The Space of Reasons 2008-03-01

On the Logic of Knowing

In epistemic logic it has become common to construe formulas of the form Kiφ, read “agent i knows φ”, in modal terms. Most notably, Hintikka has suggested the following definition of knowledge: (*) M, s ╞ Kiφ iff for all t ~ i s : M, t ╞ φ According to the above formula, an agent i knows that φ in some situation s, on some model M if and only if, for all other situations t, that i considers indistinguishable from s, t entails φ on M. On this approach an agent i is said to know a fact φ if φ is true at all the worlds she considers possible (given her current information). However, intuitively, there seems to be certain sceptical scenarios which, though remote, we still feel inclined to hold as possible (given our current information). ...

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