Jean-François Monteil, ancien maître de conférences de linguistique générale à l’Université Michel de Montaigne de Bordeaux
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In La Logique et son histoire d’ Aristote à Russell, published with Armand Colin in 1970, Robert Blanché, the author of Structures intellectuelles ( Vrin, 1966) mentions that Józef Maria Bocheński speaks of a sort of Indian logical triangle to be compared with the square of Aristotle (or square of Apuleius), in other words with the square of opposition. This logical triangle announces the logical hexagon of Blanché. It seems that with this logical triangle, Indian logic proposes a useful approach to the problem raised by the particular propositions of natural language. If Robert Blanché’s logical hexagon is something more complete and therefore more powerful as regards the understanding of the relationship between logic and natural language, it may be that on a highly important point, Indian logic is superior to the western logic proceeding from Aristotle.
Robert Blanché translated a passage of the work in Structure intellectuelles page 39 : « Hindu logic knows of three logical propositions and not the four of western logic. For it Some S are P does not signify Some S at least are P but Some S are P but not all.» This precious text shows that Indian tradition explicitly speaks of the existence of partial quantity the third quantity to be considered along with totality apprehended by A the universal affirmative of the square and zero quantity apprehended by E the universal negative of the square. To the two universals A and E entertaining a relationship of contrariety, one should add the third contrary constituted by the double negation of the first two. As the subcontrary I contradicts E and the subcontrary O contradicts A, the logical proposition apprehending partial quantity can be represented by the conjunction of I and O : I & O. In Robert Blanché’s logical hexagon dealt with in Structures intellectuelles (1966), this conjunction is symbolized by the letter Y. Let us add that the logical hexagon can be simplified into a triangle pretty easily. If we want to do justice to Indian logic, this logical triangle should be named Indian triangle. Robert Blanché published with Vrin his Structures intellectuelles in 1966, and since then, many scholars think that the logical square (or square of opposition 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. This chapter and the subsequent ones are at the origin of modal logic. Perhaps Blanché’s hexagon is particularly useful in the domain of modal logic, 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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