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RESEARCH PRODUCT

Leibniz, Modal Logic and Possible World Semantics: The Apulean Square as a Procrustean Bed for His Modal Metaphysics

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Even if Leibniz didn’t have the opportunity to actually conceive an explicit modal logic system, remains the fact that he had worked out a modal metaphysics, of which the inaugural act, in his Elementa juris naturalis (c. 1671) was an obvious reference to the Apulean square of opposition. Later, scholars acknowledged in this passage probably one of the first sketch of deontic logic of norms. His modal metaphysics rather deals with the so-called alethic modalities, sometimes expounded through a language such as R.M. Adams wondered whether Leibniz could be “a sort of grandfather of possible worlds semantics for modal logic”. In the following study, the Apulean square is used as a hermeneutic tool: however, is the square really well-fitted to express some basic implications of the modal metaphysics? The most remarkable point is that Leibniz was well aware of the K-distributive axiom □(p⊃q)⊃(□p⊃□q) common to the main modal systems today. This awareness dissuaded him to trust the too easy solution of the necessitarianism issue grounded on the well-known distinction coming from Boethius between a “necessitas consequentiae” and a “necessitas consequentis”.