La théorie leibnizienne de l'expression, centrée sur la notion de relation, introduit, entre les mots des langues naturelles et la pensée, un rapport qui n'est pas seulement de représentation. Elle introduit également une parenté entre langues naturelles et langages formels. L'objectif de l'article est de mener une confrontation entre l'analyse par Leibniz des relations dans les langues naturelles et dans les langages symboliques afin de mettre en évidence leurs analogies. L'article cherchera à montrer : l'existence d'une double articulation dans les (...) langues naturelles et les langages formels tels que les conçoit Leibniz ; le caractère mathématique de son analyse des prépositions ; l'arrière-plan logique de son analyse des dérivations sémantiques. (shrink)

This paper is concerned with De Morgan’s explanation of the validity of arguments that involve relational notions. It discusses De Morgan’s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan’s logic, and contrary to that De Morgan’s mistake is not beyond repair. The rules that determine his new logic (...) are in fact monotonie replacement rules. And provided they are restricted in the correct way, these rules are demonstrably sound. (shrink)

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)

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's treatment of the concept of res should be considered in the context of his semantic-ontological reflections on the relationship of language, thought and reality, profoundly shaped by a no...

This paper explores the theory of freedom that Emilie du Châtelet advances in her essay “On Freedom.” Using contemporary terminology, we can characterize this theory as a version of agent-causal compatibilism. More specifically, the theory has the following elements: (a) freedom consists in the power to act in accordance with one’s choices, (b) freedom requires the ability to suspend desires and master passions, (c) freedom requires a power of self-motion in the agent, and (d) freedom is compatible with moral necessity (...) but not with physical necessity. While these elements may at first appear disparate, the paper shows that they fit together quite well. The resulting theory is a surprising combination of doctrines that appear to be based on Samuel Clarke’s libertarian account of free will and doctrines that are reminiscent of the compatibilist accounts of John Locke, Anthony Collins, Gottfried Leibniz, and Thomas Hobbes. (shrink)

This paper examines the Leibnizian background to Kant's critique of the ontological argument. I present Kant's claim that existence is not a real predicate, already formulated in his pre-critical essay of 1673, as a generalization of Leibniz's reasoning regarding the existence of created things. The first section studies Leibniz's equivocations on the notion of existence and shows that he employs two distinct notions of existence ? one for God and another for created substances. The second section examines Kant's position in (...) his early paper of 1763. My claim is that Kant's view of existence in 1763, namely that it is not a predicate, is strongly related to the logical notion of possibility, formulated by Leibniz and accepted by Kant. (shrink)

Incongruent counterparts are pairs of objects which cannot be enclosed in the same spatial limits despite an exact similarity in magnitude, proportion, and relative position of their parts. Kant discerns in such objects, whose most familiar example is left and right hands, a “paradox” demanding “demotion of space and time to mere forms of our sensory intuition.” This paper aims at an adequate understanding of Kant’s enigmatic idealist argument from handed objects, as well as an understanding of its relation to (...) the other key supports of his idealism. The paper’s central finding is that Kant’s idealist argument from incongruent counterparts rests essentially on his theory of freedom. The surprising result sheds new light on deep and overlooked links among the pillars of transcendental idealism, pointing the way to a comprehensive and unified reading of Kant’s system of idealist arguments. (shrink)

Some authors have attempted to defend Leibniz’s Identity of Indiscernibles through weak discernibility. The idea is that if there is a symmetric, nonreflexive physical relation that holds between two particles, then those particles cannot be identical. In this article I focus only on Muller and Saunders’s account and argue that the means by which they achieve weak discernibility is not through a quantum mechanical observable but an alternate mathematical construction that is both unorthodox and incomplete.

Starting from an analogy with Quine’s two dogmas of empiricism, I offer a critique of two dogmas of analytic historiography: the belief in a cleavage between the justification of a ph...

