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Philosophy - Philosophical Traditions | Aristotle's Modal Proofs - Prior Analytics A8-22 in Predicate Logic

Aristotle's Modal Proofs

Prior Analytics A8-22 in Predicate Logic

Rini, Adriane

2011, VI, 246 p.

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  • Makes Aristotle’s system of modal syllogistic logic easily accessible to logicians and other logic savvy readers
  • Uses standard predicate logic translations with (exclusively) de re modality to represent Aristotle's Greek
  • Contains a line-by-line discussion of every modal syllogism in the Prior Analytics
  • Distinguishes between two kinds of syllogistic terms to simplify Aristotle's modal logic
Aristotle’s modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a ‘realm of darkness’. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle’s results. This volume provides a simple interpretation of Aristotle’s modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as ‘horse’, ‘plant’ or ‘man’, which name things in virtue of features those things must have, and green terms, such as ‘moving’, which name things in virtue of their non-necessary features. By applying this distinction to the Prior Analytics, Rini shows how traditional interpretive puzzles about the modal syllogistic melt away and the simple structure of Aristotle’s own proofs is revealed. The result is an applied logic which provides needed links between Aristotle’s views of science and logical demonstration. The volume is particularly valuable to researchers and students of the history of logic, Aristotle’s theory of modality, and the philosophy of logic in general.

Content Level » Research

Keywords » Ancient logic - Aristotle - Modal syllogistic - Predicate logic - Prior Analytics

Related subjects » Logic & Philosophy of Language - Philosophical Traditions

Table of contents 

Acknowledgements.- Introduction.- Part I: Modern Methods for Ancient Logic.- 1. The Non-Modal Syllogistic: An.Pr. A1-7.- 2. The Assertoric Syllogistic in LPC.- 3. A Realm of Darkness.- 4. Technicolour Terms.- 5. Representing Modality.- Part II: Necessity in the Syllogistic: An. Pr. 8-12.- 6. Syllogizing in Red: Trivializing the Modals.- 7. First-Figure Mixed Apodeictic Syllogisms.- 8. Modal Conversion in the Apodeictic Syllogistic.- 9. Against the Canonical Listings.- 10. Apodeictic Possibility.- Part III: Contingency in the Syllogistic: An. Pr. 13-22.- 11. Contingency (A13, A14).- 12. Realizing Possibilities.- 13. Barbara XQM.- 14. First Figure X+Q (A15).- 15. First Figure L+Q, Q+L (A16).- 16. Contingency in the 2nd Figure (A17, A18, A19).- 17. Contingency in the 3rd Figure (A20, A21, A22).- 18. Summary and Conclusion.- Appendix: The LPC Framework.- Bibliography.- Index.

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