Gottfried Wilhelm Leibniz

This paper analyses the abstractionist account of quantity championed by Leibniz, especially in the 1680s. Leibniz introduced the notion of quantity in an indirect way, via an abstraction principle. In the first part of the paper, I identify the context in which this approach arose in light of Leibniz's criticism of his earlier dream of an ‘alphabet of human thought’. Recognising the impossibility of such a project led him to realise that, when dealing with terms referring to abstract objects, we (...) should always consider them within the true sentences in which they occur. In the second part, I describe this approach in detail. This allows us to look at some key concepts of Leibniz's theory of quantity. In particular, I raise the problem of the relationship between the two sides of the abstraction principle: how should we think of the relation between the claim that a and b are equal, and the claim that the quantity of a is identical to the quantity of b? I argue that we can find a positive answer to this problem in Leibniz. (shrink)

One prominent criticism of Newtonianism held that gravitational attraction is an occult quality. The charge, pressed most forcefully by Leibniz, claims that Newton had abandoned the intelligibility of mechanism and allowed for an unexplained and inexplicable force in nature. This paper focuses on one of Newton’s replies to this accusation: his claim that gravitation is no more mysterious than phenomena like inertia and impenetrability. I argue that we can understand and motivate this Newtonian position by looking at the account of (...) material substance developed in Newton’s early manuscript essay De gravitatione. This account makes clear Newton’s sensitivity to the explanatory limits of mechanism. Newton was perceptive in noting that while the mechanical philosophy sought to provide explanations in terms of matter and motion, it failed to explain matter and motion themselves. This sheds light on the motivations behind the theory of bodies in De gravitatione. And it helps to explain why he was so unmoved by what many saw as a serious challenge to his theory of gravity. (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)

"The documents gathered in this volume cut a winding path through the tumultuous final thirty-three months of Leibniz's life, from March 1714 to his death on 14 November 1716. The disputes with Newton and his followers over the discovery of the calculus and, later, over the issues in natural philosophy and theology that came to dominate Leibniz's correspondence with Samuel Clarke certainly loom large in the story of these years. But as the title of this volume is intended to convey, (...) the letters exchanged between Leibniz and Caroline of Brandenburg-Ansbach, Electoral Princess of Braunschweig-Luneburg and later Princess of Wales, also figure prominently in their telling, and I have included their complete extant correspondence from 1714 to 1716. These letters are of particular interest inasmuch as they provide valuable insights into how and why Leibniz's correspondence with Clarke arose, and why it developed as it did, with Caroline in the role of influential go-between; whence the title, The Leibniz-Caroline-Clarke Correspondence. But there is more; for these letters provide a window into the evolving personal relationship between Leibniz and Caroline. Much of the early correspondence between Leibniz and Caroline after her arrival in England is filled with thoughtful and engaging exchanges about philosophy, literature, and politics, about people Caroline was meeting in England, about those known by Leibniz far and wide, about the new royal family in England, headed by George I (Georg Ludwig of Braunschweig-Luneburg), as well as gossip about affairs of state in both England and Europe at large. Beyond the interest they hold for Leibniz scholars in particular, many of these exchanges should also be of interest to historians of early 18th-century England and Europe, and especially to those interested in the period immediately preceding and following the Hanoverian succession to the throne of England. But even quite early on in their correspondence Leibniz seemed to sense a threat to his relationship with Caroline, and a worrisome paranoia began to creep into some of his letters to her, letters in which he expressed concerns about her continuing allegiance to him now that she had been installed in England amongst his rivals. As the correspondence progressed, Leibniz's paranoia only deepened; but it was nevertheless prophetic of a tragic truth to come. For the letters exchanged between Leibniz and Caroline document the rather sad story of the slow but steady erosion of Caroline's loyalty to Leibniz after she departed Hanover on 12 October 1714 and landed in England at Margate in Kent on 22 October as the new Princess of Wales and future Queen of England. In 1727 the Scottish poet James Thomson penned A Poem Sacred to the Memory of Sir Isaac Newton, calling him "our philosophic sun," and it was by force of the political and cultural mass of this sun that Caroline was eventually, and inexorably, drawn into its orbit, and away from Leibniz". (shrink)

We discuss the astronomical underpinning of the improved calendar of 1700. Starting from the astronomical motivation of the Gregorian calendar of 1582 and the rejection of this reform in Protestant states in Europe, we describe how the astronomical Easter reckoning based on Kepler’s Rudolphine tables led to the foundation of Berlin Observatory and enabled the founding of the Electoral Brandenburg Society of Sciences, which had to finance itself through a calendar monopoly.

