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If there isn't any designer for our world then we have no way of preferring one over the other, except that there is one of them in which we live. It seems that reasoning about all the possible worlds could be very hard, but maybe we could do something easier, maybe we could reason about the mathematical axioms that model the worlds.  Let us consider the set of axioms that define a monoid. All groups are models for this set of axioms, but intuitively a group is something more interesting than a monoid and we should include extra axioms for defining it. On the other hand, we could include all possible axioms for each model (e.g. for each monoid), uniquely identifying it, but again, intuitively this is not a useful way of modeling.For a given world, a much better set of axioms would be one that would allow us to make all possible predictions for that world.  We will call these the "too-specific problem" and the "too-general" problem. For a given world, a much better set of axioms would be one that would allow us to make all possible predictions for that world.  The term prediction is not a clear one. To make it more clear, let us restrict again the "possible worlds" term term. One option would be to make it  to denote all possible worlds that/which? have a concept of time (which is something reasonably well ordered), that/which have a concept of the state of the world at a given time, time and  for which describing the state of the world at all possible times is equivalent to describing the world, and for which given the state of the world up to a given time $t$ one could find the state of the world at a future time $s > t$. Making predictions would mean finding the state at a future time. world.  This ignores some important issues like the fact that it's reasonable to have a concept of time without having a well defined concept of "the state of the world at a given time". However, one could time", so we should  rephrase the definition above in a suitable fashion for to include  many concepts reasonable notions  of space and  time, e.g. for worlds where "point" is a concept and we can know which pairs (point, time) are before a given (point, time) pair, prediction could mean predicting the state of the world at a given point from the state of the world at previous points in time. pair.  If Then  we define "prediction" in some useful way, as suggested above, and restrict can say that prediction would mean predicting  the "possible worlds" term to state of  the ones where we can make predictions, then it makes sense to use only systems world (maybe at a given point) from the state  ofaxioms that allow predictions. This solves  the "too-general" part world at a subset  of the "too-specific/too-general" problem since such previous points in time. If we are interested in predicting the state at  a system would describe its possible worlds given point $P$, this subset should include a full section through $P$'s past (e.g. a plane which intersects it's past cone), i.e. it should separate $P$'s past in two parts, one which is "before the subset" and one which is "after the subset"; all lines which fully lie  in $P$'s past and connect  a way that does not leave out important things. Still, there point which  is nothing that prevents such before the subset with  a system from going into too much details. point which is after the subset must go through the subset. One could think of similar definitions for predicting the entire state of the world. If needed, this definition could be changed to work for more concepts of space and time.  Note that in a non-deterministic world we may not always be able to fully predict $P$'s state. In this case, the term "prediction" would mean a statistical prediction.  If we define "prediction" in some useful way, as suggested above, and restrict the "possible worlds" term to the ones where we can make predictions, then it makes sense to use only systems of axioms that allow predictions. We will always use the best possible system for predictions (statistical or not). This solves the "too-general problem" since such a system would describe its possible worlds in a way that does not leave out important things. Still, there is nothing that prevents such a system from going into too much details.  Given a specific formalism for specifying axioms, for each possible world, we could only consider the smallest set of axioms that allow predictions, smallest being defined as "having the smallest length when written on paper". This is not a well defined notion for a few reasons. First, there could be multiple systems with "the smallest length" (one obvious case is given by reordering the axioms). In such a case, we could define an order for the symbols that we are using in our formalism and we could pick the system with the smallest length and that is the smallest in the lexicographic order. Second, there could be systems of axioms of infinite length. For this, we will only consider systems which, when "written on an infinite paper", use a countable set of symbol places on that paper and we will say that all the infinite length systems have the same length, but all of them have a length greater than any finite length. We will ignore systems which need an uncountable set of symbol places. This should solve the "too-specific problem".  Now let us see if we actually need infinite length systems. We can have infinite systems of axioms, and there is no good reason to reject such systems and to ignore their possible worlds, so we will take them into account. It is less clear that we can't replace these infinite systems with finite ones. Indeed, let us use any binary encoding allowing us to represent these systems as binary strings, i.e. as binary functions over the set of natural numbers, i.e. $f:\naturale\longrightarrow \multime{0, 1}$. Then it seems likely that we can define a finite system of axioms that will allow prediction for a universe that also contains an encoding of an axiom system. While, strictly speaking, this would be a different system than the one we had at the beginning, it is also similar enough to it so one may be tempted to use only finite systems of axioms.