Saul Kripke (1940—) is a logician and professor of philosophy best known for his contributions to logic, epistemology and philosophy of language.

Kripke semantics

Kripke semantics is a method of providing semantics for non-classical logical systems. In the 1930s, Alfred Tarski provided a model theory for classical logics, but until Kripke, no such theory existed for modal logic. To remedy this, Kripke created the possible world semantics, which described the modal operators of neccessity and possibility in the context of truth in multiple possible worlds.

Kripke described a model in modal logic as an object consisting of a set of possible worlds, W, a set of binary relations between them, R and a relation between individual worlds and formulae that are true in those worlds, ⊩. Such a model is expressed through the notation 〈W, R, ⊩〉.

Thus, necessity and possibility can be semantically defined: Something is necessarily true in some world when it is true in all worlds accessible to that world, and something is possibly true in a world when it is true in at least one possible world accessible to it.

Kripke's semantics have drawn a renewed interest in modal logic and many developments in their study. It has also brought questions from those such as Quine, who ask to what one is referring when discussing possible worlds, and whether or not such semantics commit one to affirming their existence.

Works

• Naming and Necessity (Lectures, 1972)
• Wittgenstein on Rules and Private Language (1982)