Modern Logic 1850-1950, East and West

1. Front Matter

   Pages i-xiii

   PDF

2. Introduction

   • Francine F. Abeles, Mark E. Fuller

   Pages 1-4

3. Preface and Prospectus to a planned “History vs. Philosophy of Logic” Text

   • Irving H. Anellis

   Pages 5-33

4. The Historical Sources of Tree Graphs and the Tree Method in the Work of Peirce and Gentzen

   • Irving H. Anellis, Francine F. Abeles

   Pages 35-97

5. Logic and Argumentation in Belgium: The Role of Leo Apostel

   • Jean Paul Van Bendegem

   Pages 99-118

6. Tarski’s Recantation: Reading the Postscript to “Wahrheitsbegriff”

   • Philippe de Rouilhan

   Pages 119-134

7. Paradox of Analyticity and Related Issues

   • Jan Woleński

   Pages 135-138

8. Naturalizing Natural Deduction

   • David DeVidi, Herbert Korté

   Pages 139-158

9. Category Theory and the Search for Universals: A Very Short Guide for Philosophers

   • Alberto Peruzzi

   Pages 159-182

10. On the Way to Modern Logic: The Case of Polish Logic

    • Roman Murawski

    Pages 183-195

11. Russian Origins of Non-Classical Logics

    • Valentin A. Bazhanov

    Pages 197-203

12. Constructive Mathematics in St. Petersburg, Russia: A (Somewhat Subjective) View from Within

    • Vladik Kreinovich

    Pages 205-236

13. On Normalizing Disjunctive Intermediate Logics

    • Jonathan P. Seldin

    Pages 237-248

14. A Natural Axiom System for Boolean Algebras with Applications

    • R. E. Hodel

    Pages 249-258

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.

• Bertrand Russell
• Charles Sanders Peirce
• algebraic logic
• history of logic
• history of proof theory
• mathematical logic

“Modern Logic, 1850–1950, East and West is a memorial volume for the respected historian of logic Irving H. Anellis … . an excellent job identifying the distinctive features of this work in accessible terms and is able to reflect on its historical importance and broader social context from firsthand experience. … an excellent starting point for any historical study of this avenue of mathematical research. Overall, this volume is a fitting tribute to Anellis and the journal he founded.” (Andrew Aberdein, Isis, Vol. 108 (3), September, 2017)

• DepartmentsofMathematicsandComputerSci, Kean University, Union, USA

  Francine F. Abeles

• University of Wisconsin, Janesville, USA

  Mark E. Fuller

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