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#5549·Dennis HackethalOP, about 23 hours agoAs I recall, FoR has an example of a grass cure. It says something like: you could eat 1g of grass to cure some disease. If that doesn’t work, proponents of that theory can simply say you actually need to eat 0.9g. When that doesn’t work either, they can say you need 0.95g. And so on. So there is literally an uncountably infinite number of variant theories: one for each decimal number in that vicinity.
Put those variants up against a competing explanation that also has uncountably many variants. Now you can arbitrarily get a result saying to prefer one over the other by typing in fewer variants for one than for the other.
More abstractly put, we can’t always count the variants. But the algorithm, as written, expects us to.
I don't think it follows that a competing explanation would also have uncountably many working variants just because it involves continuous quantities.
The grass example is easy to vary precisely because there's no explanation for why the amount should be 1kg rather than 0.9kg, 0.95kg, etc. If 1kg doesn't work, I can just keep changing the number. Nothing in the explanatory argument constrains it.
But suppose grass really did cure the disease and we actually understood how. Maybe a particular compound in the grass interacts with some biological mechanism, and a certain concentration is required for the effect. The explanation might allow a whole range of effective dosages rather than one exact number, but that range would itself be explained and constrained by the mechanism.
I wouldn't consider every possible dosage within that range a different variation of the explanation. They're different cases covered by the same explanation. Saying “this mechanism works within this dosage range” is one explanatory claim, even if there are infinitely many numerical values inside the range.
So I think there's a difference between an explanation containing a continuous variable and an explanation whose parameters can be changed arbitrarily without explanatory reason. The first can be perfectly constrained by the explanatory structure. The second is exactly what I understand easy-to-vary to mean.
This also comes back to the point I made in #5553: the program relies on the user's understanding of the explanatory argument. A knowledgeable user wouldn't enter 0.9kg, 0.9001kg, 0.90001kg, etc. as infinitely many distinct explanatory variations if they understand them as instances of one explained dosage range.