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.
|
|
|
1 | (12) |
|
1.1 Monadic First Order Formalization of AAS |
|
|
1 | (2) |
|
1.2 Sentential Formalization of AAS |
|
|
3 | (1) |
|
1.3 Dyadic First Order Formalization of AAS |
|
|
4 | (1) |
|
1.4 Natural Deduction Formalization of AAS |
|
|
5 | (3) |
|
|
|
8 | (1) |
|
|
|
9 | (1) |
|
|
|
10 | (1) |
|
|
|
10 | (3) |
|
|
|
13 | (14) |
|
|
|
13 | (1) |
|
|
|
13 | (1) |
|
|
|
14 | (1) |
|
|
|
14 | (3) |
|
2.5 Order Models and Venn Models |
|
|
17 | (1) |
|
2.6 Models and Interpretations |
|
|
18 | (1) |
|
|
|
18 | (1) |
|
|
|
18 | (1) |
|
|
|
19 | (1) |
|
|
|
19 | (6) |
|
2.7.1 Assigning Leibniz Models |
|
|
20 | (1) |
|
2.7.2 Leibniz Soundness and Completeness |
|
|
21 | (1) |
|
|
|
22 | (1) |
|
2.7.4 Logico-Philosophical Discussion of Leibniz Models |
|
|
23 | (2) |
|
|
|
25 | (2) |
|
|
|
27 | (2) |
|
|
|
28 | (1) |
|
4 Basic Equivalence of the Four Formalizations |
|
|
29 | (2) |
|
5 Venn Soundness and Completeness |
|
|
31 | (2) |
|
|
|
32 | (1) |
|
6 Direct Way to Venn Models |
|
|
33 | (2) |
|
|
|
35 | (4) |
|
7.1 Weak Natural Deduction Formalization of AAS |
|
|
35 | (2) |
|
7.2 Proper Natural Deduction Formalization of AAS |
|
|
37 | (2) |
|
8 Direct Completion of Direct Deduction |
|
|
39 | (6) |
|
|
|
43 | (2) |
|
9 Models of NF(C) Revisited |
|
|
45 | (6) |
|
10 Decidability Revisited |
|
|
51 | (2) |
|
|
|
53 | (8) |
|
11.1 Further Extension of Direct Deduction |
|
|
54 | (5) |
|
|
|
59 | (2) |
|
|
|
61 | (8) |
|
12.1 Independence of g and Variants Thereof |
|
|
62 | (5) |
|
|
|
67 | (2) |
|
13 Algebraic Semantics of AAS, a Prelude |
|
|
69 | (4) |
|
|
|
71 | (2) |
|
14 Algebraic Interpretation of NF(C) |
|
|
73 | (2) |
|
15 Annihilators: Embedding the Partial into a Total |
|
|
75 | (4) |
|
16 Back to Algebraic Interpretation |
|
|
79 | (4) |
|
|
|
83 | (2) |
|
|
|
84 | (1) |
|
18 Inadequacy: Bounds of AAS |
|
|
85 | (4) |
|
|
|
87 | (2) |
| Appendix |
|
89 | (2) |
| Index of Symbols and Abbreviations |
|
91 | (4) |
| Subject and Names Index |
|
95 | |
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.
Daugiau apie elektronines knygas