Vulture comments on Open thread, Dec. 29, 2014 - Jan 04, 2015 - Less Wrong
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From what I understand, there is a debate in epistemology / philosophy of science regarding the concept of simplicity ("Occam's Razor"). Some hold that there is a justifiable basis for the concept in the sense that it is an indicator of which of a set of possible theories is more likely to be true. Others dispute this and say that there is no justified basis for simplicity arguments in this sense.
In a recent conversation I made the following assertion (more or less):
Those who say that simplicity arguments are unjustified are actually saying that we can never really know the truth about any theory at all, since there are always an infinite number of alternative and more complex theories that account equally for the data. The best we can do is to falsify a theory (as Karl Popper proposed), but beyond that we can never say anything about whether a theory is true.
So (I said), we have only one of two choices. We can either allow for simplicity arguments, or we can give up on ever saying anything positive about the truth (beyond falsifying a few of the infinite possible theories).
Is this correct?
In the Bayesian view, you can never really make absolute positive statements about truth anyway. Without a simplicity prior you would need some other kind of distribution. Even for computable theories, I don't think you can ever have a uniform distribution over possible explanations (math people, feel free to correct me on this if I'm wrong!); you could have some kind of perverse non-uniform but non-simplicity-based distribution, I suppose, but I would bet some money that it would perform very badly.
Damn, I didn't intend to hit that Retract button. Stupid mobile. In case it wasn't clear, I do stand by this comment aside from the corrections offered by JoshuaZ.
Consistency forces you to have a simplicity based prior if you have a counteable set of non-overlapping hypotheses described using some finite collection of symbols (and some other minor conditions to ensure non-pathology). See prior discussion here. See also here for related issues.
You can act "as if" by just using the likelihood ratios and not operating with prior and posterior probabilities.