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The Hexagon of Opposition

Throughout the western philosophical and theological tradition, scholars have assumed that the future can be adequately described in terms of what will and will not happen. In this essay I, Alan Rhoda and Tom Belt argue that this assumption is mistaken, for the logical contradictory of will is not will not but might not. Conversely, the logical contradictory of will not is not will, but might. We suggest that the traditional assumption that the future is exhaustively describable in terms of what will and will not occur is influenced by an inadequacy in Aristotle’s famous “Square of Opposition.” We correct this deficiency and demonstrate that an adequate logical model of the future must incorporate might and might not, producing a “Hexagon of Opposition” rather than a “Square of Opposition.”

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The Hexagon of Opposition: Thinking Outside the Aristotelian Box

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