Prescriptive Logic as a Tool of Cognition. A Formal Framework for Model Dynamics

Existing logical systems do not provide a formal framework that describes the dynamics of cognition, model transitions, and the prescriptive function of logic as a unified whole. This article proposes such a framework: the truth value of a proposition is interpreted as a model index on the interval [0, 1), indicating the model in which the given proposition is complete. The development of knowledge is viewed as the expansion of families of such models, with 1 as an unattainable limit. Truth is understood in a threefold manner: as a model index, as an unattainable limit, and as a measure of consistency among various statements, graphically representable on the square [0, 1) × [0, 1), where the diagonal corresponds to full consistency of indices. Negation links 0 and 1 as mirror poles; the value 0 acquires a constructive function and prescribes one of three actions (three modes of zero: accept the opposite, change the principle, or build anew). A distinction is drawn between reflective and unreflective modes of logical entailment. The Oracle returning the index prescribes one of six actions (a hex-ad), depending on whether the model is substantive, incompetent, or represents an exact inversion of truth.