LEIBNIZ AND THE TWO SOPHIES is a critical edition of all of the philosophically important material from the correspondence between the philosopher Gottfried Wilhelm Leibniz (1646-1716) and his two royal patronesses, Electress Sophie of Hanover (1630-1714), and her daughter, Queen Sophie Charlotte of Prussia (1668-1705). In this correspondence, Leibniz expounds in a very accessible way his views on topics such as the nature and operation of the mind, innate knowledge, the afterlife, ethics, and human nature. The correspondence (...) also contains the only known philosophical writings by Sophie and Sophie Charlotte, and thus provides a valuable insight into their views and concerns, as well as throwing light on their characters. The texts are accompanied by a substantial introductory essay which sets the context for the correspondence and analyzes its main philosophical themes. (shrink)

In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the (...) class='Hi'>Leibniz operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics. (shrink)

The theory of living beings as machines of nature and the conception of composite substances endowed with conjoined souls, entelechies, or monads, as well as that of organic bodies, were solidified over the course of the transformations of Leibniz's thought that issued in the New System of Nature. On this basis, the monadological versions of a system of nature centered upon the integrated organization ad infinitum of living beings were gradually articulated. Leibniz aimed to spell out a science, (...) or physiology of vital processes, that would be, as much as possible, in agreement with the epistemological exigencies of the complex metaphysical model that he had elaborated. On the one hand, Leibniz offers a critical evaluation of the methodological options that divide the allegiances of the physicians and naturalists who are his contemporaries; what is more, he determines the profile of the analyses and explications that are to be promoted. For This double preoccupation translates into the scientific exchanges and correspondences that accompany the construction of the theory of organic bodies as constituents of machines of nature. The author focuses on the particular case of the propositions concerning the science of the living that stem from his reaction to the work of Georg Ernst Stahl. (shrink)

A pair of deductive systems (S,S’) is Leibniz-linked when S’ is an extension of S and on every algebra there is a map sending each filter of S to a filter of S’ with the same Leibniz congruence. We study this generalization to arbitrary deductive systems of the notion of the strong version of a protoalgebraic deductive system, studied in earlier papers, and of some results recently found for particular non-protoalgebraic deductive systems. The necessary examples and counterexamples found (...) in the literature are described. (shrink)

A filter of a sentential logic ? is Leibniz when it is the smallest one among all the ?-filters on the same algebra having the same Leibniz congruence. This paper studies these filters and the sentential logic ?+ defined by the class of all ?-matrices whose filter is Leibniz, which is called the strong version of ?, in the context of protoalgebraic logics with theorems. Topics studied include an enhanced Correspondence Theorem, characterizations of the weak algebraizability of (...) ?+ and of the explicit definability of Leibniz filters, and several theorems of transfer of metalogical properties from ? to ?+. For finitely equivalential logics stronger results are obtained. Besides the general theory, the paper examines the examples of modal logics, quantum logics and Łukasiewicz's finitely-valued logics. One finds that in some cases the existence of a weak and a strong version of a logic corresponds to well-known situations in the literature, such as the local and the global consequences for normal modal logics; while in others these constructions give an independent interest to the study of other lesser-known logics, such as the lattice-based many-valued logics. (shrink)

One of the more exotic and mysterious features of Leibniz’s later philosophical writings is the harmony between the kingdom of nature and the kingdom of grace. In this paper I show that this harmony is not a single doctrine, but rather a compilation of two doctrines, namely (1) that the order of nature makes possible the rewards and punishments of rational souls, and (2) that the rewards and punishments of rational souls are administered naturally. I argue that the harmony (...) is best considered as Leibniz’s distinctive collation, development, and rebranding of these doctrines, which were not themselves unique to Leibniz, nor uncommon in the seventeenth century. There follows a detailed examination of various concrete examples of the harmony in operation, from which I show that it is essentially the culmination of Leibniz’s lifelong thinking about divine justice. (shrink)

This paper reexamines the historical debate between Leibniz and Newton on the nature of space. According to the traditional reading, Leibniz (in his correspondence with Clarke) produced metaphysical arguments (relying on the Principle of Sufficient Reason and the Principle of Identity of Indiscernibles) in favor of a relational account of space. Newton, according to the traditional account, refuted the metaphysical arguments with the help of an empirical argument based on the bucket experiment. The paper claims that Leibniz’s (...) and Newton’s arguments cannot be understood apart from the distinct dialectics of their respective positions vis-à-vis Descartes’ theory of space and physics. Against the traditional reading, the paper argues that Leibniz and Newton are operating within a different metaphysics and different conceptions of “place,” and that their respective arguments can largely remain intact without undermining the other philosopher’s conception of space. The paper also takes up the task of clarifying the distinction between true and absolute motion, and of explaining the relativity of motion implied by Leibniz’s account. The paper finally argues that the two philosophers have different conceptions of the relation between metaphysics and science, and that Leibniz’s attempt to base physical theory on an underlying metaphysical account of forces renders his account of physics unstable. (shrink)

At the end of 1671 and start of 1672, while in the service of the Archbishop and Elector of Mainz, Leibniz composed his Egypt Plan, which sought to persuade Louis XIV to invade Egypt. Scholars have generally supposed that Leibniz’s rationale for devising the plan was to divert Louis from his intended war with Holland. Little attention has been paid to the religious benefits that Leibniz identified in the plan, and those who do acknowledge them are often (...) quick to downplay them. This tendency to downplay or even dismiss the religious benefits Leibniz claimed of the Egypt Plan is undermotivated and stems from a very superficial reading of the documents that together comprise it. In this paper I argue that we should take seriously Leibniz’s claim that a French invasion of Egypt would bring religious benefits, and that he saw them as important and intrinsically desirable inasmuch as he came to believe that the execution of the plan would lead to the flowering of co-operation and brotherhood among Christians in a show of inter-denominational koinonia, that is, fellowship with other Christians in the participation of shared goals. (shrink)

