This book presents diverse topics in mathematical logic such as proof theory, meta-mathematics, and applications of logic to mathematical structures. The collection spans the first 100 years of modern logic and is dedicated to the memory of Irving Anellis, founder of the journal ‘Modern Logic’, whose academic work was essential in promoting the algebraic tradition of logic, as represented by Charles Sanders Peirce. Anellis’s association with the Russian logic community introduced their school of logic to a wider audience in the USA, Canada and Western Europe. In addition, the collection takes a historical perspective on proof theory and the development of logic and mathematics in Eastern Logic, the Soviet Union and Russia.
The book will be of interest to historians and philosophers in logic and mathematics, and the more specialized papers will also appeal to mathematicians and logicians.
Table of Content
Contributors.- Introduction.- Irving H. Anellis: Preface and Prospectus.- Irving H. Anellis and Francine F. Abeles: The Historical Sources of Tree Graphs and the Tree Method in the Work of Peirce and Gentzen.- Jean Paul Van Bendegem: Logic and Argumentation in Belgium: The Role of Leo Apostel.- Philippe de Rouilhan: Tarski’s Recantation: Reading the Postscript to “Wahrheitsbegriff”.- Jan Woleński: The Paradox of Analyticity and Related Issues.- David De Vidi and Herbert Korté: Naturalizing Natural Deduction.- Alberto Peruzzi: Category Theory and the Search for Universals: A Very Short Guide for Philosophers.- Roman Murawski: On the Way to Modern Logic – The Case of Polish Logic.- Valentin A. Bazhanov: Russian Origins of Non-Classical Logics.- Vladik Kreinovich: Constructive Mathematics in St. Petersburg, Russia: A (Somewhat Subjective) View from Within.- Jonathan P. Seldin: On Normalizing Disjunctive Intermediate Logic.- R.E. Hodel: A Natural Axiom System for Boolean Algebras with Applications.
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