How so? It is not obvious to me.
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Replying to @samim @PeterSjostedtH
Nothing wrong with complex numbers as long as you discretize them :)
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Discrete, like, I mean, countable, should work for any theory we can talk about (1st order), by Löwenheim-Skolem theorem. But I remember you want it finite - that sounds more restrictive to me.
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In practice you can only make finite observations and recruit finite computational resources. In theory, as soon as you introduce infinity, very ugly things happen to your axiomatic systems. Better stay clear of that stuff if you can avoid it...
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I agree regarding axiomatic systems. Regarding the world, I‘m less sure.
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How would you scrape an infinite amount of bits via your observational interface?
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I still have this distinction between world and model. I will never see infinite bits to fit my model to. But the bits are made by the world.
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But if you don't need to explain infinite amounts of bits, why would you want to burden the cosmic pattern generator with infinite complexity?
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As with most of the mathematical infinities: Assuming no end is often easier to state than to assume one, as the latter is concrete. (So called „potential infinity“ is often just the refusal to specify a concrete termination.)
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Yes, as with all agnosticism we must remain undecided about affairs for which we cannot obtain evidence. However, some possibilities require more expensive assumptions than others, so we should be biased accordingly.
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