Saul Kripke

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Saul Kripke bigraphy, stories - American philosopher

Saul Kripke : biography

November 13, 1940 –

Saul Aaron Kripke ( born November 13, 1940) is an American philosopher and logician. He is currently McCosh Professor of Philosophy, Emeritus, at Princeton University and teaches as a Distinguished Professor of Philosophy at the CUNY Graduate Center. Since the 1960s Kripke has been a central figure in a number of fields related to mathematical logic, philosophy of language, philosophy of mathematics, metaphysics, epistemology, and set theory. Much of his work remains unpublished or exists only as tape-recordings and privately circulated manuscripts. Kripke was the recipient of the 2001 Schock Prize in Logic and Philosophy. A recent poll conducted among philosophers ranked Kripke among the top ten most important philosophers of the past 200 years.Brian Leiter, Leiter Reports: A Philosophy Blog,

Kripke has made influential and original contributions to logic, especially modal logic. Unusual for a professional philosopher, his only degree is an undergraduate degree from Harvard, in mathematics. His work has profoundly influenced analytic philosophy, with his principal contribution being a semantics for modal logic, involving possible worlds as described in a system now called Kripke semantics.Jerry Fodor, "", London Review of Books, 21 October 2004 Another of his most important contributions is his argument that necessity is a ‘metaphysical’ notion, which should be separated from the epistemic notion of a priori, and that there are necessary truths which are a posteriori truths, such as "Water is H2O." He has also contributed an original reading of Wittgenstein, referred to as "Kripkenstein." His most famous work is Naming and Necessity (1980).

Modal logic

Two of Kripke’s earlier works, A Completeness Theorem in Modal Logic and Semantical Considerations on Modal Logic, the former written while he was still a teenager, were on the subject of modal logic. The most familiar logics in the modal family are constructed from a weak logic called K, named after Kripke for his contributions to modal logic. Kripke introduced the now-standard Kripke semantics (also known as relational semantics or frame semantics) for modal logics. Kripke semantics is a formal semantics for non-classical logic systems. It was first made for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The discovery of Kripke semantics was a breakthrough in the making of non-classical logics, because the model theory of such logics was absent prior to Kripke.

A Kripke frame or modal frame is a pair langle W,Rrangle, where W is a non-empty set, and R is a binary relation on W. Elements of W are called nodes or worlds, and R is known as the accessibility relation. Depending on the properties of the accessibility relation (transitivity, reflexivity, etc.), the corresponding frame is described, by extension, as being transitive, reflexive, etc.

A Kripke model is a triple langle W,R,Vdashrangle, where langle W,Rrangle is a Kripke frame, and Vdash is a relation between nodes of W and modal formulas, such that:

  • wVdashneg A if and only if wnVdash A,
  • wVdash Ato B if and only if wnVdash A or wVdash B,
  • wVdashBox A if and only if forall u,(w; R; u to uVdash A).

We read wVdash A as "w satisfies A", "A is satisfied in w", or "w forces A". The relation Vdash is called the satisfaction relation, evaluation, or forcing relation. The satisfaction relation is uniquely determined by its value on propositional variables.

A formula A is valid in:

  • a model langle W,R,Vdashrangle, if wVdash A for all w ∈ W,
  • a frame langle W,Rrangle, if it is valid in langle W,R,Vdashrangle for all possible choices of Vdash,
  • a class C of frames or models, if it is valid in every member of C.