Multivalent Beliefs

Classical logic and its supplement of traditional probability fail to account for the epistemic uncertainty that prevails in the real world. The reason is that bivalence allows representation of only two additive measures, truth and falsity. A more general logic system could enable representation of what we do not know. Degrees of belief based on multivalent logic would allow representation of how much we believe a fact, how much we disbelieve it, and how much we are in the dark as to it—while still being a valid logic system. This long chapter concludes that, in the presence of epistemic uncertainty, multivalent beliefs provide an excellent way to understand evidence and proof both in theory and as applied in legal factfinding. Section 4.1: As a descriptive and normative matter, the legal factfinder concerns itself with degrees of belief based on the evidence presented. The law already conforms to this conception, allowing it to proceed accurately without puzzles or paradoxes in its factfinding and allowing me to avoid calling for radical reform. Section 4.2: The underlying multivalent logic comprises a group of valid logic systems, such as fuzzy logic and possibility theory. They are more general than classical logic, in that they do without the classical assumption that all propositions are either true or not true. Section 4.3: Belief function theory delivers a multivalent concept whose imagery best captures and illuminates legal factfinding. A degree of belief can coexist with a degree of disbelief produced by the evidence, that is, a degree of belief in the opposite of the fact. Moreover, the factfinder facing epistemic uncertainty can leave some of its belief uncommitted when forming the degree of belief the fact is true and the degree of belief the fact is false. Combining belief functions’ imagery with multivalent logic’s operators, a very defensible move, yields “multivalent belief theory,” a very expressive system. Section 4.4: Competing theories such as inference to the best explanation, relative plausibility, and ranking theory turn out to act in the same way as multivalent belief theory. But they lack an equivalent fit with legal imagery, an equivalently strong theoretical foundation, and an equivalent ability to dispel the problems of probability. Section 4.5: Multivalent beliefs manage to resolve all of traditional probability’s problems that stem from its failure to account for epistemic uncertainty. Multivalent beliefs give a more realistic representation of human factfinding, handle weak evidence on both sides, dissipate the difficulty of infinite possibilities nimbly, provide accurate tools for aggregating uncertain evidence and combining established facts, resolve the apparent asymmetries in the treatment of plaintiffs and defendants, and capture conceptually what we intuitively think of as adequate legal proof. Section 4.6: Multivalent beliefs are the appropriate measure whenever, for the sake of accuracy, the decisionmaker needs to keep track of epistemic uncertainties in addition to any aleatory uncertainty. For example, legal factfinders must hold both kinds of uncertainty in mind when making and combining their findings. Section 4.7: The line of argument in support of multivalent belief theory can be recapitulated as a small series of simple and fairly unassailable steps.