The Organon: Or Logical Treatises of Aristotle : with the Introduction of Porphyry, Volume 2

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G. Bell, 1902 - 735 pages
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The author of the comment draws the attention of the potential reader to the importance of De Interpretatione ( On interpretation in English, Peri Hermeneias in Greek). In On interpretation, chapter 7 is to be found the origin of the square of opposition which must be advantageously replaced by the logical hexagon which Robert Blanché presented in 1966 in his work published with Vrin: Structures intellectuelles. In On interpretation chapter 9 one can find the first appearance of what is known as modal logic. As far as modal logic is concerned, the importance of the substitution of the hexagon for the square cannot be too much emphasized.
On Interpretation (Latin:De Interpretatione, Greek Perihermenias) introduces Aristotle's conception of proposition and judgment, and the various relations between affirmative, negative, universal, and particular propositions. It contains Aristotle's principal contribution to philosophy of language. It also discusses the Problem of future contingents.
The logical square or square of Apuleius has its origin in the four marked sentences to be employed in syllogistic reasoning: Every man is white, the universal affirmative and its negation Not every man is white (or Some men are not white), the particular negative on the one hand, Some men are white, the particular affirmative and its negation No man is white, the universal negative on the other. Robert Blanché published with Vrin his Structures intellectuelles in 1966 and since then many scholars think that the logical square representing four values should be replaced by the logical hexagon which by representing six values is a more potent figure because it has the power to explain more things about logic and natural language. The study of the four propositions constituting the square is found in Chapter 7 and its appendix Chapter 8. Most important also is the immediately following Chapter 9 dealing with the problem of future contingents mentioned above. This chapter and the subsequent ones are at the origin of modal logic. There is perhaps a superiority of Blanché's hexagon in the field of modal logic too in so far as it explains clearly the nature and importance of the bilateral possible. The notion of bilateral possible is crucially important to understand both logic and natural language when applied to modal values.
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