Virgil Șerbănuță edited untitled.tex  about 8 years ago

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Many people believe that the world is designed and created and that it's unreasonable to believe that any world can exist without being created, and I agree with them. However, these beliefs are not shared by everyone, so it's worth thinking about what this means. If the world is created, then it's likely to be the way it is because its Creator\footnote{Not everybody that believes that the world is created thinks that God created it. Still, I hope that they would agree that capitalizing the Creator of this world is reasonable.} wanted it to have certain properties. In order to understand why our world works the way it does, one would need to understand the intent of its Creator. While that is interesting in itself, I will not try to pursue it here.  Let us consider For  the other case: for most reminder  of this article, let us consider the other case and  assume that our world was not designed and created. If that's true then there may be other worlds\footnote{We don't have any proof for the existence of other worlds, but one could expect them to exist for the same reason that ours exists. If ours has no reason at all for existing, which is likely if it is not created, then it's likely that other worlds would also not need any reason for existing and would simply be. However, for this paper it does not matter if there are other worlds or not and probably we wouldn't be able to tell if other worlds exist or not.}. Even if there are no other worlds, one could easily imagine that ours worked in  a world where, say, different way, say that  the speed of light is different orwhere  gravity works differently. We will denote by \definitie{possible worlds} these other worlds that either are or could have been. \section{Modelling possible worlds} 

How would a possible world look like? It could have exactly the same fundamental laws as ours, but with the matter organized differently. It could have similar laws, but with different universal constants. It could have different fundamental particles (or whatever the basic building blocks of our universe are, assuming that there are any). Or it could be completely different, i.e. different in all possible ways.  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. But the \ghilimele{we could model} term here should not mean that we estimate our maximum capacity as humans to build a  model (including models which need in this universe, since that is  an infinitely long description, but which arbitrary limit, we should also allow models of infinite size that  still follow our rules for reasoning). reasoning.  This notion of model is not precise enough. Let us restrict the possible worlds term even more, to the possible worlds that we could model mathematically, even if that may leave out some worlds. 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.}.