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FUTURE LOGIC

© Avi Sion, 1990 (Rev. ed. 1996) All rights reserved.

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PART II. MODAL CATEGORICALS.

11. MODALITY: CATEGORIES AND TYPES.

1. Seeds of Growth.

2. Categories of Modality.

3. Types of Modality.

4. Extensional Modality.

5. Temporal Modality.

6. Tense and Duration.

7. Natural Modality.

8. Other Types.

12. SOURCES OF MODALITY.

1. Diversity.

2. Time and Change.

3. Causality.

13. MODAL PROPOSITIONS.

1. Categories and Types.

2. List and Notation.

3. Distributions.

14. MODAL OPPOSITIONS AND EDUCTIONS.

1. Quantification of Oppositions.

2. Basic Intramodal Oppositions.

3. Quantified Intramodal Oppositions.

4. Intermodal Oppositions.

5. Eductions.

See also, in this context, Appendix 2.

15. MAIN MODAL SYLLOGISMS.

1. Valid Modes.

2. Valid Moods.

3. Validations.

16. OTHER MODAL SYLLOGISMS

1. Secondary Modes.

2. Mixed Modes.

3. Summation.

4. General Principles.

17. TRANSITIVE CATEGORICALS.

1. Being and Becoming.

2. Various Features.

3. Various Contrasts.

4. Some Syllogisms.

18. PERMUTATION.

1. Two Senses of ‘Is’.

2. Other Permutations.

3. Verbs.

4. ‘As Such’ Subjects.

5. Commutation.

19. MORE ABOUT QUANTITY.

1. Substitution.

2. Comparatives.

3. Collectives and Collectionals..

4. Quantification of the Predicate.

Summary of findings in the chapters of this part:

Part II. Modal Categorical Logic . This is a broadening of Aristotelean logic, with the addition of modality. Though to some extent known since antiquity, this field has never been properly and fully developed as here done.

11. We distinguished the categories of modality — necessity, presence, possibility, and their negations, as well as other degrees of probability. We distinguished various types of modality, concentrating to begin with on three — the extensional, the temporal and the natural. Tense and duration were discussed incidentally.

12. We discussed certain phenomena underlying these concepts of modality, namely diversity, time and change, and causality.

13. A full list of propositions involving the various categories and types of modality under discussion was presented, and a new notation facilitating our reference to them was introduced.

14. We devised a general theory for predicting the oppositions between plural and modal forms, from the known oppositions of singular and actual forms. We applied these findings to the forms previously listed, and determined all their interrelations methodically, in enlarged diagrams and tables. We also investigated the eductions feasible from modal propositions.

15. The main valid moods of modal syllogism were listed for each type of modality, and their validations were described.

16. Valid moods of lesser or derivative significance were also listed, including moods of mixed modal types. The statistics of validity were looked into, and general principles formulated.

17. The concepts of being and becoming were analyzed, and new propositional forms concerning change (transitives) were introduced. Some important syllogistic arguments involving them were pointed out.

18. Permutation was discussed in more detail, and other copulae than those thus far considered were mentioned.

19. We looked into substitutive processes, comparative propositions, and the differences between dispensive, collective and collectional quantities; also, the doctrine of quantification of the predicate was discussed.

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