Between 1650 and 1664, a giant globe was created in Gottorf under Duke Friedrich III, which was widely known and marvelled at by many contemporaries as a wonder of the world. The scientific management of the project was the responsibility of the court mathematician and librarian Adam Olearius. The Gottorf Globe and its counterpart (a “Sphaera Copernicana”) presented the astronomical knowledge of the time in a pictorial form. The image of the earth and the cosmos was also intended to show (...) the Creator and his omnipotence. Erhard Weigel, professor of mathematics at the University of Jena from 1653, also constructed monumental globes. These baroque world models, as well as Robert Long’s 18th-century sphere, can be considered the precursors of today’s planetariums. (shrink)

In early modern times, solar eclipses were feared events that gave rise to much astrological speculation, even though these events could already be predicted long in advance. Around 1700, the situation was already different. Astrology had lost its status as a science and had largely been pushed out of the universities. On the other hand solar eclipses had become very important for cartography. From the beginning and end times of the eclipse at different locations, the differences of their geographical coordinates (...) could be calculated. The changed situation can be illustrated perfectly by the eclipses of August 12, 1654 and May 12, 1706. Whereas in 1654 there were still many astrologically influenced warnings, in 1706 there was great calm in this respect, and instead numerous astronomers tried to record the event correctly and compare their results with those of other observers. (shrink)

With an overview of the most important scientific innovations in 17th century Europe as a background, the focus is on the field of astronomy and its distinction from astrology. The essays collected in this volume are situated within this development of the early modern period.

El presente artículo aborda la pregunta por la filosofía, las ideas y la verdad en el pensamiento spinoziano, así como el camino para acceder a ellas. Para esto, trazamos un recorrido histórico que comprende una serie de cartas y comentarios que incluyen a Burgh, Steno y Leibniz. Esto nos permitirá, por un lado, mostrar la relevancia histórico-filosófica del debate y, por otro, sostener nuestra hipótesis, según la cual Spinoza consideraría su filosofía como verdadera porque parte de una concepción sobre la (...) naturaleza misma de las ideas que no otorga un estatuto de realidad al error en cuanto tal, dado que en la inmanencia spinoziana no hay ideas completamente inadecuadas o falsas. (shrink)

Leibniz considered that there are substances in a body, each of which does not solely have a shape and size and can act spontaneously. Although he started to regard bodies as having inherent substantial forces in 1678–79, what exactly led him to suppose this is not obvious. The author aims to articulate Leibniz's most important motivation for "restoring" substantial forms. He first notes that Leibniz considered that every body tends to slow down because of its natural inertia. He then discusses (...) that Leibniz had two arguments to postulate the existence of substantial forms, the first of which is based on his view that God providentially manages the universe in the most efficient way. The second and more interesting argument is based on Leibniz's understanding of science, according to which a scientific explanation of motion should be given in terms of the nature of the body. (shrink)

The aim of this chapter is to review the basics of the theory of the Leibniz hierarchy typical of abstract algebraic logic. Proofs and examples are presented in a selfcontained way, with an eye to offering a quick entry to the field to the nonspecialist.

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Reasoning with diagrams is considered to be a peculiar form of reasoning. Diagrams are often associated with imagistic representations conveyed by spatial arrangements of lines, points, figures, or letters that can be manipulated to obtain knowledge on a subject matter. Reasoning with diagrams is not just ‘peculiar’ because reasoners use spatially arranged characters to obtain knowledge – diagrams apparently have cognitive surplus: they enable a quasi-intuitive form of knowledge. The present paper analyses the issue of diagrams’ cognitive value by enquiring (...) into the tradition of symbolic cognition developed by Leibniz, Lambert, and Kant. The proposal resulting from this enquiry is to question the idea that the cognitive value of diagrams lies solely in allowing evidence for inferences. The imaginative dimension of diagrams connects reasoning to doxastic attitudes of meditation and enquiry. (shrink)

