Raymond Smullyan

Raymond Merrill Smullyan (/ˈsmʌliən/; May 25, 1919 – February 6, 2017)[1][2][3] was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher.

Raymond Smullyan
Raymond M. Smullyan in 2008.
Born
Raymond Merrill Smullyan

(1919-05-25)May 25, 1919
Far Rockaway, New York, U.S.
DiedFebruary 6, 2017(2017-02-06) (aged 97)
Hudson, New York, U.S.
NationalityAmerican
Alma materUniversity of Chicago
Princeton University (Ph.D.)
Spouse(s)Blanche
Scientific career
FieldsLogic
InstitutionsYeshiva University, City University of New York, Indiana University
ThesisTheory of Formal Systems (1959)
Doctoral advisorAlonzo Church

Born in Far Rockaway, New York, his first career was stage magic. He earned a BSc from the University of Chicago in 1955 and his Ph.D. from Princeton University in 1959. He is one of many logicians to have studied with Alonzo Church.[1]

Life

Born in Far Rockaway, New York to Eastern European Jewish parents (originally spelling their name as Schmulian), Smullyan showed musical talent from a young age, winning a gold medal in a piano competition when he was aged 12.[1] The following year, his family moved to Manhattan and he attended Theodore Roosevelt High School in The Bronx, which offered classes suited to his musical talents. He left to study on his own, as the school did not offer similar courses in mathematics.[1] He studied mathematics and music at several colleges (including Pacific University and Reed College) before receiving an undergraduate degree from the University of Chicago in 1955 and a Ph.D. in mathematics from Princeton University in 1959.[1] He completed his doctoral dissertation, titled "Theory of formal systems", under the supervision of Alonzo Church.[4]

While a Ph.D. student, Smullyan published a paper in the 1957 Journal of Symbolic Logic[5] showing that Gödelian incompleteness held for formal systems considerably more elementary than that of Kurt Gödel's 1931 landmark paper. The contemporary understanding of Gödel's theorem dates from this 1931 paper. Smullyan later made a compelling case that much of the fascination with Gödel's theorem should be directed at Tarski's theorem, which is much easier to prove and equally disturbing philosophically.[6]

Smullyan wrote many books about recreational mathematics and recreational logic.[7] Most notably, one is titled What Is the Name of This Book? ISBN 0139550623. His A Beginner's Further Guide to Mathematical Logic ISBN 978-981-4730-99-0, published in 2017, was his final book.

He was a professor of mathematics and philosophy at Lehman College, the CUNY Graduate Center and Indiana University. He was also an amateur astronomer, using a six-inch reflecting telescope for which he ground the mirror.[1] Martin Gardner was a close friend.

Logic problems

Many of his logic problems are extensions of classic puzzles. Knights and Knaves involves knights (who always tell the truth) and knaves (who always lie). This is based on a story of two doors and two guards, one who lies and one who tells the truth. One door leads to heaven and one to hell, and the puzzle is to find out which door leads to heaven by asking one of the guards a question. One way to do this is to ask, "Which door would the other guard say leads to hell?". Unfortunately, this fails, as the liar can answer, "He would say the door to paradise leads to hell," and the truth-teller would answer, "He would say the door to paradise leads to hell." You must point at one of the doors as well as simply stating a question. For example, as philosopher Richard Turnbull has explained, you could point at either door and ask, "Will the other guard say this is the door to paradise?" The truth-teller will say "No, " if it is in fact the door to paradise, as will the liar. So you pick that door. The truth-teller will answer "Yes," if it is the door to Hell, as will the liar, so you pick the other door. Note also that we are not told anything about the goals of either guard: for all we know, the liar may want to help us and the truth-teller not help us, or both are indifferent, so there's no reason to think either one will phrase answers such as to provide us with the most optimally available kind of comprehension. This is behind the crucial role of actually pointing at a door directly while asking the question. This idea was famously used in the 1986 film Labyrinth.

In more complex puzzles, he introduces characters who may lie or tell the truth (referred to as "normals"), and furthermore instead of answering "yes" or "no", use words which mean "yes" or "no", but the reader does not know which word means which. The puzzle known as "the hardest logic puzzle ever" is based on these characters and themes. In his Transylvania puzzles, half of the inhabitants are insane, and believe only false things, whereas the other half are sane and believe only true things. In addition, humans always tell the truth, and vampires always lie. For example, an insane vampire will believe a false thing (2 + 2 is not 4) but will then lie about it, and say that it is false. A sane vampire knows 2 + 2 is 4, but will lie and say it is not. And mutatis mutandis for humans. Thus everything said by a sane human or an insane vampire is true, while everything said by an insane human or a sane vampire is false.

His book Forever Undecided popularizes Gödel's incompleteness theorems by phrasing them in terms of reasoners and their beliefs, rather than formal systems and what can be proved in them. For example, if a native of a knight/knave island says to a sufficiently self-aware reasoner, "You will never believe that I am a knight", the reasoner cannot believe either that the native is a knight or that he is a knave without becoming inconsistent (i.e., holding two contradictory beliefs). The equivalent theorem is that for any formal system S, there exists a mathematical statement that can be interpreted as "This statement is not provable in formal system S". If the system S is consistent, neither the statement nor its opposite will be provable in it. See also Doxastic logic.

