''To Mock a Mockingbird and Other Logic Puzzles: Including an Amazing Adventure in Combinatory Logic'' (1985, {{isbn, 0-19-280142-2) is a book by the

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History O ...

and

logician Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...

Raymond Smullyan Raymond Merrill Smullyan (; May 25, 1919 – February 6, 2017) was an American mathematician, magician, concert pianist, logician, Taoist, and philosopher. Born in Far Rockaway, New York, his first career was stage magic. He earned a BSc from t ...

. It contains many nontrivial recreational puzzles of the sort for which Smullyan is well known. It is also a gentle and humorous introduction to

combinatory logic Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of comput ...

and the associated

metamathematics Metamathematics is the study of mathematics itself using mathematical methods. This study produces metatheories, which are mathematical theories about other mathematical theories. Emphasis on metamathematics (and perhaps the creation of the te ...

, built on an elaborate

ornithological Ornithology is a branch of zoology that concerns the "methodological study and consequent knowledge of birds with all that relates to them." Several aspects of ornithology differ from related disciplines, due partly to the high visibility and th ...

metaphor A metaphor is a figure of speech that, for rhetorical effect, directly refers to one thing by mentioning another. It may provide (or obscure) clarity or identify hidden similarities between two different ideas. Metaphors are often compared wit ...

. Combinatory logic, functionally equivalent to the

lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation th ...

, is a branch of

symbolic logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal sy ...

having the expressive power of

set theory Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concer ...

, and with deep connections to questions of

computability Computability is the ability to solve a problem in an effective manner. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is close ...

and provability. Smullyan's exposition takes the form of an imaginary account of two men going into a forest and discussing the unusual "birds" (combinators) they find there (bird watching was a hobby of one of the founders of combinatory logic,

Haskell Curry Haskell Brooks Curry (; September 12, 1900 – September 1, 1982) was an American mathematician and logician. Curry is best known for his work in combinatory logic. While the initial concept of combinatory logic was based on a single paper by ...

, and another founder Moses Schönfinkel's name means beautiful bird). Each species of bird in Smullyan's forest stands for a particular kind of

combinator Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of compu ...

appearing in the conventional treatment of combinatory logic. Each bird has a distinctive call, which it emits when it hears the call of another bird. Hence an initial call by certain "birds" gives rise to a cascading sequence of calls by a succession of birds. Deep inside the forest dwells the Mockingbird, which imitates other birds hearing themselves. The resulting cascade of calls and responses analogizes to abstract models of computing. With this analogy in hand, one can explore advanced topics in the mathematical theory of computability, such as Church–Turing computability and Gödel's theorem. While the book starts off with simple riddles, it eventually shifts to a tale of Inspector Craig of Scotland Yard, who appears in Smullyan's other books; traveling from forest to forest, learning from different professors about all the different kinds of birds. He starts off in a certain enchanted forest, then goes to an unnamed forest, then to Curry's Forest (named after Haskell Curry), then to Russell's Forest, then to The Forest Without a Name, then to Gödel's Forest and finally to The Master Forest where he also answers The Grand Question.

External links

* Keenan, David C. (2001)
To Dissect a Mockingbird.
* Rathman, Chris,

1985 non-fiction books Puzzle books Combinatory logic Alfred A. Knopf books

See also

External links