Virgil Șerbănuță edited untitled.tex  about 8 years ago

Commit id: 5fa46ced5f3efe29417b45a83b5d57e2760973c4

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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 define, say,  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, if we relax the countability requirement, 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. We will call these the \definitie{too-general} problem and the \definitie{too-specific} problem. For a given world, a \definitie{good set of axioms} would be one that would allow us to make all possible correct 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. One option would be to make it to denote all possible worlds which have a concept of time and a concept of the state of the world at a given time and for which describing the state of the world at all possible times is equivalent to describing the world.