If I understand this correctly, I disagree. Modern philosophical platonism means different things by ‘abstract’ than Tegmark’s platonism. In philosophical platonism, I accept your definition that something is abstract if it is causally inert and non-spatiotemporal. For Tegmark, this doesn’t really make sense though, since the universe is causal in the same sense that a mathematical model of a dynamical system is causal, and it is spatiotemporal in the same sense that the mathematical concept of Minkowski spacetime is spatiotemporal, since the universe is just (approximately) a dynamical system on (approximately) Minkowski spacetime. The usual definition of an abstract object implies that physical, spatiotemporal objects are not abstract, which contradicts the MUH. I don’t think we really have a precise definition of abstract object that makes sense in Tegmark’s platonism, since something like ‘mathematical structure’ is obviously imprecise.
For Tegmark, this doesn’t really make sense though, since the universe is causal in the same sense that a mathematical model of a dynamical system is causal, and it is spatiotemporal in the same sense that the mathematical concept of Minkowski spacetime is spatiotemporal
I don’t think that means that abstract objects in the ordinary sense don’t make sense. It just means that he counts a lot of things as concrete that most people might think of as abstract. We don’t need a definition of ‘mathematical structure’ for present purposes, just mathematically precise definitions of ‘causal’ and ‘spatiotemporal’.
If I understand this correctly, I disagree. Modern philosophical platonism means different things by ‘abstract’ than Tegmark’s platonism. In philosophical platonism, I accept your definition that something is abstract if it is causally inert and non-spatiotemporal. For Tegmark, this doesn’t really make sense though, since the universe is causal in the same sense that a mathematical model of a dynamical system is causal, and it is spatiotemporal in the same sense that the mathematical concept of Minkowski spacetime is spatiotemporal, since the universe is just (approximately) a dynamical system on (approximately) Minkowski spacetime. The usual definition of an abstract object implies that physical, spatiotemporal objects are not abstract, which contradicts the MUH. I don’t think we really have a precise definition of abstract object that makes sense in Tegmark’s platonism, since something like ‘mathematical structure’ is obviously imprecise.
I don’t think that means that abstract objects in the ordinary sense don’t make sense. It just means that he counts a lot of things as concrete that most people might think of as abstract. We don’t need a definition of ‘mathematical structure’ for present purposes, just mathematically precise definitions of ‘causal’ and ‘spatiotemporal’.