Leibniz is not commonly numbered amongst canonical writers on toleration. One obvious reason is that, unlike Locke, he wrote no treatise specifically devoted to that doctrine. Another is the enormous amount of energy which he famously devoted to ecclesiastical reunification. Promoting the reunification of Christian churches is an objective quite different from promoting the toleration of different religious faiths – so different, in fact, that they are sometimes even construed as mutually exclusive. Ecclesiastical reunification aims to find agreement at (...) least on the most important doctrines. Religious toleration involves accepting and respecting disagreement even on the most important doctrines. If one regards these two projects as alternative rather than complementary strategies for dealing with religious diversity, Leibniz might more readily be characterised as an ecumenist rather than a tolerationist. Such appears to be the conclusion, at any rate, implicit in the balance of critical literature on these topics: whereas a steady stream of studies has discussed Leibniz’s project of ecclesiastical reunification, only a meager trickle has been devoted to his views on toleration; and some of these studies go so far as to conclude that Leibniz had no doctrine of toleration at all. This paper will attempt to show, on the contrary, that a robust, many-layered, and unusually inclusive doctrine of toleration can be gleaned from Leibniz’s writings. This doctrine operated at least at three different levels: philosophical, theological, and pragmatic. As this implies, the doctrine of religious toleration, rather than being in collision with Leibniz’s core project of ecclesiastical reunification, was an essential element of that very project: it should be seen, in other words, not as a competing goal, but as a necessary first step toward ecclesiastical reunification. Yet at the same time it will also emerge that Leibniz’s doctrine of toleration was no mere function of this intra-Christian project of reunification: rather it was a still more fundamental principle which extended beyond the ecumenical project as well. It had the resources for accepting and respecting irreducible religious diversity and disagreement on points of importance not only between Christian communities, but also between Christians and non-Christians, including, in principle, even the atheists. These points will emerge from a discussion of statements on the philosophical, theological, and pragmatic justifications of religious toleration scattered throughout Leibniz’s sprawling corpus of writings. (shrink)

The main aim of this paper is to show that we can extract an elaborate account of phe- nomenal consciousness from Leibniz’s (1646-1716) writings. Against a prevalent view, which attributes a higher-order reflection account of phenomenal consciousness to Leibniz, it is argued that we should understand Leibniz as holding a first-order concep- tion of it. In this conception, the consciousness aspect of phenomenal consciousness is explained in terms of a specific type of attention. This type of attention, (...) in turn, is accounted for in terms of cognitive appetites aiming at knowledge about a repre- sented object by means of initiating cognitive operations on representational content. Furthermore, against the view that Leibniz holds a reifying account, it is argued that Leibniz accepts an epistemic account of phenomenal character. According to this view, the phenomenal character of phenomenally conscious states rests on the con- fusing effect of imperfect acts of attention directed towards representational contents. Holding this view, Leibniz finds fruitful middle ground between contemporary stan- dard positions like higher-order theories, representationalist conceptions, and qualia accounts of phenomenal consciousness. His position possesses resources to meet sev- eral objections these standard accounts are confronted with. (shrink)

This paper presents a unified framework that explains and extends the already successful applications of the Leibniz operator, the Suszko operator, and the Tarski operator in recent developments in abstract algebraic logic. To this end, we refine Czelakowski’s notion of an S-compatibility operator, and introduce the notion of coherent family of S-compatibility operators, for a sentential logic S. The notion of coherence is a restricted property of commutativity with inverse images by surjective homomorphisms, which is (...) satisfied by both the Leibniz and the Suszko operators. We generalize several constructions and results already existing for the mentioned operators; in particular, the well-known classes of algebras associated with a logic through each of them, and the notions of full generalized model of a logic and a special kind of S-filters. We obtain a General Correspondence Theorem, extending the well-known one from the theory of protoalgebraic logics to arbitrary logics and to more general operators, and strengthening its formulation. We apply the general results to the Leibniz and the Suszko operators, and obtain several characterizations of the main classes of logics in the Leibniz hierarchy by the form of their full generalized models, by old and new properties of the Leibniz operator, and by the behaviour of the Suszko operator. Some of these characterizations complete or extend known ones, for some classes in the hierarchy, thus offering an integrated approach to the Leibniz hierarchy that uncovers some new, nice symmetries. (shrink)

Le statut des corps dans la metaphysique de Leibniz continue de resister a tout effort de reconstitution. Qu'il n'y ait au monde que les substances simples et leurs modifications ne presente plus l'evidence d'une position philosophique achevee. Dans le meilleur des mondes possibles, les ames ne sont jamais sans corps et la moindre portion de matiere renferme un univers de creatures vivantes. Au moment meme ou Leibniz semble embrasser une position idealiste en peuplant le monde d'une infinite d'entites (...) psychiques, ne developpe-t-il pas le concept d'organisme comme en marge de cette metaphysique? Deja, dans les annees ou la celebre theorie de la notion complete servait a penser la substance individuelle, la realite du corps organique imposait l'idee d'une substantialite proprement corporelle. Composition infinie irreductible aux modalites de l'etendue, le corps organique, machine de la nature, force a repenser les conditions d'existence de l'individualite vivante, dont l'ego cartesien n'est plus qu'une problematique modele. La question n'est plus tant de savoir si Leibniz a admis l'existence de substances corporelles en sus des monades, que de comprendre en quoi la realite organique devient le modele pour penser la connexion de toutes les substances, des simples aux composees, des brutes aux raisonnables. Du moi a la monade, comment la necessaire inscription corporelle de l'individualite s'opere-t-elle? De quelles modifications du concept de substance cette exigence s'accompagne-t-elle? (shrink)

