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#5529·Dennis HackethalOP, about 20 hours agoIn a situation where both competing explanations have infinitely many variations (eg #5528), the algorithm returns an equal ranking, even though one explanation is clearly preferable over the other. (“Because of axial tilt while I wear 1 green hat”, though still bad, is intuitively preferable to “Because god did it while wearing 1 green hat.”)
As I argued in #5554, if the number of green hats is genuinely part of an explanation and can be changed arbitrarily without affecting anything, then I think that really does expose an easy-to-vary part of the explanation.
But I don't think adding “while I wear one green hat,” “while I wear two green hats,” etc. to the axial-tilt explanation necessarily varies the explanation at all.
If my explanation is that Earth's seasons result from its axial tilt and the resulting relationship between Earth and the Sun, whether I happen to be wearing one green hat or a thousand isn't part of that explanatory argument. Appending an unrelated fact to the English sentence doesn't change the explanation it expresses.
If, on the other hand, I genuinely claim that my hat is part of the explanation—say, that Earth's seasons occur because of axial tilt and because I'm wearing exactly one green hat—then changing the number of hats would be a genuine variation. But in that case I really have made the explanation worse by adding an arbitrary component that isn't constrained by what I'm trying to explain.
So I think there's a difference between varying an explanation and varying the string of English used to express it. The program relies on the user to understand that distinction, for the same reason I described in #5553: it operates on the user's understanding of the explanatory argument, not on arbitrary syntactic changes to its wording.
On that understanding, I don't think both explanations become equally easy to vary merely because infinitely many irrelevant statements can be appended to the sentences expressing them.