14 citations · 44 across the 14 of their papers we have counts for
5 papers · 1 filter
History of Archimedean and non-Archimedean approaches to uniform processes: Uniformity, symmetry, regularity
Emanuele Bottazzi, Mikhail G. Katz
We apply Nancy Cartwright's distinction between theories and basic models to explore the history of rival approaches to modeling a notion of chance for an ideal uniform physical pr…
Internality, transfer, and infinitesimal modeling of infinite processes
Emanuele Bottazzi, Mikhail G. Katz
A probability model is underdetermined when there is no rational reason to assign a particular infinitesimal value as the probability of single events. Pruss claims that hyperreal…
Infinite lotteries, spinners, and the applicability of hyperreals
Emanuele Bottazzi, Mikhail G. Katz
We analyze recent criticisms of the use of hyperreal probabilities as expressed by Pruss, Easwaran, Parker, and Williamson. We show that the alleged arbitrariness of hyperreal fiel…
On mathematical realism and the applicability of hyperreals
Emanuele Bottazzi, Vladimir Kanovei, Mikhail G. Katz +2
We argue that Robinson's hyperreals have just as much claim to applicability as the garden variety reals. In a recent text, Easwaran and Towsner (ET) analyze the applicability of m…
Fermat, Leibniz, Euler, and the gang: The true history of the concepts of limit and shadow
Tiziana Bascelli, Emanuele Bottazzi, Frederik Herzberg +6
Fermat, Leibniz, Euler, and Cauchy all used one or another form of approximate equality, or the idea of discarding "negligible" terms, so as to obtain a correct analytic answer. Th…