Evert Willem Beth (July 7, 1908 – April 12, 1964) was a Dutch philosopher and logician, whose work principally concerned the foundations of mathematics. July 7 is the 188th day of the year (189th in leap years) in the Gregorian Calendar, with 177 days remaining. ... 1908 (MCMVIII) was a leap year starting on Wednesday (link will take you to calendar). ... April 12 is the 102nd day of the year in the Gregorian calendar (103rd in leap years). ... For the Nintendo 64 emulator, see 1964 (Emulator). ... A philosopher is a person who thinks deeply regarding people, society, the world, and/or the universe. ... A logician is a philosopher, mathematician, or other whose topic of scholarly study is logic. ... Foundations of mathematics is a term sometimes used for certain fields of mathematics itself, namely for mathematical logic, axiomatic set theory, proof theory, model theory, and recursion theory. ...

Biography

Beth was born in Almelo, a small town in the eastern Netherlands. His father had studied mathematics and physics at the University of Amsterdam, where he had been awarded a Ph.D. Evert Beth studied the same subjects at Utrecht University, but then also studied philosophy and psychology. His 1935 Ph.D. was in philosophy. Almelo is a municipality and a city in the eastern Netherlands. ... Euclid, detail from The School of Athens by Raphael. ... Physics is the science of Nature. ... From Athenaeum Illustre to University In January 1632 two internationally acclaimed scientists, Caspar Barlaeus and Gerardus Vossius, held their inaugural speech in the Athenaeum Illustre - the illustrious school - which had its seat in the 14th-century Agnietenkapel. ... Doctor of Philosophy, or Ph. ... Utrecht University (Universiteit Utrecht in Dutch) is a university in Utrecht, The Netherlands. ... Philosopher in Meditation (detail), by Rembrandt Philosophy is a field of study that includes diverse subfields such as aesthetics, epistemology, ethics, logic, and metaphysics, in which people ask questions such as whether God exists, whether knowledge is possible, and what makes actions right or wrong. ... Psychology (Gk: psyche, soul or mind + logos, speech) is an academic and applied field involving the study of the mind, brain, and behavior, both human and nonhuman. ... Doctor of Philosophy (Ph. ...

In 1946, he became professor of logic and the foundations of mathematics in Amsterdam. Apart from two brief interruptions – a stint in 1951 as a research assistant to Alfred Tarski, and in 1957 as a visiting professor at Johns Hopkins University – he held the post in Amsterdam continuously until his death in 1964. His was the first academic post in his country in logic and the foundations of mathematics, and during this time he contributed actively to international cooperation in establishing logic as an academic discipline. Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... Amsterdam Location Flag Country Netherlands Province North Holland Population 742,951(1 January 2005) Coordinates Website www. ... Alfred Tarski (January 14, 1901, Warsaw Poland – October 26, 1983, Berkeley California) was a logician and mathematician of considerable philosophical importance. ... The Johns Hopkins University, founded in 1876, is a private institution of higher learning located in Baltimore, Maryland, United States. ...

Contributions to logic

Definition Theorem

The Definition Theorem states that a predicate (or function or constant) is implicitly definable if and only if it is explicitly definable.

Semantic Tableaux

A proof method for formal systems; cf. Gentzen's natural deduction and sequent calculus, or even Alan Robinson's resolution and Hilbert's axiomatic systems). It is considered by many to be intuitively simple, particularly for students not acquainted with the study of logic (Wilfred Hodges for example presents semantic tableaux in his introductory textbook, Logic, and Melvin Fitting does the same in his presentation of first-order logic for computer scientists, First-order logic and automated theorem proving). Gerhard Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician. ... In mathematical logic, natural deduction is an approach to proof theory that attempts to provide a formal model of logical reasoning as it naturally occurs. ... In proof theory and mathematical logic, the sequent calculus is a widely known deduction system for first-order logic (and propositional logic as a special case of it). ... David Robinson was PC MPP for Scarborough-Ellesmere from 1981-1987. ... In mathematical logic and automated theorem proving, a branch of the traditional artificial intelligence (see GOFAI), resolution is a theorem-proving technique for sentences in propositional logic and first-order logic. ... David Hilbert David Hilbert (January 23, 1862, Wehlau, East Prussia–February 14, 1943, Göttingen, Germany) was a German mathematician, recognized as one of the most influential mathematicians of the 19th and early 20th centuries. ... Wilfrid Hodges (born 1941) is a British mathematician, known for his work in model theory. ... Computer science is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...

One starts out with the intention of proving that a certain set Γ of formulae imply another formula φ, given a set of rules determined by the semantics of the formulae's connectives (and quantifiers, in First-order logic). The method is to assume the concurrent truth of every member of Γ and of (the negation of φ), and then to apply the rules to branch this list into a tree-like structure of (simpler) formulae until every possible branch contains a contradiction. At this point it will have been established that is inconsistent, and thus that the formulae of Γ together imply φ. In formal logic, logical connectives, also known as logical connectors and sometimes logical constants, serve to connect statements into more complicated compound statements. ... It has been suggested that Predicate calculus be merged into this article or section. ...

Beth Models

A class of models for non-classical logic (cf. Kripke semantics). Classical logic identifies a class of formal logics that have been most intensively studied and most widely used. ... Kripke semantics (also known as possible world semantics, relational semantics, or frame semantics) is a formal semantics for modal logic systems, created in late 1950s and early 1960s by Saul Kripke. ...

Books

• Evert W. Beth, Formal Methods: An introduction to symbolic logic and to the study of effective operations in arithmetic and logic. D. Reidel Publishing Company / Dordecht-Holland, 1970. ISBN 9027700699.