Gottfried Wilhelm Leibniz

In his article, Florian Vermeiren attributes to Leibniz – like other interpreters before him – the distinction of two different kinds of relations: 1) relations in the proper sense of the word as, for example, the fatherhood subsisting between Sophroniscus and Socrates, which Leibniz considers situated ‘outside the subjects’ involved; 2) relational properties, such as being a father, inherent in Sophroniscus. The distinction is clearly present in Leibniz’s writings. According to Vermeiren, Leibniz considers ‘purely mental’ only the relations ‘out of (...) the subjects’ and not the relational predicates, by means of which, on the other hand, the individuals of the Leibnizian world would be truly related. In this sense, therefore, Leibniz would admit the reality of relations, which would play an important role in his ontology. At least since 1686 (the year in which he wrote the Discourse), however, Leibniz states that the world is made only of individuals with their internal modifications: just as there are no properties with a leg in one subject and a leg in another, there are no individuals bound together by any kind of material nexus or ‘real’ ties. Thus, if we make a list of all fathers on the one hand and sons on the other, there remains the problem of how to properly connect the fathers exactly with their sons. Attributing to each of two related individuals a relational property is not enough to connect them. Being a father in David must necessarily refer in some way to Solomon as a son. Leibniz is aware of this, as his attempts to analyze relational propositions in his essays on rational grammar show. Given the sentence ‘Cajus is killed by Titius’ for example, Leibniz attempts to reduce it to an inference between a pair of categorical sentences, each of which attributes a relational predicate to the subject. Relations (and relational properties) result from the substances and their modes, “without producing any change” of themselves but only in virtue of a consequence, that is of a logical inference. The image of the world derived so from the Monadology and other Leibnizian writings is that of a world composed of a collection of isolated individuals, independent of each other and lacking mutual connections. Relational properties correspond to internal modifications of each individual: the second term, in the case of binary relations (the ‘external’ one: Helen, if Paris loves Helen) is resolved into an internal representation (of Paris, in this case). It is God who coordinates the various representations of individuals with each other, to result in a harmonious whole. Since relations are a consequence of the existence of the individual substances with their intrinsic properties, God himself can be said to be the creator of relations, in so far as he calls the individuals into existence. And this is exactly what Leibniz states, in his commentary on Temmik’s book. (shrink)

This paper challenges Mugnai’s conceptualist reading of Leibniz’s theory of relations. I specifically question his idea that relational accidents are mental additions to absolute foundations. I examine some of the evidence on which he relies. Most importantly, I question his interpretation of Leibniz’s rejection of purely extrinsic denominations (abbreviated “NPED”) as stating that relations result from non-relational foundations. Mugnai thereby understands Leibniz’s notion of ‘extrinsic’ as ‘relational’ or ‘relative’. Such a reading contradicts both Leibniz’s definition of ‘extrinsic denominations’ and the (...) scholastic meaning of this notion. Furthermore, Leibniz’s use of NPED shows that some relations are intrinsic denominations. Additionally, I argue that conceptual relations cannot do all the work in Leibniz’s metaphysics. Fundamental notions such as expression, order and, most importantly, coexistence rely on non-conceptual relations. (shrink)

Though accepting the traditional view that truth and falsity are properties of propositions and judgments, Leibniz does not refrain from predicating truth and falsity of pre-judgmental items such as ideas, which he considers to be true iff logically consistent, and false otherwise. Elsewhere, however, Leibniz claims that ideas are true or false only insofar as they include the (true or false) affirmation that their object is possible. This paper aims to cast light on Leibniz’s doctrine of ideas as truth-bearers by (...) exploring its historical background. On the one hand, Leibniz’s pronouncements reflect his reaction to the post-Cartesian debates. On the other hand, they appear to be inspired from Aquinas’s doctrine of accidental falsity. (shrink)

The paper first examines the difference between Wolff’s demonstration of my present existence and Descartes’ intuitive connection of my thinking with my existence. The results of this investigation enable us to analyse two controversial answers to the question of the knowledge of existence in Wolff’s works. The first answer is from Jürgen Stolzenberg, who discusses Wolff’s proof of the statement: I am. The second is written by Luigi Cataldi Madonna, who investigates the concept of contingent existence in Wolff’s works. The (...) problems of the interpretations they propose are different. The first uses in his analysis meanings of central terms that were foreign to Wolff. The second does not pay attention to Wolff’s framework and aims. These difficulties in their interpretations distort what Wolff does and plans in his treatment of the knowledge of existence. Wolff builds a demonstration to prove how we know that we are, because for Wolff there is only science if we prove all that we claim. According to him, philosophy is a science. With this paper I plan to clarify the context of Wolff’s demonstration of my present existence as well as the demonstration itself, to which the analysis of the above two interpretations can contribute. (shrink)

