Article abstract: Kripke provided technical and conceptual advances in modal logic but is more widely known for his work in the philosophy of language, in particular for initiating the causal theory of reference.
Saul Aaron Kripke, son of Myer Samuel and Dorothy Evelyn (Karp) Kripke, attended Harvard University, where he received a B.A. degree in 1962. In 1959, as a student, he distinguished himself by publishing an influential paper in the prestigious Journal of Symbolic Logic. Upon graduation, he received a Fulbright scholarship. A member of the Society of Fellows at Harvard in philosophy and mathematical logic, he served his alma mater as a lecturer from 1963 to 1966, when he left to take an appointment at Rockefeller University, where he stayed for ten years. In 1976, he became the McCosh Professor of Philosophy at Princeton University.
Kripke’s earliest writings and influence were in the field of modal logic. Where “standard” formal logic deals with the syntax and semantics of inference, modal logic extends these to characterize and systematize inferences involving the modalities of possibility and necessity. For example, “standard” logic does not allow the inference “If it is necessary that p, then p” or “If p, then it is possible that p.” Various systems of modal logic have been constructed to handle such inferences. One way of talking about such systems is to speak of “possible world semantics.” Although the world is the actual world, with a particular structure and history, things could have been different; facts could have been contrary to what they are. An intuitive way to speak of this is to talk of possible worlds, that is, worlds like the real world, but different in some respect or other.
To say that a proposition is possibly true simply means that, although it is false in the real world, it is true in some possible world. To say that a proposition is necessarily true simply means that it is true in all possible worlds (including the real world). Kripke’s first paper, “A Completeness Theorem in Modal Logic,” established that a formal modal system is complete: This means that any proposition p, either it or its negation, could be proven in that system (in other words, all valid inferences are shown to be valid in that system). This paper was followed by several others in the 1960’s, most notably “Semantical Considerations in Modal Logic,” in which Kripke elaborated on both technical aspects of modal logic and their wider implications and applications, including in the fields of ontology and philosophy of language.
It was these implications and applications of results in modal logic that brought Kripke his greatest renown. In 1972, he published Naming and Necessity, widely regarded as his most influential work and immediately considered a landmark in the philosophy of language. As the title indicates, he drew a connection between the modal element of necessity and the semantic issue of naming. The natural point of contact between these two, for Kripke, was the Leibnizian principle of the indiscernibility of identicals; that is, if two objects are identical, then they are indiscernible (or have all properties in common). If two objects really are identical, that is, if “a = b” is true, then, said Kripke, that identity would hold across all possible worlds (so that “a = b” would be necessarily true). From this starting point, Kripke questioned and ultimately rejected the view that names attach to objects in virtue of contingent properties associated with those names. For example, the name “Saul Kripke” attaches to a particular object not because of any contingent property that might be true of that particular object (for example, that he is the McCosh Professor of Philosophy). This is because there are possible worlds in which Saul Kripke is not the McCosh professor, but there are no possible worlds in which Saul Kripke is not Saul Kripke. Publication of Naming and Necessity, including its proposal of a new theory of reference and names, made Kripke a well-known figure not only in the community of logicians but also in the philosophical community at large.
His groundbreaking work in semantics continued throughout the 1970’s, highlighted by two more influential writings: one on truth, “Outline of a Theory of Truth,” and one on belief, “A Puzzle About Belief.” The former presented his attempt to provide a theory that both resolved paradoxes involving truth and captured basic intuitions about natural languages. Truth paradoxes have been long-standing in philosophy, the most famous being the liar paradox. This paradox is illustrated by the following sentence: “Everything I say is a lie.” If that sentence is true, then I am lying when I say that everything I say is a lie, which means that I am not lying. Another way to characterize this paradox is “This sentence is false.” If the sentence is false, then it must be true. A standard response to this paradox has been to speak of different levels of language, such that the content of that sentence is on one level, but when speaking about that sentence (for example, by calling it true or false), people are at a different level. The first level is often said to be the object language and the second level is said to be the metalanguage. Kripke, however, argued that with natural languages, people do not conceive of themselves as using different levels and do not speak of “truth-level-one,” “truth-level-two,” “truth-level-three,” and so on. A second concern for him was that, again with natural languages, people want to speak of truth-value gaps, times when we do not...
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