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Vladimir_Nesov comments on A proposal for a cryogenic grave for cryonics - Less Wrong
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Which is to say, decision theory for algorithms, understanding of how an algorithm controls mathematical structures, and how intuitions about the real world and subjective anticipation map to that formal setting.
Logics allow to work with classes of mathematical structures (not necessarily individual structures), which seems to be a good enough notion of working with "all mathematical structures". A "measure" (if, indeed, it's a useful concept) is aspect of preference, and preferences are inherently non-canonical, though I hope to find a relatively "canonical" procedure for defining ("extracting") preference in terms of an agent-program.
Any given concept is what it is. Truth about any given concept is not a matter of preference.
But in cases where there is no "canonical choice of a concept", it is a matter of choice which concept to consider. If you want a concept with certain properties, these properties already define a concept of their own, and might determine the mathematical structure that satisfies them, or might leave some freedom in choosing one you prefer for the task.
In case of quantum mechanical measure, you want your concept of measure to produce "probabilities" that conform with the concept of subjective anticipation, which is fairly regular and thus create illusion of "universality", because preferences of most minds like ours (evolved like ours, in our physics) have subjective anticipation as a natural category, a pattern that has significant explanatory (and hence, optimization) power. But subjective anticipation is still not a universally interesting concept, one can consider a mind that looks at your theories about it, says "so what?", and goes on optimizing something else.
That preference is a cause of a given choice doesn't prohibit physics to also be a cause. There is rarely an ultimate source (unique dependence). You value thinking about what is real (accords with physical laws) because you evolved to value real things. There are also concepts which are not about our physical laws which you value, because evolution isn't a perfect designer.
This is also a free will argument. I say that there is a decision to be made about which concepts to consider, and you say that the decision is already made by the laws of physics. It's easier to see how you do have free will for more trivial choices. It's more difficult to consider acting and thinking as if you live in different physics. In both cases, the counterfactual is physically impossible, you couldn't have made a different choice. Your thoughts accord with the laws of physics, caused by physics, embedded within physics. And in both cases, what is actually true (what action you'll perform; and what theories you'll think about) is determined by your decision.
As an agent, you shouldn't (terminally) care about what laws of physics say, only about what your preference says, so this cause is always more relevant, although currently less accessible to reflection.
I think Vladimir is essentially saying that caring about that objective property of that particular mathematical structure is still your "arbitrary", subjectively objective preference. I don't think I understand where the free will argument comes in either.
Free will is about dependencies: one got to say that the outcome depends on your decision. At the same time, outcome depends on other things. Here, considering quantum mechanical measure depends on what's true about the world, but at the same time it depends on what you prefer to consider. Thus, saying that there are objective facts dictated by the laws of physics is analogous to saying that all your decisions are already determined by the physical laws.
My argument was that as in the case of the naive free will argument, here too we can (indeed, should, once we get to the point of being able to tell the difference) see physical laws as (subjectively) chosen. Of course, as you can't change your own preference, you can't change the implied physical laws seen as aspect of that preference (to make them nicer for some purpose, say).