This article is written in the memory of Marcelo Dascal, and is conceived as an imaginary answer to a question put by him to the author: what is the point – given a shared non-religious, even atheistic, outlook – in translating (into the Hebrew) of Leibniz’s Théodicée? The two main theses of this imagined answer are: 1. That there is in the Théodicée a moral theory, partly implicit but irreducible and relatively independent of its theological content, and that this theory (...) is based on a paradoxical – but original and important – concept of moral necessity, extracted from the theory of the absolute need to choose the best possible; 2. That this concept of moral necessity may be developed into a theory of responsibility, looking back to the need to give accounts about what has been done (or not done), and forward, to what has to be done (or not) now. (shrink)

O pensamento de Leibniz foi, sem dúvida, essencial para o desenvolvimento das linhas fundamentais da filosofia crítico-transcendental de Kant. A interlocução entre Kant e Leibniz é evidente no decorrer do pensamento kantiano, seja diretamente, nos diversos momentos em que Kant busca um enfrentamento explícito com seu predecessor, seja indiretamente, quando Kant discute com os autores da escolástica alemã que são considerados discípulos de Leibniz Pretendo observar, em particular, que uma das discussões pouco noticiadas, mas de grande relevância para o desenvolvimento (...) do pensamento kantiano, é aquela em relação ao problema da teodiceia. Com isso em foco, meu objetivo nesse capítulo é o de tentar mostrar alguns aspectos do diálogo de Kant com a teodiceia de Leibniz. Primeiro, apresentarei alguns aspectos da teodiceia de Leibniz. Depois, mostrarei o tratamento que Kant dispensa ao problema da teodiceia em alguns de seus escritos iniciais. Por fim, apresentarei o seu tratamento no período crítico, da maneira como se expõe em um artigo de 1791 intitulado Sobre o Fracasso de todas as Tentativas Filosóficas na Teodiceia. De modo complementar, ao abordar o problema no período crítico, farei algumas remissões às três Críticas, às Lições sobre a Doutrina Filosófica da Religião de 1783/84, às Lições de Ética e à Religião nos Limites da Simples Razão de 1793. (shrink)

Nos ocupamos aquí de una cuestión de importancia para la filosofía moderna, y para la filosofía leibniziana en particular, como es el concepto de substancia. Veremos cómo, en Leibniz, la divisibilidad de la materia al infinito y la necesidad de un principio que dé razón de la unidad en la multiplicidad de los elementos que componen todo cuerpo, lo llevan a concebir unidades metafísicas que son su fundamento. Asimismo, la respuesta a esta cuestión alude al problema del cuerpo de una (...) manera que presenta una singular complejidad, y exige seguir cierto itinerario de conceptos, con especial cuidado a las variaciones que el propio Leibniz realiza en su concepción de la substancia a lo largo de la evolución de su filosofía. Finalmente, nos ocupamos de las nociones de unidad y composición, vinculadas al llamado pluralismo substancial leibniziano. (shrink)

In this article, I revisit Leibniz's early views on physical causation, more specifically, his relation to physical occasionalism focusing on the period from 1668 to 1676. An in-depth analysis of the Confession of Nature against the Atheists taken together with the Catholic Demonstrations, Leibniz's correspondence with Jakob Thomasius from 1668/69, and the Pacidius Philalethi (1676) serve as evidence that his position leads to physical occasionalism. This receives further confirmation by taking into account Leibniz's familiarity with Weigel's occasionalism in contrast to (...) Leibniz's later encounter of French occasionalism à la Cordemoy, La Forge, or Malebranche. Leibniz's exposure to Weigel's occasionalism, in turn, helps us better understand Leibniz's later critical reaction to occasionalism and how occasionalism helped him develop his own distinct views on causation as expressed in his mature philosophy. (shrink)

