Sylvia Wenmackers (2011), PhD dissertation, University of Groningen (supervisor I. E. J. Douven) — https://philpapers.org/rec/WENPOP
Key takeaways
- A fair lottery on the natural numbers, impossible under Kolmogorov’s axioms, can be modelled by a non-Archimedean probability (“normalised numerosities”) giving each ticket a non-zero infinitesimal chance, and the same non-standard strategy yields “Stratified Belief”, a contextualist resolution of the Lottery Paradox.
Seeded from the abstract and a skim, before the reading in NOTE-139. What follows is what the work says about itself.
The dissertation is a contribution to formal and computational philosophy. Its first part exploits parallels between very large finite lotteries and countably infinite ones to gain insight into both the foundations of probability and epistemology, solving their respective “adding problems” with non-standard analysis. Its second part uses computer simulation to study communities of agents who update beliefs by averaging, and computes the probability that an agent ends in an inconsistent belief state.
Standing in the record
Filed from the 2026-09-26 sweep of the papers-feed tracker for philosophy: 20 seconds of active reading over 1 session. It was filed Deferred, unread. NOTE-139 is the close reading of 2026-09-26, and it placed the work: Active — worth reading for the Ch. 1 survey of interpretations of probability and the Ch. 4 synthesis, which appear only here; for the rest, each chapter has a later journal version that is the better citation, none of them held on this record: Wenmackers & Horsten, “Fair infinite lotteries”, Synthese 190 (2013) 37–61 (Ch. 2); Wenmackers, “Ultralarge lotteries”, J. Applied Logic 11 (2013) 452–467 (Ch. 3); Wenmackers, Vanpoucke & Douven, “Probability of inconsistencies in theory revision”, Eur. Phys. J. B 85 (2012) 44 (Ch. 5); and Benci, Horsten & Wenmackers, “Non-Archimedean probability”, Milan J. Math. 81 (2013) 121–151 (the Ch. 6 outlook).
When seeded, before the reading in NOTE-139, the entry gave a priority for a deeper reading: low — brief visit (t = 20 s); a thesis whose results are better read in the author’s later journal papers, and the skim captures its claims.
What the seeding asked a deeper reading to check (NOTE-139 is that reading):
- The origin of Wenmackers’ NAP programme (later with Benci, Horsten), central to debates on regularity, infinitesimal probabilities and zero-probability events.
- Check how the ultrafilter-dependence (non-uniqueness) of the construction is handled — the main objection pressed in the later literature (e.g. Williamson-style arguments against infinitesimal regularity).
- Chapter 5’s agent-averaging model links to opinion dynamics in social epistemology.
Access when seeded: philpapers.org blocked; the full thesis PDF (180 pp.) fetched from the author’s website and read — TOC, Summary, §2.7, §6.1. published: is the public defence date printed on the title page (Monday 2 May 2011). No DOI found; the Groningen repository (research.rug.nl) also hosts it.