caa a22 4500 605539057 CHVBK 20210128100905.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s10992-014-9317-7 doi (NATIONALLICENCE)springer-10.1007/s10992-014-9317-7 Pruss Alexander Baylor University, One Bear Place 97273, 76798-7273, Waco, TX, USA aut Popper Functions, Uniform Distributions and Infinite Sequences of Heads [Elektronische Daten] [Alexander Pruss] Popper functions allow one to take conditional probabilities as primitive instead of deriving them from unconditional probabilities via the ratio formula P(A|B)=P(A∩B)/P(B). A major advantage of this approach is it allows one to condition on events of zero probability. I will show that under plausible symmetry conditions, Popper functions often fail to do what they were supposed to do. For instance, suppose we want to define the Popper function for an isometrically invariant case in two dimensions and hence require the Popper function to be rotationally invariant and defined on pairs of sets from some algebra that contains at least all countable subsets. Then it turns out that the Popper function trivializes for all finite sets: P(A|B)=1 for all A (including A = ∅ $A=\varnothing $ ) if B is finite. Likewise, Popper functions invariant under all sequence reflections can't be defined in a way that models a bidirectionally infinite sequence of independent coin tosses. Springer Science+Business Media Dordrecht, 2014 Probability nationallicence Conditional probability nationallicence Popper function nationallicence Symmetry nationallicence Group action nationallicence Independence nationallicence Infinity nationallicence Rotation nationallicence Banach-tarski paradox nationallicence Journal of Philosophical Logic Springer Netherlands 44/3(2015-06-01), 259-271 0022-3611 44:3<259 2015 44 10992 https://doi.org/10.1007/s10992-014-9317-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10992-014-9317-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pruss Alexander Baylor University, One Bear Place 97273, 76798-7273, Waco, TX, USA aut NATIONALLICENCE 773 0- Journal of Philosophical Logic Springer Netherlands 44/3(2015-06-01), 259-271 0022-3611 44:3<259 2015 44 10992