6. Old paper by Brian Weatherson

This paper by philosopher Brian Weatherson is not about fuzzy sets but I find it relevant for foundational discussions with Bayesians. Weatherson presents a Dutch Book argument which works under intuitionistic logic. An obvious implication, good news for open-minded Bayesianism, is that commitment to classical logic is not necessary in order to adhere to De Finetti's view of probability. Another implication is that adherence to the Dutch Book cannot, in and of itself, rule out other logics.

In From classical to intuitionistic probability, a bet on the occurence of A can be settled for A, against A or remain unsettled (cf. a proposition in intuitionistic logic can be true, false or neither- if it hasn't been proved true or proved false).

Accordingly, Weatherson's intuitionistic probabilities allow for the probabilities of an event and its contrary to sum up to less than 1. Thus he presents them as an alternative to belief functions.

This paper appeared in Notre Dame Journal of Formal Logic 44 (2004), 111-123.