In der vorliegenden Arbeit wird Leibniz' wahrscheinlich detailliertestes und ausgefeiltestes System untersucht: ein Kalkül der Einfügung und eine der Konjunktion ähnliche Operation, die er realis abjectio nennt. Das System soll hinreichend detailliert und mit hinreichender Präzision vorgestellt werden, um zu zeigen, daβ es ausgefeilt formal logisch ist und eine Anzahl originärer und wichtiger Züge aufweist. Neben seinem eigenständigen Interesse ist dieses System wichtig wegen seiner Auswirkungen auf andere Aspekte von Leibniz' Logik und Philosophie, und ein weiteres Ziel dieser (...) Arbeit ist, einige dieser Verbindungen aufzuspüren. (shrink)

Repetition in the strict sense of the word, which for Leibniz can only be the product of a finite description, does not know empirical reality at all, since beneath the descriptive level 'discrimina imperceptibilia' always exist that violate the assumption of eternal recurrence of the same. Thus Leibniz comes to the understanding - for speculative reasons, since the total development of the world cannot be the subject of possible experience - that the whole cosmic occurrence follows a course (...) of progress to infinity. - The universal characteristic of progress is now however not amelioration but the variation creating innovation - the transition to the new. Therefore also the world in its restless progress must not become successively better ; it suffices if it is in its course constantly the same but in changeable form complete - two hypotheses with which Leibniz repeatedly operates and which he also advances for the progress of human happiness. (shrink)

Das historische Buch konnen zahlreiche Rechtschreibfehler, fehlende Texte, Bilder, oder einen Index. Kaufer konnen eine kostenlose gescannte Kopie des Originals durch den Verlag. 1890. Nicht dargestellt. Auszug:... sicherere Prognose stellen konnte, schon drei Wochen vor dem Tode des Philosophen an Leibniz'): D. B. de S. vereor, ut brevi nos derelicturus sit, cum phtisis in dies ingravescere videatur. Funf Tage nach dem Tode Spinoza's ubermittelt Schuller diese schmerzliche Nachricht Leibniz und macht ihm dabei gleichzeitig das merkwurdige Anerbieten, er moge (...) das dem Nachlass entnommene, von Spinoza's Hand herruhrende Exemplar der Ethik fur 150 Gulden fur die Bibliothek des Herzogs von Hannover ankaufen: Caeterum te minime celare debui, clarissimum et acutissimum virum Spinozam maxima atrophia conflictatum 21./H-Februar. vitam suam cum morte commutasse. Videtur autem quod inexpectata mortis debilitate praeventus sit, quoniam sine testamento, ultimae voluntatis indice, a nobis discessit. Ethica, quam penes ipsum vidisti, in autogra-cp penes amicum asservatur2) venalisque habetur, si pretio opere tanto condigno persolvatur, ad quod nulli melius, quam Tibi significandum censui, utpote qui operis conscius principis animum dirigere poteris, ut suis sumtibus coematur3). Gegen eine solche unehrerbietige und geschaftsmassige Ausbeutung der litterarischen Hinterlassenschaft Spinoza's mussen die edler veranlagten Junger des Meisters, an ihrer Spitze wol Ludwig Meyer, entschiedene Einsprache erhoben haben. Denn im folgenden Briefe widerruft Schuller in angstlichem Tone sein unpassendes Angebot, und man merkt es den Zeilen an, dass die heftige Erregung, die uber den Nachlass im Amsterdamer Schuler ') Brief II, datirt: 6. Februar 1677. Dass das Luugenubel in seiner Familie hereditar war, ist ubrigens ein Novum. 2) Die... (shrink)

