please explain further: Why/How is computation not "just" a language specification?
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Why stop there? Nothing wrong with fairies, as long as you discretize them :)
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Do you have a set of phenomena that can be plausibly explained by fairies, a plausible implementation of faerie, and a plausible mechanism by which they came into existence?
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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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