Inspector Craig is a frequent character in Smullyan's "puzzle-novellas." He is generally called into a scene of a crime that has a solution that is mathematical in nature. Then, through a series of increasingly harder challenges, he (and the reader) begin to understand the principles in question. Finally the novella culminates in Inspector Craig (and the reader) solving the crime, utilizing the mathematical and logical principles learned. Inspector Craig generally does not learn the formal theory in question, and Smullyan usually reserves a few chapters after the Inspector Craig adventure to illuminate the analogy for the reader. Inspector Craig gets his name from William Craig.

His book To Mock a Mockingbird (1985) is a recreational introduction to the subject of combinatory logic.

Apart from writing about and teaching logic, Smullyan released a recording of his favorite baroque keyboard and classical piano pieces by composers such as Bach, Scarlatti, and Schubert. Some recordings are available on the Piano Society website, along with the video "Rambles, Reflections, Music and Readings". He has also written an autobiography titled Some Interesting Memories: A Paradoxical Life (ISBN 1-888710-10-1).

In 2001, documentary filmmaker Tao Ruspoli made a film about Smullyan called This Film Needs No Title: A Portrait of Raymond Smullyan.

Philosophy

Smullyan wrote several books about Taoist philosophy, a philosophy he believed neatly solved most or all traditional philosophical problems as well as integrating mathematics, logic, and philosophy into a cohesive whole. One of Smullyan's discussions of Taoist philosophy centers on the question of free will in an imagined conversation between a mortal human and God.[8]

Selected publications

Logic puzzles
  • (1978) What Is the Name of This Book? The Riddle of Dracula and Other Logical Puzzles ISBN 0139550623 – knights, knaves, and other logic puzzles
  • (1979) The Chess Mysteries of Sherlock Holmes ISBN 0394737571 – introducing retrograde analysis in the game of chess.
  • (1981) The Chess Mysteries of the Arabian Knights ISBN 0192861247 – second book on retrograde analysis chess problems.
  • (1982) The Lady or the Tiger? ISBN 0812921178 – ladies, tigers, and more logic puzzles
  • (1982) Alice in Puzzle-Land ISBN 0688007481
  • (1985) To Mock a Mockingbird ISBN 0192801422 – puzzles based on combinatory logic
  • (1987) Forever Undecided ISBN 0192801414 – puzzles based on undecidability in formal systems
  • (1992) Satan, Cantor and Infinity ISBN 0679406883
  • (1997) The Riddle of Scheherazade ISBN 0156006065
  • (2007) The Magic Garden of George B. And Other Logic Puzzles ISBN 9788876990663, Polimetrica (Monza/Italy)
  • (2009) Logical Labyrinths ISBN 9781568814438, A K Peters
  • (2010) King Arthur in Search of his Dog ISBN 0486474356
  • (2013) The Godelian Puzzle Book: Puzzles, Paradoxes and Proofs ISBN 0486497054
  • (2015) The Magic Garden of George B and Other Logic Puzzles ISBN 978-981-4675-05-5

Philosophy/memoir

Academic
  • (1961) Theory of Formal Systems ISBN 069108047X
  • (1968) First-Order Logic ISBN 0486683702
  • (1992) Gödel's Incompleteness Theorems ISBN 0195046722
  • (1993) Recursion Theory for Metamathematics ISBN 019508232X
  • (1994) Diagonalization and Self-Reference ISBN 0198534507
  • (1996) Set Theory and the Continuum Problem ISBN 0198523955
  • (2014) A Beginner's Guide to Mathematical Logic ISBN 0486492370
  • (2016) A Beginner's Further Guide to Mathematical Logic ISBN 978-981-4730-99-0

Bibliography

See also

References
  1. J J O'Connor and E F Robertson (April 2002). "Smullyan biography". School of Mathematical and Computational Sciences, University of St Andrews. Retrieved 5 October 2010.
  2. Osborne, Hannah (2017-02-10). "Mathematician and puzzle-maker Raymond Smullyan dead at 97". International Business Times UK. Retrieved 2017-02-10.
  3. Sandomir, Richard (2017-02-11). "Raymond Smullyan, Puzzle-Creating Logician, Dies at 97". New York Times. Retrieved 2017-02-13.
  4. Smullyan, Raymond Merrill (1959). Theory of formal systems.
  5. "Languages in which self reference is possible". The Journal of Symbolic Logic, vol. 22 no. 1 (1957), pp. 55–67.
  6. Smullyan, R M (2001) "Gödel's Incompleteness Theorems" in Goble, Lou, ed., The Blackwell Guide to Philosophical Logic. Blackwell (ISBN 0-631-20693-0).
  7. A New Kind of Science
  8. Policar, David. "Is God a Taoist?". www.mit.edu. Retrieved 8 January 2017.
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