Introduction to the Special Issue Epistemic Aspects of Many-Valued Logics

Abstract

The papers in this special issue are based on presentations delivered at the conference Epistemic Aspects of Many-valued Logics, held at the Institute of Philosophy of the Academy of Sciences of the Czech Republic, in Prague, 2010. All papers consequently revolve around the application of non-classical logical tools— mathematical fuzzy logic and/or probability theory—to epistemological issues. Timothy Williamson employs a modal epistemic logic enriched with probabilities to generalize an argument against the KK-principle. He argues that we can know a proposition even if our evidential probability for that proposition is low. In fact he argues that the evidential probability of a known proposition can be (arbitrarily) close to 0. The argument is first presented with a basic idealized model, which is then extended to much more complicated and realistic models. This then raises a problem for decision theory, since you can know that p, while your evidence tells you (strongly) that not p. Williamson argues that this problem should be understood as a failure of luminosity, i.e., that if you are in a state then you are in a position to know that you are in that state. Williamson also argues that a version of deductive closure of knowledge is defensible as long as we drop the KK-principle. Since knowledge states aren’t luminous, standard arguments against closure don’t work. Colin Howson argues the subjective interpretation of the probability calculus should be understood in the framework of many-valued higher-order logics. Howson argues that the standard objections to second-order logic rely on a misguided conception of logic, and argues that we should instead concentrate on the model-theoretic notions of consistency and consequence. He then interprets the finitely additive probability calculus using these notions, linking fair bets with probabilities a la de Finetti. The restriction to finite additivity yields two logical properties: that a consistent probability assignment is extendable to a total assignment, and that an assignment is consistent if and only if all of its restrictions