In 1959, a paper appeared in The Journal of Symbolic Logic, with the unimpressive-sounding title “A Completeness Theorem in Modal Logic.” A completeness theorem is a guarantee that every universal truth—any statement that can’t be false, no matter what—can be proved. In this case, these truths are about modality, about things that could or couldn’t happen. You could’ve gone to the store to buy milk instead of to the bar to get a drink with friends, so we say getting the milk was possible. It couldn’t have turned out that a circle isn’t a circle, so we say in philosopher-talk that it’s necessarily false. This paper, in essence, guaranteed that for a particular logical system of possibility and necessity, any universally true statement is provable. It may not sound like much, but this result is extremely important for any such system. The completeness of first-order logic, for example, was proved by no lesser a logician than the legendary Kurt Gödel, when he was 23. It is one of the signal achievements of mathematical logic.

Which makes it even more impressive that this paper’s result was proved by someone in his teens. Any way you want to measure it, Saul Aaron Kripke, son of Dorothy and Rabbi Myer Kripke of Omaha, Nebraska, was a prodigy. “Saul once told me he would have invented algebra if it hadn’t already been invented, because he came upon it naturally,” his mother told the New York Times. He mastered more mathematics by middle school than many college students ever get a handle on, and by the time he was an undergraduate at Harvard, he was teaching a graduate mathematical logic course at MIT.

After earning an undergraduate degree in mathematics and further revolutionizing modal logic, “Mr.” Kripke—he never earned a doctorate, and never needed to—went on to teach at Rockefeller University and Princeton, and eventually moved to the CUNY Graduate Center in 2002. While not a magnetic speaker, he was famed for lecturing, reading the lecture’s transcription, adding several revisions and footnotes, and sending the result off to press. This process produced his most renowned book, Naming and Necessity. Kripke died on September 15.

Great philosophers are not always great people. Allegations of sex-based harassment of students, as well as plagiarism, followed Kripke. It would be irresponsible to write of his philosophical oeuvre without recognizing this, for genius does not excuse vice. But it is also inadvisable to dismiss his brilliant output because of his deplorable behavior—because Kripke was one of the most influential American philosophers of the second half of the twentieth century, and possibly the most influential. Kripke revolutionized logic and metaphysics (philosophy about what the world is like) and made important contributions to epistemology (philosophy about knowledge and belief) and philosophy of mind.

A concept that pervades Kripke’s work is that of a possible world, first introduced by the seventeenth-century philosopher Gottfried Leibniz. Think of the milk and bar example. We cash out language like “I could’ve gotten milk” in terms of you having gotten milk in another world, one similar to this one except that you ditched your friends and went grocery shopping. We understand language like “a circle couldn’t have been square” in terms of there being no such world where that happens.

One can apply this concept in innumerable ways. I’ll mention just one, which Kripke used to argue that the mind is not identical to the body—a position called dualism. Physicalists about the mind, in contrast, think that, in some way, the mind is identical to some parts of the body.

To appreciate Kripke’s argument, we need to know something about his views on language—specifically, his views on what names are. This question occupied much of twentieth-century philosophical thought in the Anglophone world. One view, ascendant for the first half of that century, held that proper names are abbreviated descriptions: the name “Cicero” really is a collection of such descriptions as “the author of De officiis” or “the greatest orator of the late Roman republic.” Since someone else could’ve been the late greatest republican orator of Rome, the name “Cicero” doesn’t necessarily pick out Cicero. It might, say, pick out Seneca.

Not so for Kripke, who argued that names don’t pick things out by describing them. Rather, when I refer to Cicero by saying “Cicero,” I use the name the way I was taught, and the person who taught me did so how he was taught, and so on—all the way back to the initial naming event, when Cicero’s parents might have said, “Marcus Tullius Cicero es.” My use of the name extends all the way back to that “initial baptism,” and thus picks out Cicero uniquely.

Moreover, the proper name “Cicero” refers to Cicero alone in every possible world containing him. This suggests that any identity statement containing proper names—in Kripke’s example, “Cicero is Tully”—is necessarily true: there is no way the world could be where it’s false. Think about what would happen otherwise: one of the names, say “Tully,” would refer to one person in one world and another person in another. Since this can’t happen, that identity statement must be true.

If physicalism is true, then Cicero’s body is identical to Cicero’s mind. But suppose, hypothetically, that someone named Cicero’s body A and Cicero’s mind B. On Kripke’s view, since A and B are proper names, the identity statement “A is B” must be necessarily true. But this seems false: surely, even if minds are identical to bodies in this world, there’s some way the world could be where they aren’t. Descartes, who famously argued that mind and body are distinct but interacting things, could have been right.

Since it implies that something that must be true no matter what is false in some possible world, then, physicalism must be false in that world. And since these identity statements are true no matter what, physicalism must be false here, in this world. Descartes was right: mind and body are distinct.

Kripke was somewhat neutral on whether this argument proved dualism. But maybe it does. Maybe his mind is still around here somewhere, dead but dreaming of distant possible worlds.

Photo: WikiMedia Commons


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