27b. New paper by Mark Colyvan

Yet Lindley must not have made such a convincing case when, two decades later, papers like the following continue to be published.

M.Colyvan. Is probability the only coherent approach to uncertainty?, Risk Analysis, to appear.

Colyvan examines the Cox theorem from the logical point of view, more deeply than he did in an IJAR paper some years ago. Unfortunately, it is obvious from reading Lindley's testament Understanding uncertainty (Wiley, 2006) that Lindley never came to understand or accept that discussing the underlying logical assumptions is very pertinent and necessary here.

That explains that Lindley speaks of the "self-evidentiary nature" of "rules whose violation would look ridiculous" and are "dictated to us by the inexorable laws of logic" (here, p.19), whereas Colyvan puts it as follows: "Anyone wishing to argue against fuzzy methods, for instance, must not simply beg the question against those methods. To use a theorem such as Cox's theorem that is based on assumptions that fuzzy logic rejects is thus unappropriate unless the assumptions in question can be independently defended. But then the appeal to Cox's theorem is redundant" (p.11).

It is quite transparent, from the very first page of Understanding uncertainty, that Lindley lives in a world where events either happen or not happen. Thence, invoking the "inexorable laws of logic" his opponents do deny is just question-begging.