Per definitionem, possibilities don't ontologically exist, but inaccessible parts of the universe might well be implemented.
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To say that possibilities do not ontologically exist betrays the fact that one's ontology is flawed. Of course possibilities exist.
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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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"infinity leads to ugly outcomes" >> this is the heart of where we disagree. Infinity is the perfect elegance (and ugliness etc.) - how i see it.
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Infinity is a wonderful tool if you want to make stuff, a cornucopia: shake it a little, and things fall out of it without limit, but it is also infinitely hard to make by itself. No finite process can create an infinity, but once you have it, you can easily create universes.
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Does the universe you imagine here have discrete time? Infinite time?
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Relativistic time exists only for embedded observers (observed rate of change in an observer's environment, relative to its own rate of change). I don't know how to make global continuous time work without making the universe hypercomputational.
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I intended to refer to the time of the computation, not of the observer (the latter is much later in the understanding of the model). You mentioned a succession of states, step by step, that time I was asking about. Step by step -> discrete. But finite or infinite?
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I do not know how to get evidence for that. If a universe is deterministic and has finite size, it becomes periodic if you let it run for long enough, and an embedded observer cannot find out when it started, if it had a starting point.
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