Ce livre s’intéresse à une rencontre : celle de deux philosophes, mais aussi celle de deux siècles et de deux régimes de pensée. Leibniz (1646-1716) et Diderot (1713-1784) appartiennent à deux traditions en apparence opposées : on associe généralement la pensée leibnizienne aux grands systèmes métaphysiques du XVIIe siècle, et celle de Diderot à la mise en pièces de ces édifices par la voie d’une philosophie expérimentale radicalement antisystématique. Pourtant, plusieurs liens entre les deux œuvres sont visibles, qu’il s’agisse d’emprunts (...) conceptuels ou thématiques par Diderot ou de convergences plus difficiles à circonscrire. Le premier objet de ce livre est d’identifier ces liens et de faire le point sur cette sympathie entre les deux philosophies. Mais ce livre s’intéresse aussi à cette rencontre pour ses effets transformateurs, tant sur le plan des concepts, des thèses et des arguments que sur celui des méthodes. Il s’agit alors de voir comment la rencontre avec le leibnizianisme a nourri la pensée diderotienne, comment la lecture du texte leibnizien par Diderot en modifie le sens, comment elle peut parfois en être une interprétation ou un devenir possible. Pour saisir ces transformations, les auteurs ont examiné divers contextes théoriques dans lesquels les pensées de Leibniz et Diderot dialoguent : métaphysique et philosophie de la nature, épistémologie et philosophie des sciences, théorie de la perception et esthétique. À travers ce dialogue, l’ouvrage contribue à une réflexion générale sur les méthodes requises pour mettre en perspective les rapports entre des philosophies à la fois proches et éloignées. (shrink)

In this chapter, we offer a reconstruction of the evolution of Leibniz’s thought concerning the problem of the infinite divisibility of bodies, the tension between actuality, unassignability, and syncategorematicity, and the closely related question of the possibility of infinitesimal quantities, both in physics and in mathematics.Some scholars have argued that syncategorematicity is a mature acquisition, to which Leibniz resorts to solve the question of his infinitesimals – namely the idea that infinitesimals are just signs for Archimedean exhaustions, and their unassignability (...) is a nominalist maneuver. On the contrary, we show that syncategorematicity, as a traditional idea of classical scholasticism, is a feature of young Leibniz’s thinking, from which he moves away in order to solve the same problem, as he gains mathematical knowledge.We have divided Leibniz’s path toward his mature view of infinitesimals into five phases, which are especially significant for reconstructing the entire evolution. In our reconstruction, an important role is played by Leibniz’s text De Quadratura Arithmetica. Based on this and other texts, we dispute the thesis that fictionality coincides with syncategorematicity, and that unassignability can be bypassed. (In this chapter, we employ “syncategorematic” as a shorthand for “eventually identifiable with a procedure of exhaustion” and, as a consequence, “involving only assignable quantities.” We also identify syncategorematicity with potentiality, as suggested by some part of the scholastics, and in Sect. 2.2, we show that the two characterizations are equivalent, provided that “potentiality” is intended in the correct way: namely as in the unending iterative procedures of Greek mathematics.) On the contrary, we maintain that unassignability, as incompatible with the principle of harmony, is the ultimate reason for the fictionality of infinitesimals. (shrink)

In The Fold, Deleuze regards Raymond Ruyer as the most recent of Leibniz’s great disciples. This claim is not self-evident, since Ruyer often criticises Leibniz and stresses the divergence of his theory from Leibniz’s monadological metaphysics. Therefore, while Ruyer does not seem to regard himself as indebted to Leibniz, and as his psychobiology is not always reconcilable with Leibniz’s philosophy, it is necessary to explore what is at stake in Deleuze’s recognition of Ruyer as a Leibnizian thinker. This essay foregrounds (...) the tacit intertwining between Leibniz and Ruyer, which can, on the one hand, contribute to Leibniz’s scholarship and uncover the contemporaneity of his thought, and on the other hand, expose certain revealing Ruyerian moments in Deleuze’s immanent philosophy. (shrink)

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)

Since Leibniz first put forward the sufficient reason law in his philosophical work "The Monadology" (1914), the issue of the law of sufficient reason has aroused heated discussions in the field of logic in our country. The question of whether the law of sufficient reason is the basic law of formal logic was particularly heated in the domestic logic circle in 1978-1980. Since then, there has been little discussion, but from the newly compiled formal logic textbooks published one after another, (...) no consensus has been reached. Although they didn't agree on the question of "whether or not", the two sides elaborated their arguments in detail and put forward some new opinions, thus creating new conditions for solving this problem scientifically. Firstly, this paper analyzes the different viewpoints of both sides of the argument. Secondly, it analyzes whether the law of sufficient reason is the basic law of formal logic from whether Leibniz put forward the law of sufficient reason. Finally, on this basis, a new transformation method is put forward. After this transformation, the law of sufficient reason is an important basic law of deductive logic, which can be juxtaposed with the other three logical laws, such as identity, and coordinated with the "three laws" and complement each other. (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)