My intention wasn’t really to use both propositional coherence and partitions of truth—I switched from one to the other because they’re equivalent (at least, the way I did it). Probably would have been better to stick with one.
I do think this notion of ‘naturalistic’ is important. The idea is that if another computer implements the same logic ans your internal theorem prover, and you know this, you should treat information coming from it just the same as you would your own. This seems like a desirable property, if you can get it.
I can understand being suspicious. I’m not claiming that using GLS gives some magical self-reference properties due to knowing what is true about provability. It’s more like using PA+CON(PA) to reason about PA. It’s much more restricted than that, though; it’s a probabilistic reasoning system that believes GLS, reasoning about PA and provability in PA. In any case, you won’t be automatically trusting external theorem provers in this “higher” system, only in PA. However, GLS is decidable, so trusting what external theorem provers claim about it is a non-issue.
What’s the use? Aside from giving a quite pleasing (to me at least) solution to the paradox of ignorance, this seems to me to be precisely what’s needed for impossible possible worlds. In order to be uncertain about logic itself, there needs to be some “structure” what we are uncertain about: something that is really chosen deterministically, according to real logic, but which we pretend is chosen randomly, in order to get a tractable distribution to reason about (which then includes the impossible possible worlds).
(Sorry I didn’t notice this comment earlier.)
My intention wasn’t really to use both propositional coherence and partitions of truth—I switched from one to the other because they’re equivalent (at least, the way I did it). Probably would have been better to stick with one.
I do think this notion of ‘naturalistic’ is important. The idea is that if another computer implements the same logic ans your internal theorem prover, and you know this, you should treat information coming from it just the same as you would your own. This seems like a desirable property, if you can get it.
I can understand being suspicious. I’m not claiming that using GLS gives some magical self-reference properties due to knowing what is true about provability. It’s more like using PA+CON(PA) to reason about PA. It’s much more restricted than that, though; it’s a probabilistic reasoning system that believes GLS, reasoning about PA and provability in PA. In any case, you won’t be automatically trusting external theorem provers in this “higher” system, only in PA. However, GLS is decidable, so trusting what external theorem provers claim about it is a non-issue.
What’s the use? Aside from giving a quite pleasing (to me at least) solution to the paradox of ignorance, this seems to me to be precisely what’s needed for impossible possible worlds. In order to be uncertain about logic itself, there needs to be some “structure” what we are uncertain about: something that is really chosen deterministically, according to real logic, but which we pretend is chosen randomly, in order to get a tractable distribution to reason about (which then includes the impossible possible worlds).