‘Ramseyfying’ Probabilistic Comparativism

Abstract

Comparativism is the view that comparative confidences (e.g., being more confident that P than that Q) are more fundamental than degrees of belief (e.g., believing that P with some strength x). In this paper, I outline the basis for a new, non-probabilistic version of comparativism inspired by a suggestion made by Frank Ramsey in 'Probability and Partial Belief'. I show how, and to what extent, 'Ramseyan comparativism' might be used to weaken the (unrealistically strong) probabilistic coherence conditions that comparativism traditionally relies on.

Logics of imprecise comparative probability

“…Aside from being intuitively simpler and arguably closer to "ordinary" expressions of uncertainty, some authors have argued that this setting of comparative probability is perhaps uniquely suited to solving notable epistemic puzzles (Fine 1977;DiBella 2018;Eva 2019). Others have sought more ameliorative reconciliations between the quantitative and qualitative approaches so as to capitalize on the advantages of each (see, e.g., Suppes andZanotti 1976 andElliott 2020).…”

Fair Infinite Lotteries, Qualitative Probability, and Regularity

“…This construction shows that there indeed 17 See Boolos [1971] for an argument to this effect. 18 This is the reasoning Stefánsson [2018] provides to motivate his "Ratio Principle", according to which event A is twice as probable as event B just in case there is some event Elliott [2020] shows how we can understand rational probability ratio comparisons more generally in terms of qualitative probability via his "General Ratio Principle". DiBella [unpublished] generalizes still further to make sense of arbitrary real-valued probability ratios in qualitative terms.…”

“…This is the reasoningStefánsson (2018) provides to motivate his "ratio principle," according to which event A is twice as probable as event B just in case there is some event C such that (1) B C, (2) B \ C ;, and (3) A B [ C Elliott (2020). shows how we can understand rational probability ratio comparisons more generally in terms of qualitative probability via his "general ratio principle."…”