I think this is relevant: https://en.wikipedia.org/wiki/Bertrand_paradox_(probability)
The approach of the final authors mentioned on the page seems especially interesting to me. I also am interested to note that their result agrees with Jaynes'. Universability seems to be important to all the most productive approaches there.
Or arguing that the complexity ordereing is the one that produces the "true" probailities is reframing of the question whether the simplicity formulation is truth-indicative.
If the approach that says simplicity is truth-indicative is self-consistent, that's at least something. I'm reminded of the LW sequence that talks about toxic vs healthy epistemic loops.
If I encounter a working hypothesis there is no need to search for a more simpler form of it.
This seems likely to encourage overfitted hypotheses. I guess the alternative would be wasting effort on searching for simplicity that doesn't exist, though. Now I am confused again, although in a healthier and more abstract way than originally. I'm looking for where the problem in anti-simplicity arguments lies rather than taking them seriously, which is easier to live with.
Honestly, I'm starting to feel as though perhaps the easiest approach to disproving the author's argument would be to deny his assertion that processes in Nature which are simple are relatively uncommon. From off the top of my head, argument one is replicators, argument two is that simpler processes are smaller and thus more of them fit into the universe than complex ones would, argument three is the universe seems to run on math (might be begging the question a bit, although I don't think so, since it's kinda amazing that anything more meta than perfect atomist replication can lead to valid inference - again the connection to universalizability surfaces), argument four is an attempt to undeniably avoid begging the question inspired by Descartes: if nothing else we have access to at least one form of Nature unfiltered by our perceptions of simplicity : the perceptions themselves, which via anthropic type induction arguments we should assume-more-than-not to be of more or less average representativeness. (Current epistemic status: playing with ideas very nonrigorously, wild and free.)
This essay claims to refute a popularized understanding of Occam's Razor that I myself adhere to. It is confusing me, since I hold this belief at a very deep level that it's difficult for me to examine. Does anyone see any problems in its argument, or does it seem compelling? I specifically feel as though it might be summarizing the relevant Machine Learning research badly, but I'm not very familiar with the field. It also might be failing to give any credit to simplicity as a general heuristic when simplicity succeeds in a specific field, and it's unclear whether such credit would be justified. Finally, my intuition is that situations in nature where there is a steady bias towards growing complexity are more common than the author claims, and that such tendencies are stronger for longer. However, for all of this, I have no clear evidence to back up the ideas in my head, just vague notions that are difficult to examine. I'd appreciate someone else's perspective on this, as mine seems to be distorted.
Essay: http://bruce.edmonds.name/sinti/