Deleuze’s philosophy is permeated with the problem of the continuum. The idea that the coexistence of durations is implied in the concept of duration itself allows Deleuze to offer a fresh perspective on multiplicity, which is distinct from Bergson’s approach, and which proposes new perspectives on the continuum. While Deleuze critiques Leibniz’s view on this concept by highlighting the non-uniform nature of the continuum, the infinitesimal still plays a significant role in his analysis. However, in his late reading of Leibniz, (...) Deleuze emphasises that folds, rather than infinitesimals, should be considered as the smallest components of the continuum’s labyrinth. This implies that there is a union of indiscernible cuts in the continuity, cuts that do not create gaps or breaks in the overall coherence, but rather a labyrinth. I will show how, in exploring this problem, Deleuze and Guattari draw inspiration from Kafka, in order to relate continuity to contiguity. This relation reveals an internal difference that defines the distinction between what is continuous and what is contiguous. This, in our view, marks a considerable shift between Deleuze’s early reading of Bergson and his late reading of Leibniz, and it allows Deleuze to further develop his idea of the continuum. (shrink)

Die Generales Inquisitiones von 1686 stellen die wichtigste geschlossene Arbeit Leibniz' zu Fragen der Logik dar. Wie in dem ebenfalls 1686 verfaßten Discours de Métaphysique (PhB 260) wird hier Leibniz' Auffassung deutlich, in seinem Denken eine gewisse systematische Geschlossenheit gefunden zu haben.

This paper examines the development of the modern concept of substance from Leibniz to Hegel. I will focus primarily on the problem of the inner and outer nature of substance. I will show that if one considers Hegel’s discussion of substance against the background of the controversy between Leibniz and Kant about the inner and outer nature of substance, it becomes clear that for Hegel both Leibniz and Kant grasped the whole concept of substance only partially and in its abstract (...) moments. This is because they both concentrate on one aspect of substance and absolutize it. Hegel, on the other hand, not only overcomes the fundamental difference between the inner and outer of substance, but also develops the connection between the different moments of substance, causality and interaction from the rationalist concept of substance itself. (shrink)

L’exercice de la pensée est animé par une constitutive tendance à la totalité. Contre l’initiale apparence de sa vacuité, ou même de son indétermination il faut cependant lui rappeler qu’elle ne se réduit en rien à un simple exercice formel. Sa puissance propre, la « vertu de la pensée » la fait tendre à la perfection (DM XV). Reconnaître et surtout accomplir cette tendance, telle est en nous la première exigence d’une originaire fidélité. Penser constitue en nous l’activité au sens (...) propre. À... (shrink)

Si Ebehrard a forcé la note en lisant chez Leibniz une critique de la raison rendant superflue la critique kantienne, il a probablement vu juste en voyant chez le premier une pensée de la phénoménalité anticipant celle du second ainsi que sa problématique de l’objectivité.

Jean-Marc Rohrbasser propose une version française de la biographie post mortem de Gottfried Wilhelm Leibniz (1646-1716) rédigée par le philosophe allemand Christian Wolff (1679-1754), et originellement publiée dans les Actes des Savants (Acta Eruditorum) de juillet 1717. Cette version française a été établie à partir de la traduction allemande que l'on trouve dans le volume 21 des Oeuvres complètes de Wolff.

Qu'est-ce qu'un commentaire philosophique? Le cas offert par Gilles Deleuze dans son commentaire de Leibniz (Le pli) est l'occasion de saisir quelques uns des enjeux de cette pratique essentielle au travail du philosophe. En revivifiant en effet une tradition historiquement datée (Wölfflin), Gilles Deleuze s'est attaché à produire une description originale du système leibnizien. Au-delà des difficultés soulevées par la nature même de son modèle (la notion de baroque), le commentaire de Deleuze se singularise par une conception particulière de la (...) lecture philosophique comme recréation d'une pensée à partir de la description de ses conditions formelles d'existence. (shrink)

L'affirmation de l'existence du meilleur des mondes possibles est l'une des thèses leibniziennes les plus connues et sans doute l'une des plus mal comprises. Cet ouvrage en explique le sens, montre sur quels fondements théoriques elle repose et envisage ses implications sur les plans métaphysique et moral.

In this paper I argue that there is a structural parallelism between law and physics in Leibniz since his early years, which has significant influence on the formation of his views. I start by examining Leibniz's early physical system and an analogy with juridical laws that he uses to explain the structure of physical laws. Then, I argue that this analogy stems from an envisioned parallelism between law and physics. Finally, I illustrate the significance of this legal-physical parallelism by arguing (...) that it underlies some of Leibniz's mature views. Most importantly, I argue that the parallelism explains the origin of architectonic principles or optimality principles in Leibniz's mature physics. (shrink)

