Q&A: Induction and Statistics
Induction and Statistics
Question
Good morning, Rabbi. Yesterday I was reading in “Two Carts and a Hot-Air Balloon.” Can’t the problem of induction be grounded in statistics, which is based on mathematics and is therefore a priori? After all, there is no clear line for the point at which we feel comfortable using induction, and it is obvious that this is a statistical matter (the more cases there are, the more certain we feel about the generalization).
Answer
It is not for nothing that I asked you to clarify the question. I do not understand it. I would also be glad if you would give me a reference to “Two Carts.” In my opinion, you are quoting it inaccurately.
Discussion on Answer
This is not a matter of statistics. There is no statistical consideration whatsoever that instructs us that what was will be. Hume himself tried to ground this in the principle of causality (and then maybe one could talk about statistics), but rejected that too, on the grounds that causality is also not observational.
Statistics is not a priori. The theory is a priori, but its applications in the world are not. They are the product of observation, which tells us that a certain statistical theory can be applied to the case before us. Just as quantum theory is not a branch of mathematics but of physics, even though it uses mathematical description. See columns 50, 318, and others on this.
The problem Hume raised is that we cannot infer the future from what happened in the past. I am asking: why not, really? It is obvious that this is a matter of statistics, which is itself a priori (part of mathematics). It is a priori obvious that if I see ten times that different objects fall at a constant speed, that means that all objects fall at a constant speed. It is obvious that if an event happened X times, then presumably it will continue to happen. Why can’t this be grounded in statistics? The probability that a certain event happened several times shows that it will probably continue to happen.