What's wrong with probability?
I'd like to clarify the status of probability-related thinking and everyday terms like "probably", "likely", "expectation", etc.
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With an account, you can revise, criticize, and comment on ideas, and submit new ideas.Events occur or don't, and conjectures are refuted or aren't. So is it irrational to say something will "probably happen?
(Steel-manning the common sense view)
We assign implicit probabilities as an expression of our current state of knowledge.
"In the summer desert it will probably be sunny this afternoon" tends to come from some who has no reason to think it won't be sunny, but maybe hasn't investigated it enough to be confident. It roughly translates to "everything I know points to it being sunny this afternoon, but I don't have a grasp of all the factors involved, so I am allowing myself the slim possibility (lol) that I will be surprised".
No, it will or it won't, but "probably" expresses one's awareness of a lack of battletested explanations, or of their own uncertainty or lack of confidence in the prediction, etc. (cf. #4764).
It is mistaken to apply probabilistic thinking to human affairs, because they involve knowledge, and the growth of knowledge cannot be predicted.
In everyday English, we say ‘probably’ to leave room for error and communicate some uncertainty. That’s fine because everyone knows we’re not assigning actual probabilities in the sense of the probability calculus.
In math, we use the probability calculus to describe the frequency of outcomes for underlying processes that look random. Like a coin toss. That’s also fine because we know all possible outcomes and we have a measure for each.
Things go wrong when people use probability even though they don’t know the outcomes (because of the growth of knowledge, say, as you write in #4762) or they have no measure for them or the underlying phenomena don’t behave randomly (again because of the growth of knowledge). Like Elon Musk tweeting we’re 90% likely to see AGI in 2026. (Not a literal quote but he says stuff like that sometimes.)
Some people try to steal the prestige of math and hide their ignorance by using the probability calculus illegitimately.
See also https://www.youtube.com/watch?v=wfzSE4Hoxbc. It’s been years since I watched it but it’s bound to have related ideas.
I think this clarifies it, thanks. Used in common speech to express uncertainty and leave room for error, valid mathematically only when all outcomes are known and have a measure.