De Interpretatione - The Square of Opposition

The Square of Opposition

The logical square, also called "square of opposition" or "square of Apuleius" has its origin in the four marked sentences to be employed in syllogistic reasoning, as follows:

1. "Every man is white" - the universal affirmative
2. "Not every man is white" (or "Some men are not white") - the particular negative, negation of "Every man is white"
3. "Some men are white" - the particular affirmative
4. "No man is white" - the universal negative, negation of "Some men are white".

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. 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.