A competent and comprehensive critique of the ideas from your post would require much more thought and background reading than I’ve invested into it so far, but nevertheless, this key part strikes me as problematic:
[I]f you combine a functionalist view of mind with big worlds cosmology, then reality becomes the quotient of the set of all possible computations, where all sub-computations that instantiate you are identified.
To talk about a quotient set or quotient space, you need a well-defined equivalence relation. But what would it be in this instance? The set of all possible computations that “instantiate you” in any meaningful sense is necessarily an extremely fuzzy concept, for reasons I’m sure I don’t need to elaborate on here. So what exactly gets to be included into “your ‘now’”?
One way out of this, I suppose, would be to note that once you unwrap all the definitions, every mathematical object in ZFC is a set (of sets of sets of… -- perhaps infinite, and with empty sets as “bottom” elements), and then define “your ‘now’” as the class of sets that contain subsets (or sub-sub-...-sets) that are exactly isomorphic to some “yardstick” set that represents “your ‘now’.” (I.e. those instances of “you” that are different in any detail at all are in a completely different class, and have no more relation to “you” than any other ones.) Similar could be done, of course, not just in ZFC but in any other theory that is sufficient to formalize standard mathematics.
Is this anywhere close to what you have in mind, or am I just rambling in complete misapprehension?
A competent and comprehensive critique of the ideas from your post would require much more thought and background reading than I’ve invested into it so far, but nevertheless, this key part strikes me as problematic:
To talk about a quotient set or quotient space, you need a well-defined equivalence relation. But what would it be in this instance? The set of all possible computations that “instantiate you” in any meaningful sense is necessarily an extremely fuzzy concept, for reasons I’m sure I don’t need to elaborate on here. So what exactly gets to be included into “your ‘now’”?
One way out of this, I suppose, would be to note that once you unwrap all the definitions, every mathematical object in ZFC is a set (of sets of sets of… -- perhaps infinite, and with empty sets as “bottom” elements), and then define “your ‘now’” as the class of sets that contain subsets (or sub-sub-...-sets) that are exactly isomorphic to some “yardstick” set that represents “your ‘now’.” (I.e. those instances of “you” that are different in any detail at all are in a completely different class, and have no more relation to “you” than any other ones.) Similar could be done, of course, not just in ZFC but in any other theory that is sufficient to formalize standard mathematics.
Is this anywhere close to what you have in mind, or am I just rambling in complete misapprehension?
No, it is a real problem that you mention: namely that fuzziness could be hard to deal with.