The claim that an “effective method” is in the map and not the terrain feels deeply suspect to me. Separating map from terrain feels like a confusion. Like, when I’m doing math, I still exist, and so does my writing implement. When I say some x “exists”, in a more terrain-oriented statement, I could instead say it “could exist”. “there could exist some x which I would say exists”. for example, I could say that any integer can exist. I’m using a physical “exists” here, so I have to prefix it with “could”. it’s also conceivable that the thing existed before I write it, if some platonic idealism is true, and it might be. But it seems like the only reason we get to talk about that is empirical mathematical evidence, where a process such as a person having thoughts and writing them happens. Turing machines similarly seem like a model of a thing that happens in reality. It’s weirder to talk about it in the language of empiricism because of the loopiness of definitions of math that are forcibly cast into being physicalist, but I don’t think it’s obviously invalid. I do see how there’s some property of turing machines, chaos theory, arithmetic, and linear algebra that is not shared by plate tectonics, newtonian gravity, relativity, qft, etc. but all of them are models of something we see, aren’t they?
[edit: pinned to profile]
The claim that an “effective method” is in the map and not the terrain feels deeply suspect to me. Separating map from terrain feels like a confusion. Like, when I’m doing math, I still exist, and so does my writing implement. When I say some x “exists”, in a more terrain-oriented statement, I could instead say it “could exist”. “there could exist some x which I would say exists”. for example, I could say that any integer can exist. I’m using a physical “exists” here, so I have to prefix it with “could”. it’s also conceivable that the thing existed before I write it, if some platonic idealism is true, and it might be. But it seems like the only reason we get to talk about that is empirical mathematical evidence, where a process such as a person having thoughts and writing them happens. Turing machines similarly seem like a model of a thing that happens in reality. It’s weirder to talk about it in the language of empiricism because of the loopiness of definitions of math that are forcibly cast into being physicalist, but I don’t think it’s obviously invalid. I do see how there’s some property of turing machines, chaos theory, arithmetic, and linear algebra that is not shared by plate tectonics, newtonian gravity, relativity, qft, etc. but all of them are models of something we see, aren’t they?