Burden of Proof: Raymond Smullyan Puzzles Over Kurt Gödel’s Theorems

Raymond Smullyan

Best known for his Incompleteness Theorem, Kurt Gödel (1906-1978) is considered one of the most important mathematicians and logicians of the 20th century. By showing that the establishment of a set of axioms encompassing all of mathematics would never succeed, he revolutionized the world of mathematics, logic and philosophy.

Raymond Smullyan was born in 1919 in Far Rockaway, New York. He earned his B.S. at the University of Chicago in 1955 and his Ph. D. at Princeton University in 1959. Smullyan has had a remarkably diverse sequence of careers--mathematician, magician, concert pianist, internationally known writer, having authored twenty-six books on a wide variety of subjects, six of which are academic, one of them being "Gödel's Theorems". His famous puzzle books are special, in that they are designed to introduce the general reader to deep results in mathematical logic.

He currently resides in the upper Catskill Mountains, where he constantly entertains audiences with puzzles, jokes, magic, music and readings - some of which can be found on the internet.

Q: You are a trained logician having earned degrees from the University of Chicago and from Princeton University where you studied under, among others, Rudolf Carnap and Alonzo Church, respectively. On top of this, you’ve been a Professor of philosophy for many years at various colleges and universities. How did you go from writing highly technical treatises on logic to writing popular books on mathematical and logical puzzles?

A: I wanted to make puzzle books designed to enable the general reader to understand deep mathematical results in mathematical logic—particularly results related to Gödel’s famous Incompleteness Theorem, which is that in any mathematical system that contains at least elementary arithmetic, there must always be a sentence that though true is not provable in the system. Gödel proved this by showing how to construct a sentence that asserted its own non-provability in the system.

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