The paper discusses Leibniz's theory of denominations, expression, and individual notions, the central claim being that the key to many of Leibniz's fundamental theses is to consider his argument, starting from his predicate-in-subject account of truth (that in a true statement the notion of the predicate is contained in that of the subject), against purely extrinsic denominations: this argument shows why there is an internal foundation for all denominations, why everything in the world is interconnected, why each substance expresses all (...) the others, and why every change in the world is reflected as a real, internal change in every substance. (shrink)

Leibniz’s claim that it is possible for us to gain metaphysical knowledge through reflection on the self has intrigued many commentators, but it has also often been criticized as flawed or unintelligible. A similar fate has beset Leibniz’s arguments against materialism. In this paper, I explore one of Leibniz’s lesser-known arguments against materialism from his reply to Bayle’s new note L, and argue that it provides us with an instance of a Leibnizian “argument from reflection”. This argument, I further show, (...) does not constitute a flawed appeal to mere introspection, but is in fact securely grounded in an important corollary of the Principle of Sufficient Reason: Leibniz’s Principle of Intelligibility. (shrink)

This paper is concerned with De Morgan’s explanation of the validity of arguments that involve relational notions. It discusses De Morgan’s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan’s logic, and contrary to that De Morgan’s mistake is not beyond repair. The rules that determine his new logic (...) are in fact monotonie replacement rules. And provided they are restricted in the correct way, these rules are demonstrably sound. (shrink)

I present a formal framework historically faithful to Leibniz's analysis of relational sentences, which: (i) engrafts thematic roles and the non-truth-functional connective insofar as (quatenus) into the monadic fragment of first-order logic; (ii) suggests a plausible ontological picture of thematic roles and relational facts; (iii) supports argument deletion and related inferential patterns that are not taken into account by standard first-order logic.

The article attempts to reconsider the relationship between Leibniz’s and Kant’s philosophy of geometry on the one hand and the nineteenth century debate on the foundation of geometry on the other. The author argues that the examples used by Leibniz and Kant to explain the peculiarity of the geometrical way of thinking are actually special cases of what the Jewish-German mathematician Felix Hausdorff called “transformation principle”, the very same principle that thinkers such as Helmholtz or Poincaré applied in a more (...) general form in their celebrated philosophical writings about geometry. The first two parts of the article try to show that Leibniz’s and Kant’s philosophies of geometry, despite their differences, appear to be preoccupied with the common problem of the impossibility to grasp conceptually the intuitive difference between two figures (such as a figure and its scaled, displaced or mirrored copy). In the third part, it is argued that from the perspective of Hausdorff’s philosophical-geometrical reflections, this very same problem seems to find a more radical application in Helmholtz’s or Poincaré’s thought experiments on the impossibility of distinguishing distorted copies of our universe from the original one. I draw the conclusion that in Hausdorff’s philosophical work, which has received scholarly attention only recently, one can find not only an original attempt to frame these classical arguments from a set-theoretical point of view, but also the possibility of considering the history of philosophy of geometry from an uncommon perspective, where especially the significance of Kant’s infamous appeal to “intuition” can be judged by more appropriate standards. (shrink)

Imaguire-Guido_On-the-ontology-of-relations.

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles (...) and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

Whitehead's system may be interpreted as a majestic attempt at recasting Leibniz's theory of monads in terms of sounder ontological categories. After a brief introductory section on the sources of Whitehead's knowledge of Leibniz's philosophy, the paper explains why Whitehead turned to Leibniz for metaphysical inspiration. Attention then shifts to Whitehead's understanding of the problems involved with Leibniz's theory of monads and his alternative explanation of monadic causation. Whitehead's endeavour to install windows in Leibniz's monads may not be entirely convincing, (...) but there are philosophical gems scattered here and there in his analyses – true moments of insight that repay close examination. (shrink)

The paper examines three essays that Leibniz wrote in 1688, immediately after the composition of the Discourse on Metaphysics, one of his most organic philosophical works. The main topics which emerge from these essays are: the relationship between substance and accidents; the nature of accidents; and, more generally, the nature of abstract entities. Given that accidents' nature is that of changing, Leibniz sees how hard it is to give an account of the relationship between substance and accidents that does not (...) imply any change in the substance, when its accidents undergo a change. To find a way out of this problem, Leibniz assumes that abstract terms (whiteness, wisdom, etc.) do not name real properties or real parts of substances, and that any sentence containing real abstract terms can be rephrased as a sentence containing logical abstract terms, which do no imply any commitment to the existence of real properties. Coherently with this nominalistic attitude, Leibniz ends up, in the Theodicy and in his correspondence with Des Bosses, considering accidents as modes or internal modifications of the substance. (shrink)