La noción de sustancia, tal como la propongo, es tan fecunda, que de ella surgen las verdades primarias y originarias y, en realidad, referentes a Dios, las almas y la naturaleza de los cuerpos (es decir, a todo esto y a sus ámbitos). Se trata de verdades conocidas en parte pero poco demostradas; en parte desconocidas hasta ahora, sin embargo, de un gran significado para las demás ciencias.

Desde que hablamos por primera vez de una nueva ciencia de la dinámica, la cual debe aún fundamentarse, una serie de hombres destacados ha dado a conocer en diferentes lugares sus intenciones de una exposición más detallada de esta doctrina puesto que nuestro tiempo aún no es suficiente para un libro, queremos por eso presentar aquí un proyecto que al menos pueda dar ya alguna luz, y que quizás algún día nos sea restituidocon interés e interés compuesto, cuando sea logrado (...) por hombres que, al servirse tanto de una fuerza del pensamiento como de una sutileza de estilo, muevan a la manifestación de sus opiniones. Su juicio es siempre deseado por nosotros y, como ha de esperarse, útil para la realización de nuestra obra. (shrink)

La cuestión referente a la verdad y falsedad de las ideas es tratada fervorosamente en la actualidad por hombres ilustres; y puesto que el propio Descartes no ha encontrado una solución satisfactoria a este problema, el cual es de gran significado para el conocimiento de la verdad, quisiera exponer brevemente mi interpretación acerca de los rasgos característicos y los criterios de las ideas y de los conocimientos. Pues bien, un conocimiento es oscuro o claro; un conocimiento claro es a su (...) vez confuso o distinto; un conocimiento distinto, inadecuado o adecuado; simbólico o intuitivo; finalmente, el conocimiento más completo será aquel que sea al mismo tiempo adecuado e intuitivo. (shrink)

Discourse on Metaphysics and Other Essays contains complete translations of the two essays that constitute the best introductions to Leibniz's complex thought: Discourse on Metaphysics of 1686 and Monadology of 1714. These are supplemented with two essays of special interest to the student of modern philosophy, On the Ultimate Origination of Things of 1697 and the Preface to his New Essays of 1703-1705. The translations are taken from Leibniz, Philosophical Essays, edited and translated by Roger Ariew and Daniel (...) Garber (Hackett, 1989). (shrink)

In this article, I examine Leibniz’s criticism of Spinoza’s notion of priority by nature based on the first proposition in Spinoza’s Ethics. Leibniz provides two counterexamples: first, the number 10’s being 6+3+1 is prior by nature to its being 6+4; second, a triangle’s property that two internal angles are equal to the exterior angle of the third is prior by nature to its property that the three internal angles equal two right angles. Leibniz argues that Spinoza’s notion (...) cannot capture these priority relations. Although this text has received some scholarly attention, Leibniz’s objection in this text has not been fully explained yet. I argue that evaluating Leibniz’s objection relies on how to understand Spinoza’s notion of conception: first, whether conception is co-extensive with inherence and causation; second, whether conception is mental. (shrink)

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The comparison made by Ada Lovelace in 1843 between the Analytical Engine and the Jacquard loom is one of the well-known analogies between looms and computation machines. Given the fact that weaving – and textile production in general – is one of the oldest cultural techniques in human history, the question arises whether this was the first time that such a parallel was drawn. As this paper will show, centuries before Lovelace’s analogy, such a comparison was made by Gottfried Wilhelm (...) Leibniz. During the 17th century, Leibniz compared his calculating machines with another textile machine, the stocking frame, a machine which mechanized knitting and which was invented in 1589. During the following centuries, this machine was considered as a technological wonder and as a creation of God, and, during the last decades of the 17th century, Leibniz emphasized the need to consider it and other textile machines mathematically. What, then, were the reasons for the parallel drawn between this machine and Leibniz’s automatic computation machines? And what were the consequences of this analogy concerning the artisanal knowledge embedded in manual textile practices? (shrink)

The reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold provides a systematic account of the structure of Leibniz’s metaphysics in terms of its mathematical foundations. However, in doing so, Deleuze draws not only upon the mathematics developed by Leibniz—including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus—but also upon developments in mathematics made by a number of Leibniz’s contemporaries—including Newton’s method of fluxions. He also draws upon (...) a number of subsequent developments in mathematics, the rudiments of which can be more or less located in Leibniz’s own work—including the theory of functions and singularities, the Weierstrassian theory of analytic continuity, and Poincaré’s theory of automorphic functions. Deleuze then retrospectively maps these developments back onto the structure of Leibniz’s metaphysics. While the Weierstrassian theory of analytic continuity serves to clarify Leibniz’s work, Poincaré’s theory of automorphic functions offers a solution to overcome and extend the limits that Deleuze identifies in Leibniz’s metaphysics. Deleuze brings this elaborate conjunction of material together in order to set up a mathematical idealization of the system that he considers to be implicit in Leibniz’s work. The result is a thoroughly mathematical explication of the structure of Leibniz’s metaphysics. This essay is an exposition of the very mathematical underpinnings of this Deleuzian account of the structure of Leibniz’s metaphysics, which, I maintain, subtends the entire text of The Fold. (shrink)

