Beziau, Jean-Yves (Author)
Read, Stephen (Author)
History and Philosophy of Logic
Volume: 35, no. 4
Issue: 4
Pages: 315-316
Edition Details: Lead Article in a Series: “The Square of Opposition”
Language: English
This square, like every square, has four corners, the designations traditionally given to the corners being the four letters A, E, I, O. They can be understood as names for propositions. The four edges and the two diagonals of the square represent four relations between these propositions: red is the relation of contradiction, blue the relation of contrariety, green the relation of subcontrariety, black the relation of subalternation. These relations are defined as follows: two propositions are said to be contradictory iff they cannot be true and cannot be false together, contrary iff they can be false together but not true together, subcontrary iff they can be true together but not false together. A proposition is said to be subalterned to another one, if it is implied by, but is not equivalent to it. The strength of this theory is that it is at the same time fairly simple but quite rich; it can be applied to many different kinds of proposition, and also to objects and concepts. It can also be generalized in various manners, in particular, by constructing many different geometrical objects. The square of opposition is a theory mixing in a productive way logic, philosophy, linguistics and mathematics that has numerous applications ranging from algebra to theology, through music, economy and semiotics.
...MoreDescription Contents:
Article Gallagher, Robert Laurence (2014) Antiphasis as Homonym in Aristotle. History and Philosophy of Logic (pp. 317-331).
Article Chatt, Saloua (2014) Avicenna on Possibility and Necessity. History and Philosophy of Logic (pp. 332-353).
Article Benítez, Juan Manuel Campos (2014) The Medieval Octagon of Opposition for Sentences with Quantified Predicates. History and Philosophy of Logic (pp. 354-368).
Article Johns, Chris (2014) Leibniz and the Square: A Deontic Logic for the Vir Bonus. History and Philosophy of Logic (pp. 369-376).
Article Mion, Giovanni (2014) The Square of Opposition: From Russell's Logic to Kant's Cosmology. History and Philosophy of Logic (pp. 377-382).
Article Moretti, Alessio (2014) Was Lewis Carroll an Amazing Oppositional Geometer?. History and Philosophy of Logic (pp. 383-409).
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