If you start to “represent knowledge,” you inevitably fall into predicate calculus, a supermassive galactic attractor.
In which case “reasoning” is logical deduction. Which… almost never works.
Probability theory sometimes works, but *most* uncertainty doesn’t work like that.
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Project: a list of rationalist pit-traps, with a brief explanation the circumstances in which each works in practice.
• Decision theory
• Function approximation
• Objective-function maximization
• State-space search
• Kalman filters
• … add your favorite here?
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Yes! I was pretty much subtweeting that via Kalman filters, which are the underlying math for the predictive processing theory, to the extent that it has any, as far as I can tell.
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Hmm unless the search function is broken, the only mention of 'Kalman' in my copy of Surfing Uncertainty is a single footnote where it's mentioned that predictive processing 'has common ground with' Kalman filtering, so it doesn't sound like Kalman filters would be used in PP.
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My recollection when I looked into this is that Kalman filters were, in fact, part of the inspiration for the theory (I am not certain I’m remembering this right).
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The problem here is similar to that of Bayesian rationalism. On the one hand, if you think the problem Kalman filters address is the essence of cognition, then there is no real alternative to them
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Same way that if you think belief strength is the essence of rationality, there's no real alternative to probability theory (which is Cox's theorem)
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(I don't know if there's an analogously strong result in control theory—my vague recollection is that an optimality theorem hasn't been proved rigorously but it's generally taken as true. would know!)
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Not sure what you're asking. Kalman filters are a standard part of control toolkits, and they're "optimal" in the sense of being the optimal LQG solution for linear time invariant systems with gaussian noise. They rest on something called the "certainty equivalence principle"
Thanks, yeah, I was being vague. Kalman filters are optimal for the thing they are optimal for, and then there’s various broader classes of problems for which analogous things are provably optimal (?), and you’d like a strong result for a very broad class that isn’t done…
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And Friston-style stuff tries to metaphorically apply “something like” them, with vague handwaving, to an even broader class, actually the whole of being, where the control theory framework is just not meaningfully applicable.
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