According Leibniz's thesis of universal expression, each substance expresses the whole world, i.e. all other substances, or, as Leibniz frequently states, from any given complete individual notion (which includes, in internal terms, everything truly attributable to a substance) one can "deduce" or "infer" all truths about the whole world. On the other hand, in Leibniz's view each (created) substance is internally individuated, self-sufficient and independent of other (created) substances. What may be called Leibniz's expression problem is, how to reconcile these (...) views with each other, that is, how a substance that expresses the whole world, even in the sense that the whole world can be "inferred" from its complete individual notion, can be self-sufficient and internally individuated. The purpose of this paper is to give an exact account of this tricky problem of universal expression, an account that retains substances' self-sufficiency under the constraint that all truths about the whole world are to be obtained from complete individual notions. It will also be shown how the explication of universal expression to be given accounts for Leibniz's thesis of universal change, i.e. the view that any change in any substance is reflected as a real, internal change in each and every other substance. (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)

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)

Leibniz, it seems, wishes to reduce statements involving relations or extrinsic denominations to ones solely in terms of individual accidents or, respectively, intrinsic denominations. His reasons for this appear to be that relations are merely mental things (since they cannot be individual accidents) and that extrinsic denominations do not represent substances as they are on their own. Three interpretations of Leibniz''s reductionism may be distinguished: First, he allowed only monadic predicates in reducing statements (hard reductionism); second, he allowed also `implicitly (...) relational predicates'' such as `loves somebody'' (soft reductionism); third, he allowed also `explicitly relational predicates'' such as `loves Helen'' (nonreductionism). Hard reductionism is problematic with respect to Leibniz''s doctrines of universal expression and incompossibility (among other things). Nonreductionism, in turn, faces insurmountable problems with Leibniz''s doctrine of self-sufficiency and internal identification of substances, as well as with that of individual accidents. The remaining option, soft reductionism, standing between the other two interpretations, arguably avoids at least some of their problems. (shrink)

En este artículo examinamos los aspectos más relevantes de la concepción del espacio de Leibniz. A través de un enfoque genético, nuestro propósito es mostrar que, en su desarrollo evolutivo, dicha concepción sufre dos transiciones destacables, las que separan y distinguen tres versiones teóricas. En su juventud, Leibniz defiende una concepción substancialista del espacio. Sin embargo, debido a la adopción del nominalismo, dicha concepción sufre un primer giro que decanta en un monismo substancialoide, el que se consolida en el período (...) medio de la filosofía de Leibniz. Ya en el período tardío, Leibniz reformula, en una segunda transición, su concepción del espacio, la que adopta la forma definitiva de -lo que llamamos- un relacionismo substancialoide. (shrink)