If you don't see DT's laws as governing these cases, or if you think it's a critique of the use of DT that some option space is too large to be practically approximated; then I have the sense of pointing to a thing and a use that's still not in your ontology.
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DT requires a larger injection of perspective; preference as well as probability. Like thermodynamics, you can inject this subjectivity in the wrong place and imagine that nobody comprehends the motions in a spinning cylinder and that the rotation is all waste heat.
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But once you go so far as to map certain parts of the system onto preference and belief, the coherence theorems hold like the theorems they are. In that sense they're more universal, and less physically informative, than thermodynamics.
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Most mappings on the system will be useless. If you regard a particular molecule as having compact preferences and beliefs, it will probably do very poorly. Human beings do have relatively compact preferences and beliefs, on the other hand, and applying it to humans make sense.
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This is not because humans obey the prescriptions of decision theory. It is because humans are making things that can be viewed as decisions. This is not because human beliefs are coherent. It's because humans can be well-viewed as believing things even if incoherently.
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It seems to me that you don't understand the very abstract use that is being made of decision theory. It's not a recipe or an algorithm. It's a generalization relating coherent or incoherent behavior to performance, making far more minimal assumptions than you seem to think.
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Well… I *think* I understand this; but I may be wrong! We clearly have very different cognitive styles, which makes it difficult for us to understand each other.
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Returning to your Facebook post, I take it that it is an attempt to characterize the difference (Law vs Toolbox). I don’t think that is accurate; I think I understand and use both of those ways of thinking. But, I can’t be sure. And I don’t have a good alternative model!
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Btw that you think you use both styles possibly suggests that you are a toolbox thinker, according to the original argument. (The argument might be wrong, but that is a separate point.)
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