On the Logic of Self-Knowledge

Abstract

In [4]1 Jaakko Hintikka has made the most important contribution, so far, to the problem of formalizing the logic of the concept knowledge. He has construed a semantical system with a primitive modal operator 'K' governed by the rule of formation: Kap is a well-formed formula of the system, if a is a personal individual constant or a variable ranging over persons and p is a well-formed formula of the system. If a is a constant, Kap is to be interpreted as the object-language statement to the effect that the person designated by a knows that what p formulates is true. In [1] it was pointed out that Hintikka's system suffers from two serious inadequacies as a formalization of the concept knowledge. The first serious inadequacy comes about as follows. In order to meet Quine's challenges (e.g., in [5], 141-156) about the interpretation of free (but bindable) variables in referentially opaque contexts, Hintikka makes his free variables in contexts of the form Ka(. . .) range over objects or persons known to the person referred to by a. This is an ingenious device that does meet some of Quine's challenges, but it prevents Hintikka's calculus from allowing consistent formalizations of some consistent statements, e.g., There is a person such that does not know that he [the person in question] exists. The calculus does allow the natural symbolization of statements like Jones does not know that Smith is self-identical: introduce the dictionary