At Aeon, Nevin Climenhaga makes some interesting points about probability. After describing different interpretations of probability, one involving the frequency with which an event will occur, another involving its propensity to occur, and a third involving our confidence it will occur, he describes how, given a set of identical facts, each of these interpretations can lead to different numbers for the probability. He also describes how each interpretation has its problems.
He then proposes what he calls the “degree of support” interpretation. This recognizes that probabilities are relative to the information we consider. That is, when we express a probability of X, we are expressing that probability in relation to some set of data. If we take away or add new data, the probability will change.
This largely matches my own intuition of probability, that it is always (or almost always) relative to a certain perspective, to a particular vantage point. If I ask what is the probability of it raining tomorrow, you can give an answer before looking up the weather report based on what you know at that moment. It might not be a particularly precise probability, but it can still be made based on where you live and your experience of how often it typically rains there. Of course, once you look at the weather report, you’ll likely adopt the probabilities it provides (unless the forecast where you live has historically been unreliable).
(One possible exception to probabilities being relative is quantum physics. Depending on which interpretation you favor, quantum probabilities may be objective or they may be relative. In non-deterministic interpretations, they might be objective (although that depends on your interpretation of the interpretation 🙂 ). But in the deterministic interpretations, it would still be relative to our perspective.)
Every so often I do a post discussing the probability of something, such as the probability of other intelligent aliens in our galaxy. It’s not unusual for someone to comment that we don’t know enough to estimate any probabilities and that the whole exercise is then pointless. But if probabilities are relative, this position is wrong.
Of course, my estimated probabilities may be wrong, but if so the correct way to address it is in relation to the data that is being considered. Or to offer additional data that may change the probability. Or point out why some (or all) of the data should not be considered when making the estimate.
But if we have a perspective, then we have the ability to estimate probabilities from that perspective. If our perspective is one of complete ignorance, the probability should reflect it. Maybe we can only say the probability of something being true is 50%, that is, it has an equal chance of being true or false. Or if the proposition is one of ten possible outcomes, then it might be more along the lines of 10% probable.
But it doesn’t take much knowledge to shift a probability. In 1600, a natural philosopher could probably rationally argue that, based on what was then known, the probability of the heliocentric model of the solar system being true was only 50%. But after Galileo’s blurry telescopic observations a few years later, along with confirmations by other observers, the probability shifted dramatically, so much so that by Newton’s time in the latter part of that century, the probability had shot up much higher.
Does that mean the natural philosopher in 1600 was wrong in his probabilities? No, because relative to his perspective at the time, those were the probabilities. He would only have been wrong if he hadn’t used the data available to him in making his estimate, or used it correctly, or insisted due to ideological commitments that the probability was zero.
So we’re always in a position to estimate probabilities. We may not be in a position to do so precisely, since that usually requires a lot of data, but the argument that we should never try strikes me as invalid. The only valid argument is whether or not we’re doing it correctly based on what is then known.
Unless of course I’m missing something?