KK’ing Diachronically

Vincent F. Hendricks & Stig Andur Pedersen

In both epistemology and epistemic logic, a substantial amount of attention has been devoted to the famous KK-thesis. The characteristic axiom of S4 interpreted epistemically amounts to the claim that a method δ knows that it knows p when it does know p: K_{δ}p ⇒ K_{δ}K_{δ}p. There are, and have been, various arguments for an against this thesis both philosophically and logically. From the modal learning theoretical perspective [ Hendricks 00], [Hendricks & Pedersen 00a], [Hendricks & Pedersen 00b] (which is the perspective obtained by mixing modal, tense and epistemic logic with concepts drawn from formal learning theory) the KK -problem is somewhat more interesting to study because δ may be subject to various program commands like data consistency, data-retentiveness and data-entailment. It turns out that the KK -thesis is valid diachronically in the sense that δ has to converge to the antecedent claim first, then wait, and then converge to the consequent claim observing a special consistency command. For instance if δ obeys data-retentiveness and thus tries to converge to the consequent claim as soon as it converges to the antecedent claim, hence attempts a synchronic validation of KK, then the KK -thesis is impossible to learn. Thus, the KK -thesis requires the agent to behave quite strategically in order to succeed on KK.

[ Hendricks 00] Hendricks, Vincent F. (2000). The Convergence of Scientific Knowledge a view from the limit. In press: Studia Logica’s Trends in Logic Series, Kluwer Academic Publishers.

[ Hendricks & Pedersen 00a] Hendricks, Vincent F. & Stig Andur Pedersen (2000). Operators in Philosophy of Science. In preparation.

[ Hendricks & Pedersen 00b] Hendricks, Vincent F. & Stig Andur Pedersen (2000). ”Assessment and Discovery in the Limit of Scientific Inquiry”. To appear in Proceedings of the XI International Congress on Logic Methodology and Philosophy of Science (LMPS’99), Kluwer Academic Publishers.

Addresses Vincent F. Hendricks: Dept. of Philosophy, University of Copenhagen, Njalsgade 80, DK-2300 Copenhagen S, Denmark

E-mail: vincent@hum.ku.dk

Stig Andur Pedersen: Depts. of Philosophy and Mathematics, University of Roskilde, P. O. Box 260, 4000 Roskilde, Denmark

E-mail: sap@ruc.dk