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.

Autorentext

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.

Inhalt

1. Formalizations of AAS2. Semantics of AAS3. Decidability4. Basic equivalence of the four formalizations5. Venn soundness and completeness6. Direct way to Venn models7. Variations on NF(C)8. Direct completion of direct deduction9. Models of NF(C) revisited10. Decidability revisited11. Sorites12. Independence13. Algebraic semantics of AAS, a prelude14. Algebraic interpretation of NF(C)15. Annihilators: Embedding the partial into a total16. Back to algebraic interpretation17. Leibniz and Boole18. Inadequacy: bounds of AASAcknowledgementsAppendix