In the first paper of this series (Cogito, 1992) the author outlined ‘the showdown phenomenon’: a live sequence of events of two distinct kinds, ‘red’ and ‘green’, which was experienced by the would-be predictor as absolutely and irreducibly unpredictable, because the predictor invariably got his or her predictions wrong. (In a second paper (Cogito, 1993) he argued that the showdown phenomenon is an epistemological landmark, because it establishes a clearly conceptualized, tangible, localized ‘limit of knowledge’.) At the end of the original paper the author remarked that if we actually experienced suchabsolute, relentless unpredictability, we would infer the existence of another ‘out there’ doing this to us ... In the current paper he returns to this ontological aspect of the new Cogito and fills out some of the thinking which lies behind it.

The first paper of this series (Cogito, 1992) outlined ‘the showdown phenomenon’: a live sequence of events of two distinct kinds, ‘red’ and ‘green’, which was experienced by the would-be predictor as absolutely and irreducibly unpredictable, because the predictor invariably got his or her predictions wrong. We can clearly and distinctly imagine this happening: so a perverse-random experience of this sort is evidently ‘logically possible’. This raises the question of the relation of the new sequences to ordinary ‘random’ sequences. In this paper an account is developed of the relationship of ‘perverse-randomness’ to ‘randomness’. Such an account may assist us in achieving a new, firmer conceptualization of ordinary probability, and hence in making sense of this notoriously elusive idea.