I rather like this way of thinking. Clever intuition pump.
What are we actually optimizing the level-two map for, though?
Hmmm, I guess we’re optimizing out meta-map to produce accurate maps. It’s mental cartography, I guess. I like that name for it.
So, Occam’s Razor and formal logic are great tools of philosophical cartographers. Scientists sometimes need a sharper instrument, so they crafted Solomonoff induction and Bayes’ theorem.
Formal logic being a special case of Bayesian updating, where only p=0 and p=1 values are allowed. There are third alternatives, though. Instead of binary Boolean logic, where everything most be true or false, it might be useful to use a 3rd value for “undefined”. This is three-value logic, or more informally, Logical Positivism. You can add more and more values, and assign them to whatever you like. At the extreme is Fuzzy Logic, where statements can have any truth value between 0 and 1. Apparently there’s also something which Bayes is just a special case of, but I can’t recall the name.
Of all these possible mental cartography tools though, Bayes seems to be the most versatile. I’m only dimly aware of the ones I mentioned, and probably explained them a little wrong. Anyone care to share thoughts on these, or share others they may know? Has anyone tried to build a complete ontology out of them the way Eliezer did with Bayes? Are there other strong metaphysical theories from philosophy which don’t have a formal mathematical corollary (yet)?
I rather like this way of thinking. Clever intuition pump.
Hmmm, I guess we’re optimizing out meta-map to produce accurate maps. It’s mental cartography, I guess. I like that name for it.
So, Occam’s Razor and formal logic are great tools of philosophical cartographers. Scientists sometimes need a sharper instrument, so they crafted Solomonoff induction and Bayes’ theorem.
Formal logic being a special case of Bayesian updating, where only p=0 and p=1 values are allowed. There are third alternatives, though. Instead of binary Boolean logic, where everything most be true or false, it might be useful to use a 3rd value for “undefined”. This is three-value logic, or more informally, Logical Positivism. You can add more and more values, and assign them to whatever you like. At the extreme is Fuzzy Logic, where statements can have any truth value between 0 and 1. Apparently there’s also something which Bayes is just a special case of, but I can’t recall the name.
Of all these possible mental cartography tools though, Bayes seems to be the most versatile. I’m only dimly aware of the ones I mentioned, and probably explained them a little wrong. Anyone care to share thoughts on these, or share others they may know? Has anyone tried to build a complete ontology out of them the way Eliezer did with Bayes? Are there other strong metaphysical theories from philosophy which don’t have a formal mathematical corollary (yet)?