“The “immeasurability” of the future that Vaden has highlighted has nothing to do with the literal finiteness of the timeline of the universe. It has to do, rather, with the set of all possible futures (which is provably infinite). This set is immeasurable in the mathematical sense of lacking sufficient structure to be operated upon with a well-defined probability measure. “
“The “immeasurability” of the future that Vaden has highlighted has nothing to do with the literal finiteness of the timeline of the universe. It has to do, rather, with the set of all possible futures (which is provably infinite). This set is immeasurable in the mathematical sense of lacking sufficient structure to be operated upon with a well-defined probability measure. “
This claim seems confused, as every nonempty set allows for the definition of a probability measure on it and measures on function spaces exist ( https://en.wikipedia.org/wiki/Dirac_measure , https://encyclopediaofmath.org/wiki/Wiener_measure ). To obtain non-existence, further properties of the measure such as translation-invariance need to be required (https://aalexan3.math.ncsu.edu/articles/infdim_meas.pdf) and it is not obvious to me that we would necessarily require such properties.
See discussion below w/ Flodorner on this point :)You are Flodorner!