The main aim of our paper is to implement Leibniz's analysis of the conditional right in the framework of a dialogical approach to Public Announcement Logic. According to our view, on one hand: PAL furnishes a dynamic epistemic operator which models communication exchange between different agents that seems to be very close to Leibniz understanding of the dynamics between the truth of a proposition and the knowledge of the truth of that proposition (Leibniz calls the latter (...) certification of its truth); on the other hand, the dialogical approach provides a semantics for the dynamic epistemic operator in the context of conditional right by means of which: (i) the exchange between agents leading to a public announcement amounts to the (contractual) interaction of commitments of both the benefactor and the beneficiary of a conditional right (ii) the notion of certification is understood as an action, namely as a move where the beneficiary asks the benefactor to stand to his commitments, (iii) some restrictions specific to the logical nature of the head and the tail of the conditional right can be implemented by combining PAL with some features of linear logic within the same theory of meaning. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Leibniz and the Two ClocksDavid ScottAnyone familiar with Leibniz’s philosophy in general and with his critique of occasionalism in particular is likely familiar with his example of two clocks. Generally speaking, the example illustrates a range of hypotheses that, according to Leibniz, might possibly explain the connections between substances in the world. The most important of these hypotheses are Leibniz’s own doctrine of the preestablished (...) harmony and the occasionalist—for present purposes, Malebranche’s—doctrine of causation. In Leibniz’s mind at least, the two clocks example (so-called because substances are represented by two clocks) illustrates the superiority of the hypothesis of the preestablished harmony over occasionalism. Whether the example in fact succeeds in this regard is the primary question of this paper.Given the times, Leibniz’s choice of example is understandable. A clock is ideally suited to represent a mechanism, of course; and in view of the general “mechanization of the world view” of that time, the example seems to have been in the air.1 Spring-driven clocks had appeared at the outset of the sixteenth century, and the kind of clock Leibniz seems to have in mind in his example, namely, one driven by a pendulum, was the invention, in about 1656, of Christian Huygens, who was a significant influence on Leibniz. Huygens’s invention in fact provided the impetus for a broadening of the importance and extent of horology.2Although Leibniz’s choice of example was understandable, it was not a happy one, and the general importunity of his use of this example was [End Page 445] recognized by both his contemporary critics and his subsequent commentators.3 In fact his choice of the example becomes almost ironic when it is recalled that Geulincx, who is most commonly associated with the example, was an occasionalist. The operations of two clocks, between which there is a constant and fixed relation, say, of keeping the same time, cannot normally be said to be “related.” The example is more intuitively taken to indicate the random, accidental, unnecessary, and unconnected nature of the otherwise constant and regular relation between the clocks; and so one would think the example more suited to an occasionalist’s position than to that of Leibniz.In what follows I aim to judge the effectiveness—in Leibniz’s own terms—of the two clocks example. In gauging the effectiveness of Leibniz’s use of the example, I expect that a few things can be learned about Leibniz’s system in general and about his critique of occasionalism in particular. My procedure will be to examine separately what I take to be four significant occasions in which Leibniz compares things or substances in the world and clocks. The passages in question date from a period spanning ten years, and in each instance the example is put to service in Leibniz’s attempt to better occasionalism.Beyond this, although the comparison is employed or appraised in slightly different ways each time, the uses to which it is put are basically two. In the first two instances examined below, it is employed primarily to distinguish the preestablished harmony from occasionalism. I will be arguing that, to the extent that it fails to illustrate his point, Leibniz fails adequately to distinguish these two doctrines. This was Arnauld’s criticism.4 In the third and fourth instances, however, the example is employed solely to illustrate certain features of the preestablished harmony. On my analysis, it does not appear to fulfill this role either. [End Page 446]First Use of the ExampleOne of the more well known statements of the two clocks example is from an explanation Leibniz gives to Basnage de Beauval in 1696 of his “New System” (1695):Imagine two clocks or watches which are in perfect agreement. Now this can happen in three ways. The first is that of a natural influence.... The second way of making two clocks, even poor ones, agree is always to assign a skilled craftsman to them who adjusts them and constantly sets them in agreement. The third way is to construct these two timepieces at the beginning with such skill and accuracy that one can... (shrink)

After giving a short summary of the traditional theory of the syllogism, it is shown how the square of opposition reappears in the much more powerful concept logic of Leibniz. Within Leibniz’s algebra of concepts, the categorical forms are formalized straightforwardly by means of the relation of concept-containment plus the operator of concept-negation as ‘S contains P’ and ‘S contains Not-P’, ‘S doesn’t contain P’ and ‘S doesn’t contain Not-P’, respectively. Next we consider Leibniz’s version of (...) the so-called Quantification of the Predicate which consists in the introduction of four additional forms ‘Every S is every P’, ‘Some S is every P’, ‘Every S isn’t some P’, and ‘Some S isn’t some P’. Given the logical interpretation suggested by Leibniz, these unorthodox propositions also form a Square of Opposition which, when added to the traditional Square, yields a “Cube of Opposition”. Finally it is shown that besides the categorical forms, also the non-categorical forms can be formalized within an extension of Leibniz’s logic where “indefinite concepts” X, Y, Z\ function as quantifiers and where individual concepts are introduced as maximally consistent concepts. (shrink)

Leibniz’s Most Determinate Path Principle in Tentamen Anagogicum is an optimization-type law of physics falling into the category of “final cause,” one of “two realms” under discussion there. The other is the “mechanistic/causal.” To be explanatory for Leibniz laws have to be grounded in a causal agency, in the case of the mechanistic realm, the grounding agency is material. I accept, and philosophically defend through a thought experiment, a modern form of this principle, “If a pattern of events (...) is not governed by the laws of chance (are not statistically independent) then there is a causal agency operating to link the events” (The General Version of Leibniz’ Postulate). In Leibniz exegesis, against McDonough, I argue that optimization laws lack an appropriate grounding agency : they are true, predictive and heuristic but not explanatory. So the mechanistic realm is explanatorily fundamental for Leibniz. But Planck maintains the converse: the optimization laws (The Principle of Least Action in his case) are fundamental. (Planck’s Postulate) I defend this postulate against Leibniz and show that if both postulates are right, and a certain plausible condition in theoretical physics holds, the ground for the explanatory power of such laws must lie in Divine Reason. (shrink)

A language for quantum physics is derived from set theory by replacing the classical predicate algebra (Boolean) by a certain quantum predicate algebra (rational projective), time space and the Hamilton-Schroedinger dynamics by a Feynman-like graph dynamics, and the Dirac spin operators by topological switching operators on the graph. The development is described from the basic level of elementary monadic processes to the level of the free Dirac equation.

