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The Dice Room, Human Extinction, and Consistency of Bayesian Probability Theory

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Predicting Organizational Behavior

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Free Applied Instrumental Rationality Webinar

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For-Profit Rationality Training

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Applied Rationality Practice

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Bayesian probability theory as extended logic -- a new result

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Recent Comments

What do you mean by "phenomenally conscious"? You seem to be suggesting that any automaton with memory is "phenomally conscious", which would does violence to the usual use of the word "conscious" and would make even a vending machine "phenomally conscious".

I'd be interested in reading what you come up with once you're ready to share it.

One thing you might consider is whether sigma-completeness is really necessary, or whether a weaker concept will do. One can argue that, from the perspective of constructing a logical system, only *computable* countab...(read more)

If you haven't already, I would suggest you read Carnap's book, The Logical Foundations of Probability (there's a PDF of it somewhere online). As I recall, he ran into some issues with universally quantified statements -- they end up having zero probability in his system.

Epistemic probabilities / plausibilities are not properties of the external world; they are properties of the information you have available. Recall that the premise X contains all the information you have available to assess plausibilities. If X does not rule out a possible world, what basis do you...(read more)

Sure it does. Haven't you heard of Cox's Theorem? It singles out (Bayesian) probability theory as the uniquely determined extension of propositional logic to handle degrees of certainty. There's also my recent paper, "From Propositional Logic to Plausible Reasoning: A Uniqueness Theorem"

https://na...(read more)

I appreciate your explanation, and it makes sense to me. But I still can't find any hint in Gendlin's writing that he's speaking metaphorically.

I'm reading Gendlin's book _Focusing_ and struggling with it -- it's hard for me to understand why you and Anna think so highly of this book. It's hard to get past all the mystic woo about knowledge "in the body"; Gendlin seems to think that anything not in the conscious mind is somehow stored/proc...(read more)

Actually, no, improper priors such as you suggest are not part of the foundations of Bayesian probability theory. It's only legitimate to use an improper prior if the result you get is the limit of the results you get from a sequence of progressively more diffuse priors that tend to the improper pri...(read more)

Note that

P(you are in batch t | murders batch t & you are kidnapped)

cannot be 9/10 for all t; in fact, this probability must go to 0 in the limit as t -> infinity, regardless of what prior you use.