In a recent paper, Sylvia Wenmackers and Leon Horsten discuss how the concept of a fair infinite lottery can best be extended to denumerably infinite lotteries. Their paper uses and builds on the alpha-theory of Vieri Benci and Mauro Di Nasso. The purpose of this paper is to demonstrate a potential problem for alpha-theory.

From the second half of the 16th century the question about Platonis Aristotelisque Concordia is no more a merely doctrinal problem, but it involves a discussion about methodus and ordo, according to the importance given to them in the coeval philosophical debate. In many cases underscoring Plato’s scientific merits, not only about inventio but also about the transmission of knowledge, meant promoting Platonism as a philosophy suitable for University. In this context the need for Platonic handbooks is perceived as compelling, (...) due to the recognised didactic superiority of Aristotle’s writings. The Compendio and the Vere Conclusioni are the specific contribution of Francesco Verino secondo, who gave holiday lectures on Plato at the Florentine Studium from 1576 to 1579. The present study focuses on the platonism of Francesco Verino, covering nearly all his works, printed and manuscript, in a constant comparison with his noble predecessors Marsilio Ficino, Giovanni Pico della Mirandola and Francesco Cattani da Diacceto. In order to give light to Verino’s lectureship, particular attention is paid to glosses in his working and teaching copy of Platonis Opera. (shrink)

A probability distribution is regular if no possible event is assigned probability zero. While some hold that probabilities should always be regular, three counter-arguments have been posed based on examples where, if regularity holds, then perfectly similar events must have different probabilities. Howson (2017) and Benci et al. (2016) have raised technical objections to these symmetry arguments, but we see here that their objections fail. Howson says that Williamson’s (2007) “isomorphic” events are not in fact isomorphic, but Howson is (...) speaking of set-theoretic representations of events in a probability model. While those sets are not isomorphic, Williamson’s physical events are, in the relevant sense. Benci et al. claim that all three arguments rest on a conflation of different models, but they do not. They are founded on the premise that similar events should have the same probability in the same model, or in one case, on the assumption that a single rotation-invariant distribution is possible. Having failed to refute the symmetry arguments on such technical grounds, one could deny their implicit premises, which is a heavy cost, or adopt varying degrees of instrumentalism or pluralism about regularity, but that would not serve the project of accurately modelling chances. (shrink)