02 July 2015

Existing, non-existing and other universes

“According to modal realism, possible worlds really exist” writes Jennifer Fisher in his book On Philosophy of Logic (p. 91.). This approach is based on modal logic that interprets true and false statements in relation to possible worlds: E.g. necessity means that the statement “is true in all possible words” (Ibid, p. 75.) and our actual world is nothing more than a world which was chosen from the set of other, existing ones. I don’t accept modal realism’s logic (after all, possibility isn’t equal to existence), but it is interesting from our point of view that the logic of modal worlds is similar to the logic of classic multiverse hypothesis that assumes the existence infinitely many words and this similarity shall lead us to a strange type of imaginable universes.
Max Tegmark interprets the multiverse as the manifestation of every mathematically possible world. It is a form of mathematical Platonism, and the main thesis is that on the one hand, anything is possible mathematically exists in reality. On the other hand, everything is governed by the rules of mathematics. “Mathematical” means in this case that every combination of different sets of physical laws and constants, or even different equations exist. In other words: according to Tegmark, all words can be described by mathematics and every imaginable combination is manifested in a really existing world. The core of Tegmark’s concept is that mathematics is equal to physics in a certain sense, since it describes the world ruled by physical laws.
But it is not sure that even our universe can be described perfectly by mathematics and perhaps only our belief suggests that every natural phenomenon is controlled by either deterministic, or probability or evolutionary laws. Inter alia, it is possible that the Great Unified Theory (GUT) doesn’t exist, since there is no mathematics to describe every connection. It is perhaps only about our inability to give a coherent description about reality, since our tools (including our minds, mathematics and logic) aren’t appropriate for it.
Or, it is imaginable that there are universes that cannot be described by mathematics at all: after all, mathematics is based on the presumption of the conservation of some rules. Thus, it is not necessarily well-founded to state that every universe is mathematical in nature. So we can imagine whole universes (albeit they wouldn’t be biofil) without mathematically interpretable natural laws. In other words: although they exist, they cannot be described by one or other mathematical form of physical laws.
Traditionally, we distinguish existing and non-existing worlds and the main sin of modal realism is that it intermixes these two categories. Now we can introduce a third kind of universes which differ from both the “existing” and “non-existing” ones and since per definitionem it is impossible to give a scientific description about their features, they don’t belong to the realm of physics.

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