Categorical formal epistemology

Abstract

The main point of article is to employ the potential of categorical logic methods in order to expand the scope of formal epistemology, taking into account that modern formal epistemology is in fact an interdisciplinary research program that includes philosophical, mathematical, computational, statistical, psychological, and economic aspects that require the use of logical, mathematical, and computer methods along with correct strategies for reasoning about the knowledge, beliefs and judgments. The exploitation of systems of categorical logic instead of systems of modal epistemic logic makes it possible to include in the orbit of The main point of article is to employ the potential of categorical logic methods in order to expand the scope of formal epistemology, taking into account that modern formal epistemology is in fact an interdisciplinary research program that includes philosophical, mathematical, computational, statistical, psychological, and economic aspects that require the use of logical, mathematical, and computer methods along with correct strategies for reasoning about the knowledge, beliefs and judgments. The exploitation of systems of categorical logic instead of systems of modal epistemic logic makes it possible to include in the orbit of consideration not only the degrees of belief of judgments (epistemic or subjective probability), but also the degrees of belief of epistemic conclusions and their interconnection. To assess these connections, agency and “Bayesian” parameterization of epistemic conclusions are introduced by assigning the conditional probability of deriving some epistemic judgments from others. To achieve this goal, a transition is made from categories to 2-categories, in which the objects are already the conclusions themselves. Degrees of belief in two-level deductive 2-categories can be introduced by parameterizing the values of the conditional probability of the second-level arrows (2-arrows or, in other terminology, 2-cells). In this case, we are already talking about the degree of conditional reliability of certain conclusions, characterizing the choice of one or another conclusion as reliable with the help of categorical constructions on the second-level arrows. At the same time, by associating conditional probability with epistemic conclusions, we reduce in categorical epistemology the degree of belief for the case of complex conclusions, while increasing it simultaneously for the case of simpler conclusions between the same formulas.