It is a fundamental limitation to base probability theory on bivalent logic

Probability theory has long played-and is continuing to play-the role of the principal tool for dealing with problems in which uncertainty is a significant factor. The history of probability theory is a history of important advances in our understanding of decision-making in uncertain environments. But what we see alongside the brilliant successes are problem areas in which progress has been elusive. An example is the class of problems in which probabilities, utilities and relations are ill-defined in ways that put such problems well beyond the reach of existing methods. A thesis that is put forth is that standard probability theory, call it PT, has fundamental limitations-limitations which are rooted in the fact that PT is based on bivalent logic. It is this thesis that underlies the radically-sounding title of the paper: It is a fundamental limitation to base probability theory on bivalent logic. The principal rationale for this thesis is that the conceptual structure of PT is directed at addressing the partiality of certainty but not the partiality of possibility and, most importantly, the partiality of truth. A direct consequence of these omissions is that PT lacks the capability to deal with information which is not just partially certain but also partially possible and/or partially true. An example is: Most analysts believe that it is very unlikely that there will be a significant increase in the price of oil in the near future.