Belief, Knowledge and Possibility

By applying the extended system of modal logic developed in [32], we present a logical analysis of the Gettier problem. Based on the result, in particular, we clarify the following point. In the literature on the Gettier problem, most authors seem to share the opinion that in general ‘belief’ precedes ‘knowledge’: we believe a proposition while we do not necessarily believe ourselves to have known it to be true. Interestingly, our analysis suggests that the story is the other way round in a sense: in general, for some proposition p, we believe that we have known that p, then we believe that p. Accordingly, even if given some reason for wanting to believe that p, we usually do not have the bare belief that p. Instead, in such a situation, more deliberately we think that it might be that p, or it can be hypothesized that p. Then, we can say, what we have at the start is not the bare belief that p, but “might possibility” or “hypothetical possibility” that p, which presumably involves abductive reasoning.