Leibniz's conceptual containment theory says that singular propositions of the form a is F are true when the complete concept of being a contains the concept of being F. In this paper, I provide a new semantics for first-order logic built around this idea. The semantics resolves longstanding problems for Leibniz's theory and can represent, without possible worlds, both hyperintensional distinctions among properties and a certain kind of presumably impossible situation that standard approaches cannot represent. The semantics also captures the (...) strong soundness and completeness of classical first-order logic. (shrink)

This essay argues that, with his much-maligned “infinite analysis” theory of contingency, Leibniz is onto something deep and important – a tangle of issues that wouldn’t be sorted out properly for centuries to come, and then only by some of the greatest minds of the twentieth century. The first two sections place Leibniz’s theory in its proper historical context and draw a distinction between Leibniz’s logical and meta-logical discoveries. The third section argues that Leibniz’s logical insights initially make his “infinite (...) analysis” theory of contingency more rather than less perplexing. The last two sections argue that Leibniz’s meta-logical insights, however, point the way towards a better appreciation of (what we should regard as) his formal theory of contingency, and its correlative, his formal theory of necessity. (shrink)

Marco Messeri offers a new solution to the problem of lucky proof (an influen­tial objection to Leibniz’s infinite-analysis theory of contingency. Messeri claims that contingent truths like “Peter denies Jesus” cannot be proved by a finite analysis because predicates like “denies Jesus” are infinitely complex. I argue that infinitely complex predicates appear in some necessary truths, and that some contingent truths have finitely complex predicates. Messeri’s official account is disjunctive: a truth is contingent just in case either it contains an (...) infinitely complex predicate or it concerns existence. I argue against Messeri’s official account and suggest that some other disjunctive account might be appropriate. (shrink)