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Vladimir_Nesov comments on No Universal Probability Space - Less Wrong
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Please specify in what sense the first line was correct, or declare it an error. Pronouncing assertions known to be incorrect and then just shrugging that off shouldn't be acceptable on this forum.
O.K.
One wants an universal probability space where one can find the probability of any event. This is possible:
One way of making such a space is to take all recursive functions of some universal computer, run them, and storing the output, resulting in an universal probability space because every possible set of events will be there, as the results of infinitely many recursive functions, or programs as they are called. The probabilities corresponds to the density of these outputs, these events.
A counterargument is that it is too dependent on the actual universal computer chosen. However, theorems in algorithmic information theory shows that this dependence converges asymptotically as information increases, because the difference of densities of different outputs from different universal computers can at most be 2 to the power of the shortest program simulating the universal computer in another universal computer.
Kim Øyhus
OK....
what!? You haven't yet described a probability space. The aforementioned set is infinite, so the uniform distribution is unavailable. What probability distribution will you have on this set of recursive-function-runs. And in what way is the resulting probability space universal?