It is well known that in his logical writings Leibniz typically disregarded the operation of disjunction, confining himself to the theory of conjunction ajid negation. Now, while this fact has been interpreted by Couturat and others as indicating a serious incompleteness of the Leibnizian calculus, it is shown in this paper that actually Leibniz's conjunction-negation logic, with 'est Ens', i. e. 'is possible' as an additional logical operator, is provably equivalent to Boolean algebra. Moreover, already in the (...) Generales Inquisitiones of 1686 Leibniz had established all basic principles that are necessary for a complete axiomatization of "Boolean" algebra. In this sense Leibniz should be acknowledged as the true inventor of the algebra of sets. (shrink)

We add to our relational semantics for system r of relevant implication an s4-Type semantics for necessity, Thus furnishing a semantics for system nr (believed to coincide with e). In an nr-Structure m=(o,K,R,S, ), O is in k, Is an operation on k, And r and s are relations on set k which are restrained by reflexivity, Transitivity and monotonicity requirements. Interpretations on m, Which are restricted by an ordering requirement, Are distinguished from modal evaluations by adequate rules for implication (...) and negation. The main work of the paper goes into proving semantical completeness of nr. The semantics is applied to show that rule gamma holds for nr, And that r and nr are reasonable in the sense of hallden and hence have normal characteristic matrices. (shrink)

Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non-protoalgebraic logics, paralleling the well-known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibniz operator was recently extended to cover the case of, the so-called, protoalgebraic π-institutions. In the present work, following the lead of Czelakowski, an attempt is made at lifting parts of the theory of (...) the Suszko operator to the π-institution framework. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume: Between Leibniz and Kant (The role of pre-established harmony in Hume's philosophy) Vadim Vasilyev 1. Introduction In the history of eighteenth century European philosophy, Hume appears as an important connecting link between Leibniz and Kant. I mean, however, not only the well-known historical fact that Hume "awakened Kant from his dogmatic slumber" (and it was the "dogmatism" ofLeibnizian metaphysics), but I shall try to show that (...) it is true from the philosophical point of view as well. The first problem I would like to discuss is the actual relationship between Hume and Leibniz. Hume never openly criticized the views of Leibniz. On the other hand, Hume did not admit himself to be a follower of him. Did Hume everread any works ofLeibniz? Hume has never said thathe did. Hume also hasn't directly quoted these works, so it looks like Hume wasn't acquainted with them at all. Nonetheless, we can show that already in 1739 Hume had known Theodicée which can be considered as the main treatise ofLeibniz. In his Abstract Hume writes: The celebratedMonsieurLeibnitz has observed it tobe a defect in the common systems of logic, that they are very copious when they explain the operations ofthe understanding in the forming ofdemonstrations, but are too concise when they treat of probabilities, and those other measures of evidence on which life and action entirely depend, and which are our guides even in most of our philosophical speculations. In this censure, he comprehends the essay on human understanding, Ie recherche de la vérité, and l'art dépenser.1 The fragment is a rendering of the following passage from Theodicée: caril n'y a rien de plus impartaitqui nostre Logique, lorsqu'on va au delà des argumens nécessaires; et les plus excellens philosophes de nostre temps, tels que les Auteurs de l'Art de penser, de la Recherche de la vérité, et de l'Essai sur Volume XLX Number 1 19 VADIMVASILYEV l'entendment, ont été fort éloignés de nous marquer les vrais moyens propres à aider cette faculté qui nous doit faire peser les apparences du vrait et du faux: sans parler de l'art d'inventer.2 So, it is highly probable that Hume knew Theodicée. The ideas ofLeibniz in Hume's philosophy The most important philosophical ideas of Theodicée are: the definitions ofpossibility and oftwo kinds ofnecessity, a theory of"the best possible world" and a conception ofthe pre-established harmony. As we shall see, all these ideas, one way or another, were assimilated by Hume. In his Theodicée Leibniz states that a distinction should be made between two kinds of necessity and, correspondingly, between two kinds ofnecessary knowledge: metaphysical and moral.? ne faut done que bien entendre des distinctions, comme celle que nous avons pressée bien souvent entre le necessaire et le certain, et entre la nécessité métaphysique et la nécessité morale. (Theodicée, 284, par. 282) Metaphysical or mathematical truths are such that propositions which are opposite to them imply contradictions. Or les vérités de la Raison sont de deux sortes; les unes sont ce qu'on appelle les Vérités Eternelles, qui sont abolument nécessaires, en sorte que l'opposé implique contradiction. (Theodicée, 50, par. 2) Not so regarding the moral truths; the opposite statements may be false but they imply no contradictions and are possible: "? est vray qu'il n'y auroit point eu de contradiction dans la supposition que Spinosa fût mort à Leide, et non pas à La Haye; il n'y auroit rien de si possible" (Theodicée, 218, par. 174). The possibility is equivalent to logical consistency and what is possible may be distinctly conceived: puisqu'il y a bien des choses qui ne sont jamais arrivées et n'arriveront jamais, et qui cependant sont concevables distinctement, et n'impliquent aucune contradiction, comment peut on dire qu'elles sont absolument impossibles? (Theodicée, 257, par. 234) 20Hume Studies HUME: BETWEEN LEIBNIZ AND KANT Hume uses all these definitions. The following fragment is a good example. The non-existence ofany being, without exception, is as clear and distinct an... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume: Between Leibniz and Kant (The role of pre-established harmony in Hume's philosophy) Vadim Vasilyev 1. Introduction In the history of eighteenth century European philosophy, Hume appears as an important connecting link between Leibniz and Kant. I mean, however, not only the well-known historical fact that Hume "awakened Kant from his dogmatic slumber" (and it was the "dogmatism" ofLeibnizian metaphysics), but I shall try to show that (...) it is true from the philosophical point of view as well. The first problem I would like to discuss is the actual relationship between Hume and Leibniz. Hume never openly criticized the views of Leibniz. On the other hand, Hume did not admit himself to be a follower of him. Did Hume everread any works ofLeibniz? Hume has never said thathe did. Hume also hasn't directly quoted these works, so it looks like Hume wasn't acquainted with them at all. Nonetheless, we can show that already in 1739 Hume had known Theodicée which can be considered as the main treatise ofLeibniz. In his Abstract Hume writes: The celebratedMonsieurLeibnitz has observed it tobe a defect in the common systems of logic, that they are very copious when they explain the operations ofthe understanding in the forming ofdemonstrations, but are too concise when they treat of probabilities, and those other measures of evidence on which life and action entirely depend, and which are our guides even in most of our philosophical speculations. In this censure, he comprehends the essay on human understanding, Ie recherche de la vérité, and l'art dépenser.1 The fragment is a rendering of the following passage from Theodicée: caril n'y a rien de plus impartaitqui nostre Logique, lorsqu'on va au delà des argumens nécessaires; et les plus excellens philosophes de nostre temps, tels que les Auteurs de l'Art de penser, de la Recherche de la vérité, et de l'Essai sur Volume XLX Number 1 19 VADIMVASILYEV l'entendment, ont été fort éloignés de nous marquer les vrais moyens propres à aider cette faculté qui nous doit faire peser les apparences du vrait et du faux: sans parler de l'art d'inventer.2 So, it is highly probable that Hume knew Theodicée. The ideas ofLeibniz in Hume's philosophy The most important philosophical ideas of Theodicée are: the definitions ofpossibility and oftwo kinds ofnecessity, a theory of"the best possible world" and a conception ofthe pre-established harmony. As we shall see, all these ideas, one way or another, were assimilated by Hume. In his Theodicée Leibniz states that a distinction should be made between two kinds of necessity and, correspondingly, between two kinds ofnecessary knowledge: metaphysical and moral.? ne faut done que bien entendre des distinctions, comme celle que nous avons pressée bien souvent entre le necessaire et le certain, et entre la nécessité métaphysique et la nécessité morale. (Theodicée, 284, par. 282) Metaphysical or mathematical truths are such that propositions which are opposite to them imply contradictions. Or les vérités de la Raison sont de deux sortes; les unes sont ce qu'on appelle les Vérités Eternelles, qui sont abolument nécessaires, en sorte que l'opposé implique contradiction. (Theodicée, 50, par. 2) Not so regarding the moral truths; the opposite statements may be false but they imply no contradictions and are possible: "? est vray qu'il n'y auroit point eu de contradiction dans la supposition que Spinosa fût mort à Leide, et non pas à La Haye; il n'y auroit rien de si possible" (Theodicée, 218, par. 174). The possibility is equivalent to logical consistency and what is possible may be distinctly conceived: puisqu'il y a bien des choses qui ne sont jamais arrivées et n'arriveront jamais, et qui cependant sont concevables distinctement, et n'impliquent aucune contradiction, comment peut on dire qu'elles sont absolument impossibles? (Theodicée, 257, par. 234) 20Hume Studies HUME: BETWEEN LEIBNIZ AND KANT Hume uses all these definitions. The following fragment is a good example. The non-existence ofany being, without exception, is as clear and distinct an... (shrink)

