Description
This monograph develops a general theory of un-Bayesian updating, in which inference is reconceptualized as a transformation of epistemic fields rather than a revision of probability distributions. Departing from the classical paradigm - where evidence is given and updating followsBayes’ rule - the theory posits that evidence is constructed through interpretation, and thatupdating operates on structured objects defined by local sensitivity, global coherence, andmemory. The formal framework integrates S-theory as a microfoundation of interpretation with the General Theory of Signature Space (GTSS) as a geometric representation of epistemic states. Each state isrepresented as a signature, where parameters encode phase, curvature, and memory. Updating is modeled as motion in this space, governed by nonlinear operators, configurational interactions, and renormalization flows across scale. Within this geometry, classical Bayesian inference emerges as a local limit corresponding to stableregions of the space. Deviations from Bayesian rationality - such as order effects, framing, confirmation bias, and polarization - are shown to arise naturally from field dynamics, includingnon-commutativity, path dependence, and phase transitions. The framework further unifies andextends existing approaches, embedding Prospect Theory, reinforcement learning, and quantum cognition as partial cases within a broader field-theoretic structure. This monograph develops a general theory of un-Bayesian updating, in which inference is reconceptualized as a transformation of epistemic fields rather than a revision of probability distributions. Departing from the classical paradigm - where evidence is given and updating follows Bayes’ rule - the theory posits that evidence is constructed through interpretation, and thatupdating operates on structured objects defined by local sensitivity, global coherence, andmemory. The formal framework integrates S-theory as a microfoundation of interpretation with the General Theory of Signature Space (GTSS) as a geometric representation of epistemic states. Each state isrepresented as a signature, where parameters encode phase, curvature, and memory. Updating is modeled as motion in this space, governed by nonlinear operators, configurational interactions, and renormalization flows across scale. Within this geometry, classical Bayesian inference emerges as a local limit corresponding to stableregions of the space. Deviations from Bayesian rationality - such as order effects, framing, confirmation bias, and polarization - are shown to arise naturally from field dynamics, including non-commutativity, path dependence, and phase transitions. The framework further unifies andextends existing approaches, embedding Prospect Theory, reinforcement learning, and quantum cognition as partial cases within a broader field-theoretic structure.