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E.W. Beth als logicus
van Ulsen, P.
Publication date
2000
Link to publication
Citation for published version (APA):
van Ulsen, P. (2000). E.W. Beth als logicus. ILLC dissertation series 2000-04.
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Abstract t
E . W .. B e t h a s a l o g i c i a n
T h ee s u b j e c t of this dissertation is the logical work of E . W . B e t h . In addition, theree is a s h o r t biography and an introduction to some of B e t h ' s methodological a n dd philosophical ideas.
E v e r tt Willem B e t h (1908-1964) was b o r n in Almelo, a small town near t h ee D u t c h - G e r m a n border. He was the son of H . J . E . B e t h a n d H. de G r o o t . Hiss father studied m a t h e m a t i c s and physics a t the University of A m s t e r d a m , wheree he received his Ph.D. in m a t h e m a t i c s , thereafter working as teacher in m a t h e m a t i c ss a n d physics in secondary schools. E . W . B e t h s t u d i e d m a t h e m a t i c s a n dd physics a t t h e University of Utrecht, followed by a s t u d y in philosophy a n d psychology.. E v e r t Beth's P h . D . (1935) was in philosophy (faculty of a r t s ) , becausee t h e b o r d e r l a n d between philosophy a n d m a t h e m a t i c s did not yet exist ass an a c a d e m i c discipline in the faculty of science a t t h a t t i m e .
Inn 1946 B e t h b e c a m e in A m s t e r d a m t h e first professor of logic a n d founda-tionss of m a t h e m a t i c s in t h e Netherlands. He held this position in A m s t e r d a m untill his d e a t h in 1964. He also held two positions outside Holland: in 1951 ass research assistent of A. Tarski in Berkely (UC) a n d in 1957 as professor of m e t h o d o l o g yy a t J o h n s Hopkins University in Baltimore.
T h ee aim of this s t u d y is to show the diversity of Beth's logical systems a n d w h a tt b i n d s t h e m ( b o t h systematically and historically) together. B e t h ' s m a i n c o n t r i b u t i o n ss t o logic were t h e definition theorem, semantic t a b l e a u x a n d t h e Bethh models. T h e foundation of his work was Gcntzen's e x t e n d e d H a u p t s a t z , t h ee subformula theorem and an extensive use of (Tarskian) model theory.
B e t h ' ss work was a combination of syntactical a n d semantical c o m p o n e n t s . T h ee definition t h e o r e m (1953) is a counterpart of deductive completeness. B e t h ' s prooff is p r i m a r i l y syntactic: he uses t h e midsequent. topology a n d reduced logic.
W i t hh his Definition Theorem a n d his non-normal valuations, B e t h created t h ee tools for t h e next stage in his development, t h e semantic t a b l e a u x (1954-1955).. W i t h t h e semantic t a b l e a u x Beth explored different areas: classical logic,, m o d a l logic a n d intuitionistic logic. T h e semantic: t a b l e a u x give a rapid decisionn p r o c e d u r e , their basis is a bhiairy splitting tree. In c o m b i n a t i o n with his