My aim in this chapter is to explain how and why all human cognition depends on the body for Leibniz. I will show that there are three types of dependence: (a) the body is needed in order to supply materials, or content, for thinking; (b) the body is needed in order to give us the opportunity for the discovery of innate ideas; and (c) the body is needed in order to provide sensory notions as vehicles of thought. The third (...) type is intimately connected to the faculty of the imagination, which supplies the sensory vehicles of thought. Hence, the paper will also examine Leibniz’s account of that faculty and its operations. Before doing any of this, however, I will address the elephant in the room: Leibniz’s claim that mind and body do not interact at all, metaphysically speaking. The correspondence between mind and body is merely a matter of what he calls ‘pre-established harmony’. At first glance, this Leibnizian doctrine may suggest a radical disembodiment of all human cognition. Yet, I will argue that this is not the case and that, quite to the contrary, pre-established harmony requires that cognition is embodied in one important sense. (shrink)

This article discusses some reasons for taking a reconstructive approach to the argumentative structure of Leibniz’s metaphysics. One reason is the fragmentary nature of the countless notes and letters that constitute by far the largest part of Leibniz‘s philosophical output. Another reason is that conjecturing how the many isolated arguments proposed by Leibniz fit into a large-scale argumentative structure could yield insights into how Leibniz made use of the method of intuition – both in his analysis (...) of mind and in his analysis of matter. Contemporary critics have objected that the method of intuition leads to philosophical conservatism, arbitrary choices between conflicting intuitions, and a preoccupation with psychological facts rather than with reality. By contrast, reconstructing the methodology behind Leibniz’s metaphysics could indicate how intuitions could be used in a way that sidesteps these problems. Leibniz gives priority to intuitions concerning the structure of mental operations over intuitions concerning the structure of material objects; this is why intuitions concerning the structure of material objects can be replaced by innovative philosophical theories; these theories, however, make use of metaphysical concepts implied by the analysis of mind and, thereby, can capture facts both about psychology and about the structure of extra-mental reality. (shrink)

When Heidegger pursues his destructive interpretation of Leibniz's doctrine of judgment, he identifies a principle of abyssal ground and a concealed metaphysics of truth that undermine the priority of logic with respect to ontology. His reading turns on an account of Leibniz's methodological generation of metaphysical principles and the relation between reason and identity, which, I argue, is at once deeply flawed and extremely productive. This essay pursues the implications of Heidegger's quickly abandoned suggestion that Leibniz's principle (...) of identity is reflexively self-grounding, arguing that this claim makes possible a rigorous interpretation of Leibnizian method as an abyssal logic of repetition. I hold that the identification of such a methodology requires a modified account of the metaphysics of truth operative in Leibniz that reinvigorates Heidegger's reading even while moving beyond his now exhausted trope of a hidden presupposition of subjectivity. (shrink)

Kant’s avowed commitment to the basic principles of Leibniz’s metaphysics is evident throughout the critical project and stated explicitly in the Prize Essay. However, it is not until the Critique of Judgment, wherein Kant recognizes that Judgment operating in its reflective mood can engender synthetic a priori claims, that Kant is fully capable of appropriating the basic tenets of Leibniz’s metaphysics. This paper examines Kant’s treatment of Leibniz from the perspective of the Critique of Judgment. It is (...) argued that from this vantage point the metaphysics of Leibniz is viewed as fundamental for Kant’s critical project. Moreover, it is argued that it is not until the retrieval of Leibniz’s metaphysics that Kant has a basis for seeking the unity of pure and practical reason. (shrink)

The main purpose of this article is to present new material concerning Leibniz's use of indivisibles and infinitesimals in his early mathematical texts. Most of these texts are contained in hitherto unpublished manuscripts and are soon to be printed in volume VII, 4 of the Academy Edition. They present examples which illustrate how Leibniz operated with concepts such as indivisibles and infinitesimals in that period of his development.

