Leibniz claims that for every possible substance S there is an individual concept that includes predicates describing everything that will ever happen to S, if S existed. Many commentators have thought that this leads Leibniz to think that all properties are had essentially, and thus that it is not metaphysically possible for substances to be otherwise than the way their individual concept has them as being. I argue against this common way of reading Leibniz’s views on the metaphysics of modality. (...) I develop a model in which individual concepts are innocent; that is, individual concepts are divine ideas that permit God to know everything that will ever happen to all possible substances, if created, but these individual concepts neither require that all properties are had essentially nor require that it is metaphysically necessary for substances to be the way their individual concepts have them as being. (shrink)

Leibniz thinks that every created substance is causally active, and yet causally independent of every other: none can cause changes in any but itself. This is not controversial. But Leibniz also thinks that every created substance is existentially independent of every other: it is metaphysically possible for any to exist with or without any other. This is controversial. I argue that, given a mainstream reading of Leibniz’s essentialism, if one accepts the former, uncontroversial interpretation concerning causal independence, then one ought (...) also to accept the latter, controversial one concerning existential independence. This is a new way to defend the ‘existential independence’ interpretation. Moreover, this defense provides a new approach for defending the broadly ‘non-logical’ interpretive camp in the longstanding debate over Leibniz’s views on incompossibility, against perhaps the strongest objection leveled by advocates of the opposing broadly ‘logical’ interpretation. (shrink)

In this presentation, I first outline three different notions of concepts: one derives from Leibniz, while the other two derive from Frege. The Leibnizian notion is the subject of his “calculus of concepts” (which is really an algebra). One notion of concept from Frege is what we would call a “property”, so that when Frege says “x falls under the concept F”, we would say “x instantiates F” or “x exemplifies F”. The other notion of concept from Frege is that (...) of the notion of sense, which played various roles within Frege's theory. This notion of concept can be generalized and, as such, accounts for our intuitive talk of “x's concept of …”, where the ellipsis can be filled in with a name for individual, a property, or a relation, etc. After outlining these three notions, I then discuss how (axiomatic) object theory offers a distinct, precise regimentation of each of the three notions. (shrink)

In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. (...) The fundamental theorem of Leibniz's modal metaphysics of concepts is proved, namely, whenever an object x has F contingently, then (i) the individual concept of x contains the concept F and (ii) there is a (counterpart) complete individual concept y which doesn't contain the concept F and which `appears' at some other possible world. Finally, the author shows how the concept containment theory of truth can be made precise and made consistent with a modern conception of truth. (shrink)

Si Dios es la razón suficiente del mundo, entonces parece seguirse que todos los eventos son consecuencia necesaria de un ser necesario. Para evadir esta conclusión, Leibniz formula en la década de 1670 una concepción modal que funda la contingencia en un rasgo lógico e intrínseco de las ideas de las cosas: la posibilidad de concebir la idea contraria sin contradicción. Hacia 1686, Leibniz complementa esta primera concepción con lo que considera su solución definitiva al problema de la contingencia: la (...) teoría del análisis infinito. Sin embargo, en otros escritos de ese año, propone dos vías alternativas de fundamentación de la contingencia. Este trabajo sugiere que esa pluralidad de modelos explicativos converge en una concepción integral de las modalidades que subyace como trasfondo de la reflexión modal leibniziana. If God is the sufficient reason for this world, then it seems to follow that every event is a necessary consequence of a necessary being. in order to avoid this conclusion, Leibniz states, during the 1670's, a modal conception that grounds contingency on a logical feature which is intrinsic to the ideas of things: the possibility of conceiving the opposite idea without contradiction. Towards 1686, Leibniz complements this first conception with what he considered to be his definitive solution to the problem of contingency: the theory of infinite analysis. However, in other writings from the same year, he proposes two different ways to explain contingency. This paper suggests that this plurality of models converges in a global conception of modalities, which lies at the background of Leibniz's modal thought. (shrink)

The proposition "God chooses the best" is for Leibniz an undeniable truth, as well as a fundamental premise in both his explanation of this world's existence and his theodicy. Leibniz thought it was necessary to clarify its modal status, in virtue of this matter's connection with God's freedom. Nevertheless, while dealing with this problem, he was led to violate his own modal theory's principles, in order to sustain the contingency of that proposition. This paper intends to show that Leibniz's main (...) view regarding the modality of this proposition represents a sort of exception in the framework of his modal conception, and that this uncertainty reveals the profound reasons of his numerous textual hesitations on the subject. (shrink)