@nntaleb@__mharrison__ Why topological space? As multilinear maps I would say the next smallest ensemble which contains them would be infinitely differentiable functions or analytic functions where it has a meaning.
@nntaleb There is a slight typo in the equation (2.3): the tau ought be in the integration domain and t ought to be use symbolically for the differential form.
@jahskillen@DrCirillo@dmi3k@HarryDCrane@ole_b_peters I read quickly this paper but it seems to me it shows de Finetti’s coherence implies logical consistency, which is afaik a less strong notion than consistency in the framework of Cox theorem. And as pointed by Jaynes, if there is no *equivalence* then problems may arise.
@jahskillen@DrCirillo@dmi3k@HarryDCrane@ole_b_peters Harry’s consistency here indicated as “coherence” was not proven to the date of PTLOS to match Cox theorem definition of consistency. See the third argument below. It’s then possible than de Finetti system could admit processes that would violate Cox theorem.
@jahskillen@DrCirillo@dmi3k@HarryDCrane@ole_b_peters Seems - to me - like an overly complicated way to replicate Jaynes approach which works just fine by considering that probabilities are an extension of Aristotelian logic under the cox theorem
@DrCirillo@dmi3k@HarryDCrane As Jaynes stated, even if your worldview is subjective, the process by which you compute probabilities in accordance to the laws of logic within this worldview is objective. I think yudkowski called it subjective objectivism