Aristotelian Assertoric Syllogistic: Incorporating the Aristotelian Assertoric Syllogistic in the Contemporary Symbolic Logic

ISBN-13: 9783030873400 / Angielski / Miękka / 2022 / 116 str.

Mohamed A. Amer

Spis treści

1. Formalizations of AAS

2. Semantics of AAS

3. Decidability

4. Basic equivalence of the four formalizations

5. Venn soundness and completeness

6. Direct way to Venn models

7. Variations on NF(C)

8. Direct completion of direct deduction

9. Models of NF(C) revisited

10. Decidability revisited

11. Sorites

12. Independence

13. Algebraic semantics of AAS, a prelude

14. Algebraic interpretation of NF(C)

15. Annihilators: Embedding the partial into a total

16. Back to algebraic interpretation

17. Leibniz and Boole

18. Inadequacy: bounds of AAS

Acknowledgements

Appendix

O autorze

Mohamed Amer is Professor of Mathematics at the Faculty of Science, Cairo University in Egypt.

He obtained his B.Sc. in Mathematics in 1962, at Cairo University in Egypt and his Ph. D. in Mathematics in 1969 at the University of California in Berkeley, USA.

Mohamed Amer is a member of The Egyptian Mathematical Society, The American Mathematical Society, and The Association for Symbolic Logic.

Blurb

This book is a treatise on Aristotelian assertoric syllogistic, which is currently of growing interest. Some centuries ago, it attracted the attention of the founders of modern logic, who approached it in several (semantical and syntactical) ways. Further approaches were introduced later on. In this book these approaches (with few exceptions) are discussed, developed and interrelated. Among other things, different facets of soundness, completeness, decidability, and independence for Aristotelian assertoric syllogistic are investigated. Specifically arithmetization (Leibniz), algebraization (Leibniz and Boole), and Venn models (Euler and Venn) are examined. The book is aimed at scholars in the fields of logic and history of logic.