"Is infinite precision useful here? yes/no."Just mentioning a quantity in some way doesn't contradict CR.Fully agreed - but:The question is, "Have I done enough effort? Should I do more effort or stop now?" That is a boolean question.Not really, because the answer is a continuum. If X effort is not enough and X+Y effort is enough, then maybe X+Y/2 effort is enough and maybe it isn’t. And, oh dear, one can continue that binary chop forever, which takes infinite time because each step takes finite time. I claim there’s no way to short-circuit that that uses only yes/no questions.
"Is one decimal enough precision for solving the problem we're trying to solve? yes/no"
You don't have to use only yes/no questions, but they play a key role. After these two above, you might use some method to figure out the answer to adequate precision. Then there'd be some more yes/no questions:
"Was that method we used a correct method to use here?"
"Is this answer we got actually the answer that method should arrive at, or did we follow the method wrong?"
"Have we now gotten one answer we're happy with and have no criticism of? Can we, therefore, proceed with it?"
Plus, in the real world, at some point in that process one will in fact decide either that both the insufficiency of X and the sufficiency of X+Y are rebutted, or than neither of them is (which of the two depending on one’s standard for what constitutes a rebuttal) - which indeed terminates the binary chop, but not usefully for a pure-CR approach.Rebuttals are useful because they have information about the topic of interest. What to do next would depend on what the rebuttals are. Typically they provide new leads. When they don't, that is itself notable and can even be thought of as a lead, e.g. one might learn, "This is much more mysterious than I previously thought, I'll have to look for a new way to approach it and use more precision" – which is a kind of lead.
The standard of a rebuttal, locally, is: does this flaw pointed out by criticism prevent the idea from solving the problem we're trying to solve? yes/no. If no, it's not a criticism IN CONTEXT of the problem being addressed.
But the full standard is much more complicated, because you may say, "Yes that idea will solve that problem. However it will cause these other problems, so don't do it." In other words, the context being considered may be expanded.
There's a big perspective gap here.Why not roll dice to decide between those remaining ideas? That would be some CR, and timely. Do you think that's an equally good approach? Perhaps better because it eliminates bias.Actually I’m fine with that (i.e., I recognise that the triage is functionally equivalent to that). In practice I only roll the dice when I think I’m sure enough that I know what the best answer is - so, roughly, I guess I would want to be rolling three dice and going one way if all of them come up six and the other way otherwise - but that’s still dice-rolling.
I had in mind rolling dice with equal probability for each result.
If all you do is partial CR and have two non-refuted options, then they have equal status and should be given equal probability.
When you talk about amounts of sureness, you are introducing something that is neither CR nor dice rolling.
Also, if you felt 95% sure that X was a better approach than Y – perhaps a lot better – would you really want to roll dice and risk having to do Y, against your better judgment? That doesn't make sense to me.
Continue reading the next part of the discussion.