Comprendre ce que les philosophes du XVIIe siècle entendaient par représentation est essentiel à l'intelligence de leurs conceptions des idées et de la vérité. Ce livre renouvelle notre approche du problème à travers des lectures de Descartes, Leibniz, Locke, Pascal, en reliant leurs analyses philosophiques à leurs textes scientifiques. Les figures de la Dioptrique et de la Géométrie éclairent chez Descartes le contenu de l'idée sensible, le rapport du clair et du confus, la nature de la couleur et celle (...) de l'existence. Les anamorphoses de l'Essai sur l'entendement humain de Locke donnent à voir comment les idées renvoient aux choses. Et l'hexagramme pascalien raconte l'herméneutique des Pensées. La représentation classique s'avère l'effet d'une transformation qui affecte en même temps la science et la philosophie. À l'encontre des lectures qui ont insisté sur les filiations avec les pensées médiévales et tenté de réduire la nouveauté de la pensée classique, ce livre retrouve une thèse essentielle de Michel Foucault dans Les Mots et les Choses sur la rupture inaugurant l'âge classique. Mais il découvre dans cette rupture l'effet d'une opération matérielle, qui conduit à un nouveau mode d'existence concret des images et des signes dans les textes du savoir, analysable à l'intérieur de dispositifs textuels. Ce qui l'amène enfin à déplacer profondément les analyses de Foucault et à interroger les présupposés de son archéologie du savoir. (shrink)

Many of the problems traditionally related to the interpretation of Leibniz' theory of relations may be seen in a better light considering essentially two factors: 1) the different plans (ontological, metaphysical, psychological and logical-linguistic) implied by Leibniz reflections on the subject; 2) the reference to scholastic and late-scholastic texts read or consulted by Leibniz. Relations for Leibniz are, from a metaphysical point of view, denominations only seemingly external, they are in reality denominationes intrinsecae, and are founded (...) on the general connection of all things. From a psychological point of view they are abstract entities that our mind builds by resemblance. From an ontological point of view they are individual accidents inherent to the substances. From a logical-linguistic point of view they are abstract structures that connect the one to the other at least two subjects. The propositions in which they appear, as for example the proposition “Paris loves Helen” are transformed by Leibniz in equivalent propositions joined by operators, which in medieval logic were known as termini reduplicantes (terms which define mostly intensional contexts). This may be seen with sufficient clarity examining the last part, until now inedited, of the famous passage about Paris and Helen published by Couturat in his Opuscules. (shrink)

In this dissertation it is argued that Kant's critique of Leibniz as found in the amphiboly chapter of the Critique of Pure Reason derives from his theory of reflection. It is argued further that this unfocused and fragmentary amphiboly chapter, which contains the Leibniz-critique, can be seen to have a previously unsuspected unity to it. The keys to perceiving this unity are the appendix's purpose, structure and mosaic composition. ;The primary purpose of the appendix is not to present (...) Kant's criticisms of Leibniz as is commonly thought, but rather it is to sketch his theory of reflection. Not only is this attested to by Kant himself , it is also made evident by the structure of the appendix. Structurally, the appendix is built around an introduction to the operation of transcendental reflection and a discussion of the concepts of reflection, this being the structure of each of the first three sections. By means of each pair of concepts of reflection Kant claims to summarize the basic tenets and origin of Leibniz's philosophy. Kant also claims that Leibnizls whole philosophy rests on one seminal error, which will be shown to be the omission of the operation of transcendental reflection. To be sure, Kant claims Leibniz made a number of other errors, but these various errors all derive from the omission of transcendental reflection. ;While this omission can be used to explain the other more well-known epistemological mistakes with which Kant charges Leibniz, it is undeniable that there are certain textual difficulties with the appendix. These can be dealt with by the hypothesis that the different sections were composed at different times and than pieced together without detailed revisions. If such a mosaic composition is granted, then some allowance can be made for the noticeable incongruities between these sections and for occasional problematic passages. This does not, however, warrant the claim that the appendix is not properly placed or unimportant. On the contrary, supplemented by clearer statements of Kant's theory of reflection and of his Leibniz-critique, the following interpretation shows that the appendix is properly placed and integral to the primary aims of the Critique of Pure Reason. (shrink)

The book offers the first analysis of the influence exercised by the concept of space on the emergence and continuing operation of international law. By adopting a historical perspective and analysing work of two central early modern thinkers – Leibniz and Hobbes – it offers a significant addition to a limited range of resources on early modern history of international law. The book traces links between concepts of space, universality, human cognition, law, and international law in these two early (...) modern thinkers in a comparative fashion. Through this analysis, the book demonstrates the dependency of the contemporary international law on the Hobbesian concept of space. Although some Leibnizian elements continue to operate, they are distorted. This continuing operation of Leibnizian elements is explained by the inability of international law, which is based on the Hobbesian concept of space, to ensure universality of its normative foundation. (shrink)

