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By Occam's razor, a simpler theory that could explain all the phenomena is more likely correct.

But there are factors in the universe that are just random. (Even if not, we could think about a hypothetical universe that has random factors everywhere.)

If we write down all the random factors about the universe, the complete description would be larger than, say, the space outside of what humans have explored is just an arbitrary gigantic video (with a few additional features) played to the humans. Why do we prefer the farther part of the universe exist, instead of assuming it is just a video?

Actually I have an idea. We could have a macroscopic formulation of the theory that involve much less of the randomness. Its probability is the probability of all microscopic complete descriptions combined. It could be mathematically equivalent to a description of the video, but with its internal logic preserved and much better compressed.

But it still attracts ideas that are too strong, such as every far enough star has perfect properties, say being a perfect sphere (or ellipsoid), unless we have the ability to measure otherwise, which is less probable but possibly simpler to describe; or too weak, such as a part of the universe is either real or a meaningless video, but we don't know which is the case, which is technically more probable but more contrived to describe.

Is there a formulation of the Occam's razor that takes randomness (or unobserved arbitrary information) into consideration and works well in such cases? In case that this is not what Occam's razor is supposed to solve, is there another principle of science beside Occam's razor that could solve such problems?

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  • I am not sure what you mean by "random factors about the universe", and how "the space outside of what humans have explored is just an arbitrary gigantic video" is a way of explaining them. The idea that unobserved parts of the universe are radically different from observed ones is not very parsimonious, it raises question why and answers none. What are "microscopic complete descriptions combined" and how are we to measure their probability? See IEP, Simplicity in the Philosophy of Science for an overview of how Occam's razor is used in science.
    – Conifold
    Oct 23, 2020 at 20:44
  • @Conifold Random factors means things like the exact positions of stars, and the elemental composition and their distribution of a planet, which the physical laws doesn't specify exactly, but mostly just happen to be what they are.
    – user23013
    Oct 24, 2020 at 11:18
  • @Conifold It's more like saying the unobserved parts are overly idealistic, or simply don't exist, rather than radically different. A better or worse example might be, if we measured some physical constant to be some value with error, why don't we say in the best theory it is exactly this value, because we could write it using less digits? It might be doubtful to consider a meaningless real number simpler than another. But now consider a planet to be a perfect sphere with error.
    – user23013
    Oct 24, 2020 at 11:19
  • @Conifold And I'd say obviously we won't like such theories more than others. But the question is, are we rejecting them being better exactly because of the Occam's razor? If so, I don't see how it is logically deduced using the common formulation of the Occam's razor. If not, what other reasons are we using to reject them?
    – user23013
    Oct 24, 2020 at 11:33
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    I believe medieval paradigm considered stars as lightbulbs in a ceiling. The lack of better data made that a more credible theory than a vast space. E.g. consider how Giordano Bruno only had a theory, but not sufficient observations to convince many others. Some other astronomers and philosophers held similar beliefs, but it took Friedrich Vessels optical measurement of the distance to 61 Cygni in 1838 to actually make a vast space instead of a flat ceiling accepted as fact.
    – tkruse
    Oct 26, 2020 at 1:39

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