Bovens and Hartmann on Coherence
Wouter Meijs · Mind · 2005
In 'Solving the Riddle of Coherence' (2003), Luc Bovens and Stephan Hartmann present a new and ambitious probabilistic theory of coherence. This note argues that their theory sits badly with some pre-theoretical convictions regarding the notion of coherence. We start by outlining the theory, then state two intuitive counterexamples to it, and finally describe a general method for generating such counterexamples. Call any finite set of propositions one has acquired through consulting information sources an information set. It is assumed that one has been informed about each item in an information set by a separate source, that the sources are independent of one another, and that they are equally reliable to a degree r E (o, 1), where r = 1 indicates full reliability and r = o full unreliability (so the sources are assumed to be neither fully reliable nor fully unreliable). Given an information set S = {R1, . . ., Rn} and a probability distribution pt ) over the elements of S, let 'ai' stand for the sum of the probabilities of all conjunctions of n i elements of S and the negations of the remaining i elements of S. So, for instance, if S = {R1, R2}, then aO = p(Rl / R2), al = p(Rl A mR2) + p('R / R2) and a2 = p('Rl / 'R2). In contrast to other recent probabilistic theories of coherence, Bovens and Hartmann do not attempt to define a measure that determines the absolute degree of coherence for any information set. Rather their approach is a comparative one, central to which is the two-place relation of being no less coherent than, '> '. For any two information sets S = {R1, ..., Rm}) S = {R 1) ) R n}) this relation is defined as follows: