Evert Willem Beth

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 PhD. Evert Beth studied the same subjects at Utrecht University, but then also studied philosophy and psychology. His 1935 PhD was in philosophy.

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.

In 1953 he became member of the Royal Netherlands Academy of Arts and Sciences.{{sfn|Digitaal Wetenschapshistorisch Centrum}}

He died in Amsterdam.

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The Beth definability theorem states that for first-order logic a property (or function or constant) is implicitly definable if and only if it is explicitly definable. Further explanation is provided under Beth definability.

Beth's most famous contribution to formal logic is semantic tableaux, which are decision procedures for propositional logic and first-order logic. It is a semantic method—like Wittgenstein's truth tables or J. Alan Robinson's resolution—as opposed to the proof of theorems in a formal system, such as the axiomatic systems employed by Frege, Russell and Whitehead, and Hilbert, or even Gentzen's natural deduction. Semantic tableaux are an effective decision procedure for propositional logic, whereas they are only semi-effective for first-order logic, since first-order logic is undecidable, as showed by Church's theorem. This method is considered by many to be intuitively simple, particularly for students who are not acquainted with the study of logic, and it is faster than the truth-table method (which requires a table with 2ⁿ rows for a sentence with n propositional letters). For these reasons, Wilfrid 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.

One starts out with the intention of proving that a certain set $\backslash Gamma\; \backslash ,$ of formulae entail another formula $\backslash varphi\backslash ,$, 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 $\backslash Gamma\; \backslash ,$ and of $\backslash neg\; \backslash varphi$ (the negation of $\backslash varphi\backslash ,$), 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 $\backslash Gamma\; \backslash cup\; \backslash \{\; \backslash neg\; \backslash varphi\; \backslash \}$ is inconsistent, and thus that the formulae of $\backslash Gamma\backslash ,$ together entail $\backslash varphi\; \backslash ,$.

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These are a class of relational models for non-classical logic (cf. Kripke semantics).

• {{cite book

| last = Beth

| first = Evert W.

| title = The Foundations of Mathematics: A Study in the Philosophy of Science

| publisher = North-Holland

| year = 1959

| location = Amsterdam

| pages = XXVI + 722

}}

• {{cite book

| last1 = Beth

| first1 = Evert W.

| author1-mask = 1

| last2 = Piaget

| first2 = Jean

| title = Épistémologie mathématique et psychologie

| publisher = Presses Universitaires de France (P.U.F.)

| year = 1961

| location = Paris

| pages = 352

}}

• {{cite book

| last = Beth

| first = Evert W.

| author-mask = 1

| title = Formal Methods: An Introduction to Symbolic Logic and to the Study of Effective Operations in Arithmetic and Logic

| publisher = D. Reidel Publishing Company

| year = 1962

| location = Dordrecht-Holland

}}

• {{cite book

| last = Beth

| first = Evert W.

| author-mask = 1

| title = Moderne logica

| language = nl

| publisher = Van Gorcum & Comp. N.V.

| year = 1969

| location = Assen, Nederland

| quote = Uitgegeven met steun van het {{ill|Prins Bernhard Fonds|nl|het Cultuurfonds}}

}}

• {{cite book

| last = Beth

| first = Evert W.

| author-mask = 1

| title = Aspects of Modern Logic

| publisher = D. Reidel Publishing Company

| year = 1971

| location = Dordrecht-Holland

}}

• Gerrit Mannoury
• Arend Heyting

{{reflist}}

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• {{cite journal

| last = Francella

| first = Miriam

| title = Evert Willem Beth's Scientific Philosophy

| journal = Grazer Philosophische Studien

| year = 1999

| volume = 57

| pages = 221–236

| doi = 10.5840/gps19995712

}}

• {{cite journal

| last = Heyting

| first = Arend

| authorlink = Arend Heyting

| title = In memoriam: Evert Willem Beth (1909–1964)

| journal = Notre Dame Journal of Formal Logic

| year = 1966

| volume = 7

| issue = 4

| pages = 289–295

| doi = 10.1305/ndjfl/1093958744

| doi-access = free

}}

• {{cite encyclopedia

| last = Mooij

| first = J. J. A.

| title = Beth, Evert Willem (1908–1964)

| encyclopedia = Biographical Dictionary of the Netherlands: 1880–2000

| url = http://www.historici.nl/Onderzoek/Projecten/BWN/lemmata/bwn2/beth

| access-date = 2013-04-22

}}

{{Refend}}

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• {{cite web

| author = Digitaal Wetenschapshistorisch Centrum

| url = http://www.dwc.knaw.nl/biografie/pmknaw/?pagetype=authorDetail&aId=PE00002175

| title = Evert Willem Beth (1908 - 1964)

| publisher = Royal Netherlands Academy of Arts and Sciences

| accessdate = 2025-03-18

}}

• {{cite web

| url = http://institucional.us.es/folliweb/index.php?option=com_content&view=article&id=81&Itemid=69

| archive-url = https://archive.today/20130701104936/http://institucional.us.es/folliweb/index.php?option=com_content&view=article&id=81&Itemid=69

| archive-date = 2013-07-01

| url-status = dead

| title = Beth Prize 2013

| access-date = 2025-03-18

}}

• {{cite web

| url = https://www.knaw.nl/en/funds-and-prizes/evert-willem-beth-foundation

| archive-url = https://archive.today/20160623063809/http://www.knaw.nl/en/awards/subsidies/evert-willem-beth-stichting/evert-willem-beth-foundation

| archive-date = 2016-06-23

| url-status = live

| title = Evert Willem Beth Foundation

| publisher = Royal Netherlands Academy of Arts and Sciences (KNAW)

| access-date = 2025-03-18

}}

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{{DEFAULTSORT:Beth, Evert Willem}}

Category:1908 births

Category:1964 deaths

Category:Mathematical logicians

Category:Dutch logicians

Category:Formal methods people

Category:Academic staff of the University of Amsterdam

Category:Utrecht University alumni

Category:People from Almelo

Category:20th-century Dutch mathematicians

Category:Members of the Royal Netherlands Academy of Arts and Sciences

Category:20th-century Dutch philosophers