Leibniz sought to solve the metaphysical problem of reality, avoiding ontological premises. His intensional method was aimed at the logical solution of the problem, preserving the objectivity and unobstructed metaphysical research. Metaphysics can provide a certain level of coherence to the phenomena of physics and make them more real. Leibniz was convinced that physics, for its part, should be grounded in metaphysical principles. This promotes a reciprocal relationship between physics and metaphysics, where metaphysical principles derive their reality from physical principles, (...) and the two fields are interrelated. If we recognize the reality of the laws of physics, then we must also recognize the reality of the concept of substance. His position is that the laws of mathematical physics predict the existence of real substances, which makes it possible to move from mathematical objects to real substances. This method of substantiating the reality of substance and metaphysical principles can be considered as the foundations of the transcendental method. Leibniz's metaphysical approach is that necessary truths exist by themselves and do not depend on specific objects of study or perception. He regarded these truths as eternal. (shrink)

***Angaben zur beteiligten Person Kühn: Dr. Sebastian Kühn, wissenschaftlicher Mitarbeiter.

As recent scholarship has repeatedly shown, the history of Vienna Circle is to some extent rooted in the tradition of Austrian Philosophy which Neurath considered as not involved in the “Kantian interlude”. Nevertheless, it seems that the heritage of Leibniz and, in particular, of his “reform of logic” has been hitherto neglected. Indeed, Leibnizianism (along with Herbartianism) represents a main feature of this tradition stretching from Bolzano to quite forgotten figures as Exner and Zimmermann, and still influent on the Brentano (...) circle. This paper attempt to highlight the role played by Leibniz in framing of the “scientific world conception”, focusing in particular both on Carnap’s and Neurath’s stance towards the characteristica universalis underlying the project of the encyclopedia Leibniz aimed to realize. (shrink)

The article offers an attempt to understand the present state of Kant’s legacy in Russia on the threshold of the Tercentenary. An explanans is found in the metaphors of “ tabula rasa ” and “unplowed virgin soil,” first used by Leibniz in relation to Russia in his letters and memoranda addressed to tsar Peter I and other members of the Russian elite, which became the country’s “absolute metaphors to live by” up to present time. Several known and unknown episodes from (...) the history of the reception of Kantian ideas, his followers in Russia, and the transformation of the urban environment of Kant’s life in Königsberg, as it was becoming Kaliningrad, are presented through the prism of this metaphor. Without hoping to make specific recommendations of any use from such metaphorical grounds, this study aims to emphasize the depth, interconnectedness, and basic, metaphysical tension of the relationship between Europe and Russia, which cannot be terminated at will by either side, or by a third party. In a situation where the sides are doomed to dialog, Kant, appropriated by Russia as its “subject,” occupies the unique position of mediator of philosophical understanding and peaceful action. (shrink)

This is the first volume compiling English translations of Leibniz's journal articles on natural philosophy, presenting a selection of 26 articles, only three of which have appeared before in English translation. It also includes in full Leibniz's public controversies with De Catelan, Papin, and Hartsoeker. The articles include work in optics, on the fracture strength of materials, and on motion in a resisting medium, and Leibniz's pioneering applications of his calculus to these issues by construing them as mini-max and inverse (...) tangent problems. Other topics covered by the articles include: criticisms of the Cartesian estimate of motive force and Leibniz's proposal of a different way of estimating force to replace it; a proposed theory of celestial motions and gravitation, and derivation of the inverse square law; challenge problems concerning the isochronous curve and the catenary; a sample of work on gaming theory; and Leibniz's critique of atomism. (shrink)

En este trabajo nos proponemos acercarnos a la noción del conocimiento simbólico en la obra de Gottfried Leibniz, rastreándola en diversos textos de su autoría en que se encuentra diseminada. Comenzamos con la importante distinción entre idea y concepto, que separa el planteo de nuestro autor de las formulaciones de otros como Descartes, Malebranche y Spinoza. Seguimos con la clasificación de los tipos de conceptos que el filósofo de Leipzig lleva acabo, en la que divide a los conceptos simbólicos de (...) los intuitivos. Abordamos después las ventajas epistemológicas que presenta el pensamiento simbólico frente al pensamiento verbal, analizando sus funciones cognitivas y su rol en diferentes tipos de sistemas semióticos. Continuamos asentando el simbolismo epistemológico dentro de una teoría general de la representación, que sostiene cierto isomorfismo entre las esferas del lenguaje, el pensamiento y la realidad. Finalmente, fundamentamos ontológicamente esta analogía representativa estructural en la noción leibniziana de expresión y la vinculamos con el perspectivismo monadológico, poniendo de relieve su cercanía con algunos planteos fenomenológicos y hermenéuticos de nuestros días. (shrink)