Raymond Merrill Smullyan (/ˈsmʌliən/; May 25, 1919 – February 6,
2017) was an American mathematician, concert pianist,
logician, Taoist, and philosopher.
Born in Far Rockaway, New York, his first career was stage magic. He
then earned a
BSc from the
University of Chicago
University of Chicago in 1955 and his Ph.D.
Princeton University in 1959. He is one of many logicians to have
studied with Alonzo Church.
4 Selected publications
6 See also
8 External links
Born in Far Rockaway, New York to Jewish parents (originally
Schmulian), Raymond showed musical talent from a young age, winning a
gold medal in a piano competition when he was aged 12. The
following year, his family moved to
Manhattan and he attended Theodore
Roosevelt High School in
The Bronx as this school offered courses
suited to his musical talents, but he left to study on his own as the
school did not offer similar courses in mathematics. He studied
mathematics and music at several colleges (including Pacific
University and Reed College) before receiving an undergraduate degree
University of Chicago
University of Chicago and a
Ph.D. in mathematics from
Princeton University in 1959.
Ph.D. student, Smullyan published a paper in the 1957 Journal
of Symbolic Logic showing that Gödelian incompleteness held for
formal systems considerably more elementary than that of Gödel's 1931
landmark paper. The contemporary understanding of Gödel's theorem
dates from this 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
Smullyan is the author of many books on recreational mathematics and
recreational logic. Most notably, one is titled What Is the Name of
This Book? ISBN 0139550623. A Beginner's Further Guide to
Logic ISBN 978-981-4730-99-0 was his final book.
He was a professor of 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
Martin Gardner was a close friend.
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?". 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.
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 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.
This section needs expansion. You can help by adding to it. (December
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.
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(1978) What Is the Name of This Book? The Riddle of Dracula and Other
Logical Puzzles ISBN 0139550623 – knights, knaves, and other
Chess Mysteries of Sherlock Holmes ISBN 0394737571 –
introducing retrograde analysis in the game of chess.
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
To Mock a Mockingbird ISBN 0192801422 – puzzles based on
(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
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
(2015) The Magic Garden of George B and Other
(1977) The Tao is Silent ISBN 0060674695
(1980) This Book Needs No Title ISBN 0671628313
(1983) 5000 B.C. and other philosophical fantasies
(2002) Some Interesting Memories: A Paradoxical Life
(2003) Who Knows?: A Study of Religious Consciousness
(2009) Rambles Through My Library ISBN 9780963923165, Praxis
(2015) Reflections: The Magic, Music and
Mathematics of Raymond
Smullyan ISBN 978-981-4644-58-7
(2016) A Mixed Bag: Jokes, Riddles, Puzzles and Memorabilia
(1961) Theory of Formal Systems ISBN 069108047X
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
Is God a Taoist? by Raymond Smullyan, 1977.
Planet Without Laughter by Raymond Smullyan, 1980.
An Epistemological Nightmare by Raymond Smullyan, 1982.
Alice's Adventures in Wonderland
The Lady, or the Tiger
^ a b c d e f 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.
^ Osborne, Hannah (2017-02-10). "Mathematician and puzzle-maker
Raymond Smullyan dead at 97". International Business Times UK.
^ Sandomir, Richard (2017-02-11). "Raymond Smullyan, Puzzle-Creating
Logician, Dies at 97". New York Times. Retrieved 2017-02-13.
^ "Languages in which self reference is possible". The Journal of
Symbolic Logic, vol. 22 no. 1 (1957), pp. 55–67.
^ Smullyan, R M (2001) "Gödel's Incompleteness Theorems" in Goble,
Lou, ed., The Blackwell Guide to Philosophical Logic. Blackwell
^ Policar, David. "Is God a Taoist?". www.mit.edu. Retrieved 8 January
Wikiquote has quotations related to: Raymond Smullyan
Media related to Audio files of classical music by Raymond Smullyan
at Wikimedia Commons
Raymond Smullyan's website at Indiana University.
Raymond Smullyan at the MacTutor History of
Raymond Smullyan at the
Mathematics Genealogy Project.
Raymond Smullyan at Piano Society
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