Epistemic justification. I’ll focus, rather, on the “genuinely random” ontic and epistemic randomness. a priori probability, Bayes, Carnap, evidence, objective epistemic probability, propensity probability, reasonableness of belief, subjective Bayesian probability. For contemporary followers of Carnap and Solomonoff, see Tooley (2012) and Rathmanner and Hutter (2011), respectively. Grundbegriffe der Wahrscheinlichkeitrechnung (Ergebnisse Der Mathematik); translated as Foundations of probability (New York: Chelsea Publishing Company, 1950). I will resist the temptation to get into the topics to which this may lead us, regarding, for example, the so-called measurement problem involving neat stuff like wave function collapse and other questions about the relation between the models of quantum mechanics and the actual world. Examples of the first kind include tossing dice or spinning a roulette wheel; an example of the second kind is radioactive decay. Priority Space (Baltag and Smets 2008a). Sack (2009) extended the work of Kooi (2003) and van Benthem, Gerbrandy, and Kooi (2009b) to full probability spaces (based on σ-algebras of events). To conclude, assuming that “randomness” is not epistemic and subjective, or making a big deal about the distinction between “ontological randomness” and “epistemic randomness,” implies some scientific autism… (Taleb Loc 6363). A major source of error in current probability theory arises from an unthinking failure to perceive this. First, I suppose I must ask myself to what degree I’ve satisfied Chakraborty’s to understand randomness (before endeavoring to understand probability). In Section 1, we follow the presentation, definitions, and results of Baltag and Smets (2008a) in extending this work over finite spaces to DEL, thereby implementing the fifth and final design principle. I likely won’t. It seems to me that, in principle, those things are indeed knowable. To philosophers it refers to a particular theory of physical probability, one that has more or less been abandoned. It is, as I shall put it, both aleatory and epistemological. It is epistemic because it is a measure of the degree of reasonableness of believing something; it is objective because it is independent of the beliefs of any person or group. (2010). (Subsection 3.5), Hanna goes on to note that “micro events of the sort associated with quantum phenomena” raise problems outside of his present concerns, he specifically intends, to include macro consequences of micro events in the account. For an quick and thought-provoking account of the phenomenon, see this two-part series from the Hi-Phi Nation podcast (a show I value for its regular inclusion of philosophers among its guest experts): Hackedmics I: The Control [Episode 6, 3/6/17; Centers on ESP as studied by scientists, culminating with Bem’s article]; Hackademics II: The Hackers [Episode 7, 3/14/17; Centers on Brian Nosek et al’s efforts that resulted in the concretization of the phenomenon as we think of it today]). I will not enter into this debate but it is clear that Diaconis was only attempting to, Click to share on Facebook (Opens in new window), Click to share on Twitter (Opens in new window), Click to share on LinkedIn (Opens in new window), Click to share on Reddit (Opens in new window), Click to share on Tumblr (Opens in new window), Click to share on Pinterest (Opens in new window), Click to share on Pocket (Opens in new window), Click to share on Telegram (Opens in new window), Click to share on WhatsApp (Opens in new window), Click to share on Skype (Opens in new window), Click to email this to a friend (Opens in new window). These points have been explained in some detail by Jaynes (1986d, 1989, 1990a, 1992a). Again it does not mean that there is no law. I defend an answer to the structural question on which basic probabilities are the probabilities of atomic propositions conditional on potential direct explanations. Logical foundations of probability.