The thing about positivism is it pretends to be a down-to-earth common-sense philosophy, and then the more you think about it the more it turns into this crazy surrealist madhouse. So we can’t measure parallel universes and there’s no fact of the matter as to whether they exist. But people in parallel universes can measure them, but there’s no fact of the matter whether these people exist, and there’s a fact of the matter whether these universes exist if and only if these people exist to measure them, so there’s no fact of the matter whether there is a fact of the matter whether these universes exist. And meanwhile to the extent that these people exist, some of them claim there is no fact of the matter as to whether we exist, so really there’s not one positivism, but there’s a positivism for every quantum world. And in each of these positivisms, which worlds it’s meaningful to talk about the existence of gets determined by some random process many times each second. And the question of whether other people in the same universe as you exist is meaningless too, because it makes no predictions that differ from those of the interpretation that other people are all well-disguised walruses who act exactly like people. And if you make an identical copy of yourself, you could end up being either one of them, so there’s a 50% chance that there’s a fact of the matter whether each continuation is a walrus. Etc.
I’m fine with throwing away positivism, as long as we find something viable to replace it with. If you think yielding identical observations does not make two theories equivalent, then what is your criterion for equivalence of theories? Or are all theories different and incompatible, so only one definition of real numbers can ever be “true”? This looks like replacing one surrealist madhouse with another.
If you think yielding identical observations does not make two theories equivalent, then what is your criterion for equivalence of theories?
I could accept that two theories are equivalent if they yield identical observations to every possible observer, everywhere, or better yet, if they yield identical output for any given input if implemented as programs. If you write a program which simulates the laws of physics, and then you write another program which simulates “Odin” calling a function that simulates the laws of physics and doing nothing else, then I would accept that they represent equivalent theories, if they really do always result in the exact same (or isomorphic) output under every circumstance. (Though an Odin that impotent or constrained would be more of a weird programming mistake than a god.) But if the two programs don’t systematically produce equivalent output for equivalent input, then they are not equivalent programs, even if none of the agents being simulated can tell the difference.
The thing about positivism is it pretends to be a down-to-earth common-sense philosophy, and then the more you think about it the more it turns into this crazy surrealist madhouse. So we can’t measure parallel universes and there’s no fact of the matter as to whether they exist. But people in parallel universes can measure them, but there’s no fact of the matter whether these people exist, and there’s a fact of the matter whether these universes exist if and only if these people exist to measure them, so there’s no fact of the matter whether there is a fact of the matter whether these universes exist. And meanwhile to the extent that these people exist, some of them claim there is no fact of the matter as to whether we exist, so really there’s not one positivism, but there’s a positivism for every quantum world. And in each of these positivisms, which worlds it’s meaningful to talk about the existence of gets determined by some random process many times each second. And the question of whether other people in the same universe as you exist is meaningless too, because it makes no predictions that differ from those of the interpretation that other people are all well-disguised walruses who act exactly like people. And if you make an identical copy of yourself, you could end up being either one of them, so there’s a 50% chance that there’s a fact of the matter whether each continuation is a walrus. Etc.
I’m fine with throwing away positivism, as long as we find something viable to replace it with. If you think yielding identical observations does not make two theories equivalent, then what is your criterion for equivalence of theories? Or are all theories different and incompatible, so only one definition of real numbers can ever be “true”? This looks like replacing one surrealist madhouse with another.
I could accept that two theories are equivalent if they yield identical observations to every possible observer, everywhere, or better yet, if they yield identical output for any given input if implemented as programs. If you write a program which simulates the laws of physics, and then you write another program which simulates “Odin” calling a function that simulates the laws of physics and doing nothing else, then I would accept that they represent equivalent theories, if they really do always result in the exact same (or isomorphic) output under every circumstance. (Though an Odin that impotent or constrained would be more of a weird programming mistake than a god.) But if the two programs don’t systematically produce equivalent output for equivalent input, then they are not equivalent programs, even if none of the agents being simulated can tell the difference.