
 Logic and computability (from logic, philosophy of)  Encyclopædia Britannica 
  These findings of Gödel and Montague are closely related to the general study of computability, which is usually known as recursive function theory (see mathematics, foundations of: The crisis in foundations following 1900: Logicism, formalism, and the metamathematical method) and which is one of the most important branches of contemporary logic. 
  fundamental principles of logic: (1) law of contradiction—something cannot exist and not exist at the same time; (2) law of excluded middle—something either exists or it does not, no middle condition is possible; (3) law of identity—something is always identical with itself; 20thcentury philosophers have criticized, even rejected, the laws, which derive from ancient... 
  Discusses the Aristotelean logic, predicate calculus, geometry of Euclid, formal theories of mathematics, and Plato and Aristotle’s philosophy of mathematics. 
 www.britannica.com /eb/article36296 (895 words) 
