Aristotelian Assertoric Syllogistic : Incorporating the Aristotelian Assertoric Syllogistic in the Contemporary Symbolic Logic (Springerbriefs in Philosophy)

Amer, Mohamed A.

Springer Nature Switzerland AG（2022/03発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 98 p.
• 言語 ENG
• 商品コード 9783030873400

Full Description

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.

Contents

Acknowledgements.- ​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.- Appendix.