Virgil Șerbănuță edited untitled.tex  about 8 years ago

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It could be that our logic and reasoning are universal instruments, but it could also be that some of these possible worlds could be beyond what our reasoning can grasp and others could have properties for which our logic is flawed. Aknowledging that, let us see if we can say anything about the possible worlds that we could understand and could model in some way. In the following, the \definitie{possible worlds} term will denote only the possible worlds which we could model (including models which need an infinitely long description, but which still follow our rules for reasoning).  This notion of \ghilimele{model} is not precise enough. Let us restrict the \ghilimele{possible worlds} term even more, to the possible worlds that we could model mathematically, even if that may leave out some worlds. This was done for simplicity, the constructions made below only require that a significant part of the world can be modelled mathematically.  We will also do the reverse and say that all the models of any set of mathematical axioms which is at most countable\footnote{We could also go beyond countable axiom sets, but that would complicate things without any benefit.} and has at least a model are possible worlds\footnote{Even if some of those models seem outlandish, there could be something that follows those rules and that is completely separated from anything else, not interacting with any other universe in any way. I would say that this something would be an universe. If you don't like it, in the following I am going to restrict what I call a possible universe.}. If nobody designed our world then we have no way of preferring a possible world over another, except that there is one of them in which we live. In other words, if our world is the only one that exists, then any other possible world is as likely to have existed as well. If multiple worlds exist, by picking a random world, ours has a the same chance of being picked as any other.