Raymond Merrill Smullyan
(born May 25, 1919) is an American mathematician, concert
pianist, logician, Taoist philosopher, and
magician.
Born in
Far
Rockaway, New
York, his first career (like Persi Diaconis a generation later) was stage
magic. He then earned a BSc from the University of
Chicago in 1955 and his Ph.D. from Princeton
University in 1959. He is one of many outstanding
logicians to have studied under
Alonzo
Church.
Life
While a 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 philosophically. The
culmination of Smullyan's lifelong reflection on the classic
limitative theorems of mathematical logic is his quite
readable:
- Smullyan, R M (2001) "Gödel's Incompleteness Theorems" in
Goble, Lou, ed., The Blackwell Guide to Philosophical
Logic. Blackwell (ISBN 0-631-20693-0).
Smullyan is the author of many books on
recreational mathematics,
recreational logic, etc. Most notably, one is titled
.
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 doesn't. 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. A sane vampire knows 2
+ 2 is 4, but will lie and say it isn't. 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.
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.
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 has recently
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.
Philosophy
Smullyan has written several books about
Taoist
philosophy, which he believes neatly solves most or all
traditional
philosophical
problems as well as integrating
mathematics,
logic, and
philosophy into a cohesive whole.
Selected publications
Logic Puzzles
- (1978) - knights, knaves, and other logic
puzzles
- (1979) - introducing retrograde analysis in the game of
chess.
- (1981) - second book on retrograde analysis chess
problems.
- (1982) - ladies, tigers, and more logic
puzzles
- (1982)
- (1985) - puzzles based on combinatory
logic
- (1987) - puzzles based on undecidability in formal
systems
- (1992)
- (1997)
- (2007) , Polimetrica
- (2009) , A K
Peters
Philosophy/Memoir
Academic
- (1961)
- (1968)
- (1992)
- (1993)
- (1994)
- (1996)
Quotations from people who respect Smullyan
- I now introduce Professor Smullyan, who will prove to you
that either he doesn't exist or you don't exist, but you won't know
which. --Melvin Fitting
See also
Bibliography
External links