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Aristotle's modal syllogisms

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Provability, Computability and Reflection.

Abstract: Provability, Computability and Reflection

Author(s): Aristotle.; McCall, Storrs
Series: Studies in logic and the foundations of mathematics 31
Publisher: North Holland,Elsevier
Year: 1963

Language: English
Pages: 109
City: Burlington
Tags: Aristotle.;Syllogism.;Modality (Logic);PHILOSOPHY -- Logic.

Content: Front Cover
Aristotle's Modal Syllogisms
Copyright Page
Contents
Preface
Notation
Chapter I. The Problem of the Apodeictic Moods
1. Introduction
2. Historical survey
3. Aristotle's system of apodeictic syllogisms
4. Aristotle on the two Barbaras
5. Hintikka's dilemma
6. Theophrastus and Lukasiewicz on the two Barbaras
7. Concrete examples of the two Barbaras
8. The Becker approach and its congeners
9. Rescher's interpretation
10. Completion of Rescher's interpretation
Chapter II. The System of Apodeictic Moods
11. Systematization of the assertoric moods. 12. Modal logic of propositions13. Opposition of modal premisses
14. Axiomatization of the apodeictic moods. The L-X-M calculus
15. The laws of subalternation
16. The laws of conversion
17. The laws of modal subordination
18. The LLL, LXL and XLL moods
19. Further L-X-M moods
Chapter III. Decision Procedure for the Apodeictic Moods
20. The mechanism of rejection
21. A decision procedure for the L-X-M calculus
Chapter IV. The Contingent Moods
22. General remarks. The contingency operator
23. Conversion and opposition of contingent premises. 24. Can contingency be defined in terms of possibility and necessity?25. Axiomatization of the contingent moods. The Q-L-X-M calcdus
26. The laws of complementary conversion
27. The laws of subalternation
28. The laws of ordinary conversion
29. The laws of modal subordination
30. Conspectus of Aristotle's contingent moods
31. The QQQ moods
32. The QXQ and XQQ moods
33. The QXM and XQM moods
34. The QLQ and LQQ moods
35. The QLX and LQX moods
36. The QLM and LQM moods
37. Summary of the Q-L-X-M moods
38. Conclusion
Index.