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This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1random. Although these occur with low probability, their very existence implies that the nosignaling (...) 

Do scientific theories limit human knowledge? In other words, are there physical variables hidden by essence forever? We argue for negative answers and illustrate our point on chaotic classical dynamical systems. We emphasize parallels with quantum theory and conclude that the common real numbers are, de facto, the hidden variables of classical physics. Consequently, real numbers should not be considered as ``physically real" and classical mechanics, like quantum physics, is indeterministic. 

In a wellknown paper, Timothy Williamson claimed to prove with a coinflipping example that infinitesimalvalued probabilities cannot save the principle of Regularity, because on pain of inconsistency the event ‘all tosses land heads’ must be assigned probability 0, whether the probability function is hyperrealvalued or not. A premise of Williamson’s argument is that two infinitary events in that example must be assigned the same probability because they are isomorphic. It was argued by Howson that the claim of isomorphism fails, but (...) 

A recent proposal to formulate physics in terms of finiteinformation variables is examined, concentrating on its consequences for classical mechanics. Both shortcomings and promising avenues are discussed. 