The Philosophy of Leibniz and the Ontology of Properties

Abstract

In LP — given its current interpretation, which validates the axioms AP1 — AP6, AP7+, AP8+ and AP10 (and AP9+, if “L” is added to LP) — the ontological ideas of Leibniz can be represented in a most satisfactory manner. We have already considered: the intensional interpretation of Boolean algebra, individuals as quasi-identical with maximally consistent properties, exemplification as a special case of property-inclusion, Leibnizian determinism, Leibnizian “contingency” (which obviously requires that the universe of properties be infinite, as is asserted by AP10), the principle of the identity of indiscernibles. But this is not all. It was one of the most cherished ideas of Leibniz that every “concept” (first intension; in our terminology concepts are always linguistic entities; not so for Leibniz or Frege) is composed out of intensionally smallest atomic “concepts” in a purely “additive” or conjunctive manner. And Leibniz was right in this. On the basis of APl — AP6 we can prove: all x(x=conj y(EL(y) and yPx)) (by TP31, TP42 and DP20) — “every first intension is the sum of the elementary first intensions it contains.”[*1]