There is a single ideal mathematical intuition, which, given a particular amount of resources, and a particular game, determines a unique function M mapping {inputs} x {outputs} x {execution histories} --> [0,1] for a UDT1 agent in that game. This ideal mathematical intuition (IMI) is defined by the very nature of logical or mathematical inference under computational limitation. So, in particular, it’s not something that you can talk about choosing using some arbitrary tie-breaker like lexicographic order.
Now, maybe the IMI requires that the function M be binary in some particular game with some particular amount of resources. Or maybe the IMI requires a non-binary function M for all amounts of computational resources in that game. Unless you can explain exactly why the IMI requires a binary function M for this particular game, you haven’t really made progress on the kinds of questions that we’re interested in.
More or less. Of course there is no point in going for a “single” mathematical intuition, but the criteria for choosing one shouldn’t be specific to a particular game. Mathematical intuition primarily works with the world program, trying to estimate how plausible it is that this world program will be equivalent to a given history definition, under the condition that the agent produces given output.
Okay, I understand you to be saying this:
There is a single ideal mathematical intuition, which, given a particular amount of resources, and a particular game, determines a unique function M mapping {inputs} x {outputs} x {execution histories} --> [0,1] for a UDT1 agent in that game. This ideal mathematical intuition (IMI) is defined by the very nature of logical or mathematical inference under computational limitation. So, in particular, it’s not something that you can talk about choosing using some arbitrary tie-breaker like lexicographic order.
Now, maybe the IMI requires that the function M be binary in some particular game with some particular amount of resources. Or maybe the IMI requires a non-binary function M for all amounts of computational resources in that game. Unless you can explain exactly why the IMI requires a binary function M for this particular game, you haven’t really made progress on the kinds of questions that we’re interested in.
Is that right?
More or less. Of course there is no point in going for a “single” mathematical intuition, but the criteria for choosing one shouldn’t be specific to a particular game. Mathematical intuition primarily works with the world program, trying to estimate how plausible it is that this world program will be equivalent to a given history definition, under the condition that the agent produces given output.