In General Inquiries on the Analysis of Notions and Truths, Leibniz articulates for the first time his favourite solution to the problem of contingency and displays the main features of his logical calculus. Leibniz composed the work in 1686, the same year in which he began to correspond with Arnauld and wrote the Discourse on Metaphysics. General Inquiries supplements these contemporary entries in Leibniz's philosophical oeuvre and demonstrates the intimate connection that links Leibniz's philosophy with the (...) attempt to create a new kind of logic. This edition presents the text and translation of the General Inquiries along with an introduction and commentary. Given the composite structure of the text, where logic and metaphysics strongly intertwine, Mugnai's introduction falls into two sections, respectively dedicated to logic and metaphysics. The first section ('Logic') begins with a preliminary account of Leibniz's project for a universal characteristic and focuses on the relationships between rational grammar and logic, and discusses the general structure and the main ingredients of Leibniz's logical calculus. The second section ('Metaphysics') is centred on the problem of contingency, which occupied Leibniz until the end of his life. Mugnai provides an account of the problem, and details Leibniz's proposed solution, based on the concept of infinite analysis. (shrink)

Bringing together Leibniz's writings on God and religion for the very first time, Leibniz on God and Religion: A Reader reflects the growing importance now placed on Leibniz's philosophical theology. This reader features a wealth of material, from journal articles and book reviews published in Leibniz's lifetime to private notes and essays, as well as items from his correspondence. Organised thematically into the following sections, this reader captures the changes in Leibniz's thinking over the course (...) of his career: The Catholic Demonstrations The existence and nature of God Reason and faith Ethics and the love of God The Bible Miracles and mysteries The churches and their doctrines Grace and predestination Sin, evil, and theodicy The afterlife Non-Christian religions In preparing this reader, Strickland has returned to Leibniz's original manuscripts to ensure accurate translations of key texts, the majority of which have not been available in English before. The reader also contains a number of texts previously unpublished in any form. Alongside the translations, this reader contains an introductory essay, explanatory notes on all of the texts, and suggestions for further reading. This valuable sourcebook enables students of all levels to achieve a well-rounded understanding of Leibniz's philosophical theology. (shrink)

_The first unabridged English translation of the correspondence between Gottfried Wilhelm Leibniz and Georg Ernst Stahl detailing their opposing philosophies_ The correspondence between the eighteenth-century mathematician and philosopher G. W. Leibniz and G. E. Stahl, a chemist and physician at the court of King Friedrich Wilhelm I of Prussia, known as the Leibniz-Stahl Controversy, is one of the most important intellectual contributions on theoretical issues concerning pre-biological thinking. Editors François Duchesneau and Justin E. H. Smith offer readers (...) the first fully annotated English translation of this fascinating exchange of philosophical views on divine action, the order of nature, causality and teleology, and the soul-body relationship. (shrink)

Leibniz standardly associates “mechanism” with extended material bodies and their aggregates. In this paper, I identify and analyze a further distinct sense of “mechanism” in Leibniz that extends, by analogy, beyond the domain of material bodies and applies to the operations of immaterial substances such as the monads that serve, for Leibniz, as the metaphysical foundations of physical reality. I argue that in this sense, Leibniz understands “mechanism” as an intelligible process that is capable of providing (...) a sufficient reason for a series of changes. I then apply these findings to enrich our understanding of Leibniz’s well-known mill argument in Monadology ¶17: although material machines and mechanisms cannot produce perceptions, the perceptual activity of immaterial monads is to be understood as “mechanical” according to this analogical sense. (shrink)

This paper focuses on Leibniz’s conception of modality and its application to the issue of natural laws. The core of Leibniz’s investigation of the modality of natural laws lays in the distinction between necessary, geometrical laws on the one hand, and contingent, physical laws of nature on the other. For Leibniz, the contingency of physical laws entailed the assumption of the existence of an additional form of causality beyond mechanical or efficient ones. While geometrical truths, being necessary, (...) do not require the use of the principle of sufficient reason, physical laws are not strictly determined by geometry and therefore are logically distinct from geometrical laws. As a consequence, the set of laws that regulate the physical laws could have been created otherwise by God. However, in addition to this, the contingency of natural laws does not consist only in the fact that God has chosen them over other possible ones. On the contrary, Leibniz understood the status of natural laws as arising from the action internal to physical substances. Hence the actuality of physical laws results from a causal power that is inherent to substances rather than being the mere consequence of the way God arranged the relations between physical objects. Focusing on three instances of Leibniz’s treatment of contingency in physics, this paper argues that, in order to account for the contingency of physical laws, Leibniz maintained that final causes, in addition to efficient and mechanical ones, must operate in physical processes and operations. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

The Discourse on Metaphysics is one of Leibniz's fundamental works. Written around January 1686, it is the most accomplished systematic expression of Leibniz's philosophy in the 1680s, the period in which Leibniz's philosophy reached maturity. Leibniz's goal in the Discourse is to give a metaphysics for Christianity; that is, to provide the answers that he believes Christians should give to the basic metaphysical questions. Why does the world exist? What is the world like? What kinds of (...) things exist? And what is the place of human beings in the world? To this purpose Leibniz discusses some of the most traditional topics of metaphysics, such as the nature of God, the purpose of God in creating the world, the nature of substance, the possibility of miracles, the nature of our knowledge, free will, and the justice behind salvation and damnation. This volume provides a new translation of the Discourse, complete with a critical introduction and a comprehensive philosophical commentary. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

About the text and translation -- The Monadology -- The structure of the Monadology -- The Monadology : text with running commentary -- Appendix: Theodicy -- The principles of nature and grace, founded on reason -- Leibniz to Nicole Remond : appendix on monads.