The history of the relations between Leibniz and Spinoza is a matter of philosophical and scholarly controversy. This chapter aims to refer to the first thesis as the Necessity of Actuality and to the second thesis as the Plenitude of Possibilities. It examines how Leibniz's stance with respect to these two theses, and more generally his views on modality, grew out as a response to Spinoza's views. Leibniz explicitly connects Spinoza's attributes with the concept of a world. (...) As most commentators, Leibniz reads Spinoza as a necessitarian, which is a natural interpretation. The difference between Leibniz's and Spinoza's views would reside in their conceptions of God and of the mechanism whereby the actual world comes to exist. Leibniz entertains the hypothesis of reality encompassing a plurality of actual worlds, which seems to achieve the Plenitude of Possibility. (shrink)

Leibniz’s interest in the Talmud and in Jewish philosophy and theology in general, is well established in the scholarly literature. In this paper, we suggest a short comparative study of Leibniz’s concept of the monad and the Talmudic idea of “Malchut.” Our study is based, specifically, on a tractate of the Talmud titled Yoma. This tractate is mainly focused on the Jewish Atonement Day, in which Jews are judged by God for their sins in the previous year. In (...) particular, in pages 38a-b of Yoma, the Talmud reads: “By your name they shall call you, and in your place they shall seat you, and from your own they shall give you; No person may touch that which is prepared for another, and one Malchut does not touch another even to the extent of a hairbreadth.” The Talmud suggests here that even though we somehow influence one another’s life, one cannot directly affect others’ predetermined place in the world or interfere in the individual paths prepared for others. In this paper, we aim to indicate the similarities between such Talmudic notions and Leibniz’s ideas in the Monadology – such as the ideas that monads have “no windows” and that a pre-established harmony is set among all monads by God – as a ground for future research. (shrink)

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)

The main concern of this essay is to make a case for the thesis that Leibniz conceived of his philosophy as a way of life in something like the sense articulated in the works of Pierre Hadot. On this view, philosophy was a type of conduct, or a mode of existing‐in‐the‐world, which had to be practised at each instant, with the goal of transforming the whole of the individual’s life. The essay also serves as an introduction to some of (...) the main themes in Hadot’s work. While it includes a brief discussion of a number of the central components of Leibniz’s philosophy conceived as a way of life, the essay does not aim to do so in great detail. Rather, it offers a manifesto and initial road map. (shrink)

Both bosons and fermions satisfy a strong version of Leibniz’s Principle of the Identity of Indiscernibles (PII), and so are ontologically on a par with respect to the PII. This holds for non-entangled, non-product states and for physically entangled states—as it has been established in previous work. In this paper, the Leibniz strategy is completed by including the (bosonic) symmetric product states. A new understanding of Pauli’s Exclusion Principle is provided, which distinguishes bosons from fermions in a peculiar (...) ontological way. Finally, the program as a whole is defended against substantial objections. (shrink)

Adams presents an in-depth interpretation of three important parts of Leibniz's metaphysics, thoroughly grounded in the texts as well as in philosophical analysis and critique. The three areas discussed are the metaphysical part of Leibniz's philosophy of logic, his essentially theological treatment of the central issues of ontology, and his theory of substance. Adams' work helps make sense of one of the great classic systems of modern philosophy.

This book presents fresh interpretations of Gottfried Leibniz's theories of time, space, and the relativity of motion, based on a thorough examination of Leibniz's manuscripts as well as his published papers. These are analysed in historical context, but also with an eye to their contemporary relevance.

The central task of this dissertation is to develop a new interpretation of Leibniz's famous claim that there are no purely extrinsic denominations . Though Leibniz regarded NPE as one of his most important doctrines, he nowhere offers an explicit statement as to what he meant by it. One interpretation of NPE, which enjoys a modest consensus among interpreters, is that all extrinsic denominations reduce to intrinsic denominations. According to the reductionist view, things only have intrinsic denominations as (...) properties; extrinsic denominations are not genuine properties of things. Critics of reductionism have argued that the textual case for it is inconclusive at best, and I share this assessment with them. However, in my opinion, a satisfactory non-reductionist understanding of NPE has not been offered. The goal of my dissertation is to provide such a non-reductionist account. I contend that NPE, far from being a claim of the reducibility of extrinsic denominations, is actually an assertion that extrinsic denominations are genuine properties of the things they denominate. ;To establish my reading of NPE, I examine a line of textual evidence to which interpreters have paid little attention: the way Leibniz argues for NPE. In some passages Leibniz derives NPE from his predicate-in-subject principle of truth. In others, he employs his doctrine of the interconnection of all things to reach NPE. Elsewhere, he bases NPE on the principle of the identity of indiscernibles. Though, as mentioned, Leibniz never explicitly defines NPE, he does have much to say by way of explicit definition of each of these three principles. A consideration of what version of NPE could plausibly be drawn from them is thus a revealing way to proceed. In the case of each argument, I show that my interpretation of NPE is the conclusion naturally suggested by the given principle, while the reductionist version of NPE forms only an awkward, textually implausible fit with it. The result of the examination is an original and serious critique of the reductionist reading of NPE, as well as the development of a far more plausible understanding of that claim. (shrink)