Kurt Gödel

Kurt Friedrich Gödel (/ˈkɜːrt ˈɡɜːrdəl/;German: [ˈkʊʁt ˈɡøːdəl]; April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher. Considered with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel made an immense impact upon scientific and philosophical thinking in the 20th century, a time when others such as Bertrand Russell,A. N. Whitehead, and David Hilbert were pioneering the use of logic and set theory to understand the foundations of mathematics.

Gödel published his two incompleteness theorems in 1931 when he was 25 years old, one year after finishing his doctorate at the University of Vienna. The first incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers (for example Peano arithmetic), there are true propositions about the naturals that cannot be proved from the axioms. To prove this theorem, Gödel developed a technique now known as Gödel numbering, which codes formal expressions as natural numbers.

Godel (disambiguation)

Kurt Gödel (28 April 1906 – 14 January 1978) was an Austrian (later American) logician, mathematician and philosopher.

Godel or similar may also refer to:

Other people with the surname Godel include:

See also

Gödel (programming language)

Gödel is a declarative, general-purpose programming language that adheres to the logic programming paradigm. It is a strongly typed language, the type system being based on many-sorted logic with parametric polymorphism. It is named after logician Kurt Gödel.

Features

Gödel has a module system, and it supports arbitrary precision integers, arbitrary precision rationals, and also floating-point numbers. It can solve constraints over finite domains of integers and also linear rational constraints. It supports processing of finite sets. It also has a flexible computation rule and a pruning operator which generalises the commit of the concurrent logic programming languages.

Gödel's meta-logical facilities provide support for meta-programs that do analysis, transformation, compilation, verification, and debugging, among other tasks.

Sample code

The following Gödel module is a specification of the greatest common divisor (GCD) of two numbers. It is intended to demonstrate the declarative nature of Gödel, not to be particularly efficient. The CommonDivisor predicate says that if i and j are not zero, then d is a common divisor of i and j if it lies between 1 and the smaller of i and j and divides both i and j exactly. The Gcd predicate says that d is a greatest common divisor of i and j if it is a common divisor of i and j, and there is no e that is also a common divisor of i and j and is greater than d.