Truth and probability

Abstract

Probability serves as the logic of partial belief, distinct from both statistical frequencies and unperceivable logical relations. Degrees of belief represent causal dispositions measurable by an agent’s willingness to act or accept specific wagers. By employing a schematic psychological model where actions maximize expected utility, numerical values are assigned to beliefs through preferences between conditional options involving ethically neutral propositions. Coherence within this framework requires that partial beliefs adhere to the standard calculus of probability, as any violation results in internal inconsistency or a “book” being made against the agent. This “lesser logic” of consistency remains separate from the “larger logic” of truth, which evaluates inductive habits based on their pragmatic success and frequency of leading to true outcomes. Induction is thus characterized not as a formal deduction but as a vital mental habit justified by its reliability within a regular world. Objective chances are further interpreted as degrees of belief derived from simplified systems of natural laws, which are selected by balancing structural simplicity against the maximum likelihood of observed facts. Ultimately, the quantification of probability facilitates consistent decision-making under conditions of uncertainty and serves as a foundational tool for scientific and logical ratiocination. – AI-generated abstract.