was driving somewhere. That looks a lot like a ball Charlie plays with. Fastidious Alice might have been here, but I can’t see why she’d leave a ball lying about. Et cetera. You must play detective.
Means, motive, opportunity. That’s what detectives look for, because why? Because these items identify all aspects of the cause of the event. Detectives know they might not always guess right, that the wrong man is sometimes pegged, that some motives are opaque, and on and on. Detectives also know that the defense attorneys are free to form their own list of probative evidence, and so will come to different probabilities, decisions, and understandings of cause.
The possibility of differences in assumptions is the key to understanding the IBE’s general weakness—and it’s sometime usefullness.
It is the freedom to choose the evidence, and that there is no algorithm that leads us to the right set of perfect evidence that results in uncertainty. Uncertainty is often our lot.
Of course, there will always be a right set of perfect evidence that puts the probability at 0 or 1, as the case may be, evidence that results in a flawless decision, and that nails all parts of the cause. Our goal is to get as close as we can to this perfect set. But there is no guarantee we will even come close to it much of the time. (And there is even proof that in some cases, such as in quantum mechanics, it is impossible to come to it.)
A strange blip on the bubble chamber screen. Something caused it. What? The physicist must piece together the evidence. Means, motive, opportunity. In the end, and especially if the blip never repeats, he may just shrug his shoulders and say “Chance”—which is only and ever a euphemism for “I don’t know.”
The nature of evidence is the same at home, in science, in math, and in religion. Why something is is different from that or how it is. (I won’t prove here it works in math, but I do prove it here.)
None of this is controversial, except to die-hard followers of IBE who somehow believe that if only they exerted themselves sufficiently, they can always come to the best explanation of all aspects of a case—which is not synonymous with true. When IBE works, it’s really common sense, carefully explicated.
Next week we’ll see how Shapiro’s use of IBE to dismiss miracles relies on premises he didn’t know he was assuming, on how he did not account for the freedom to assume what evidence is probative, and how he didn’t grasp all aspects of cause.
Update Since it has arisen, there are other interpretations of quantum mechanics which differ from the classical ones. For instance: Quantum Potency & Probability, which restores Heisenberg’s original surmise. About cause. Now everything potential that becomes actual only can do do by something actual—a fancy way of saying QM events are not “uncaused”, as some would have it. On the nature of cause in QM see inter alia Wolfgang Smith’s The Quantum Enigma: Finding the Hidden Key (3rd Edition) Scholastic Metaphysics: A Contemporary Introduction. There is another recent monograph by (I think) a Dominican scientist on the same subject which is escaping my memory. When I recall, I’ll post.