Abner Shimony called it coherence; John Kemeny called it strict fairness; today many people speak of strict coherence. According to Shimony's definition, a set of betting rates on a series of propositions hi and ei is strictly incoherent, when “there exists a choice of stakes Si such that, if X accepts the series of bets at these stakes, then no matter what the actual truth values of hi, and ei may be, X can at best lose nothing, and in at least one possible eventuality he will suffer a positive loss” ([3], p. 9).