Virgil Șerbănuță edited untitled.tex  about 8 years ago

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In this case one could study each planet and add a specific description of the laws for each, but at any moment in time the humans in this world would only have a finite part of an infinite set of laws, so we wouldn't be able to say that they cover a non-zero fraction of the laws or a non-zero fraction of the world. If one would think that they cover a non-zero fraction because (say) they know a non-trivial part of the fundamental forces, even though they don't know the exact functions that describe them, then we could also vary the type of all forces from one planet to the other or we could add a new set of forces for each planet. The point is that we can have a case when the fraction of the universe that can be axiomatized at any moment is zero and one can't improve this fraction, even if one is able to model new meaningful things about the universe and the part of the world that is covered by the axiom set is continuously extended.  We should note that in the second and third cases it can also happen that one can’t improve their the  axiom set to cover more even when using a statistical axiom set. One such case would be when the perceived laws of the universe change in unpredictable ways from day to day (of course, this can happen without any change in the actual axiom set for the universe). Let us denote by \definitie{observable description} of a possible universe $U$ for some intelligent beings $B$ inside $U$ any axiom set that, from the point of view of the beings $B$, can predict everything\footnote{With the assumptions above there is an axiom set that can predict everything. In general, an observable description would have to predict as much as it's possible.} that is reasonable\footnote{i.e. the \ghilimele{good enough} requirement from above.} about $U$ in the best way possible (i.e. predict precisely when possible or in a statistical way if not).