Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these (...) components of Leibniz’s theory can be represented for investigation by means of automated theorem provers and finite model builders. The fundamental theorem of Leibniz’s theory is derived using these tools. (shrink)

Leibniz propôs que demonstrações fossem reformuladas como deduções a partir de identidades, e que proposições do tipo A = A fossem a fonte única de verdade. Neste artigo, procuro explicar essa teoria da prova (e do conhecimento), assim como seus conceitos elementares, ou seja, os conceitos de identidade, verdade (ou possibilidade) e proposição (inclusive a teoria leibniziana da redutibilidade a proposições sujeito-predicado). Leibniz proposed that demonstrations be reformulated as deductions from identities, and that propositions of the type A = A (...) be the only source of truth. In this article, I aim to explain this theory of proof (and knowledge), as well as its elementary concepts, such as identity, truth (or possibility) and proposition (including Leibniz's theory of reducibility of propositions to subject-predicate form). (shrink)

The aim of this paper is to trace in Leibniz’s drafts the sketched outline of a conceptual framework he organized around the key concept of ‘requisite’. We are faced with the project of a semi-formal theory of conditions, whose logical skeleton can have a lot of different interpretations. In particular, it is well suited to capture some crucial relations of ontological dependence. Firstly the area of ‘mediate requisites’ is explored - where causal and temporal relations are dealt with (...) on the basis of a general theory of ‘consequence’.Then the study of ‘immediate requisites’ is taken into account - a true sample of mereological inquiry, where Leibniz strives for a unitary treatment of part-whole relation, conceptual inclusion and inherence. Far from simply conflating these relations one with another and with causality, therefore, Leibniz tried to spell them out, while at the same time understanding them within a single conceptual framework. (shrink)

The aim of this paper is to trace in Leibniz’s drafts the sketched outline of a conceptual framework he organized around the key concept of ‘requisite’. We are faced with the project of a semi-formal theory of conditions, whose logical skeleton can have a lot of different interpretations. In particular, it is well suited to capture some crucial relations of ontological dependence. Firstly the area of ‘mediate requisites’ is explored - where causal and temporal relations are dealt with (...) on the basis of a general theory of ‘consequence’.Then the study of ‘immediate requisites’ is taken into account - a true sample of mereological inquiry, where Leibniz strives for a unitary treatment of part-whole relation, conceptual inclusion and inherence. Far from simply conflating these relations one with another and with causality, therefore, Leibniz tried to spell them out, while at the same time understanding them within a single conceptual framework. (shrink)

Many interpreters have supposed that the root of contingency in Leibniz's thought is that it is contingent rather than necessary that God chooses to create the best possible world. It is far from clear, however, that Leibniz believed this. This chapter argues that Leibniz did believe two theories of contingency: one based on the notion of a thing's being possible in itself whether or not a perfectly wise and good God could choose it, and one based on an identification of (...) necessity with provability, where an infinite analysis does not count as a proof. It emerges that Leibniz's conception of possible worlds is not exactly the same as that now used in possible worlds semantics. (shrink)

Leibniz’s metaphysics has been cited as a source of the dynamic and organic worldview of romantic Naturphilosophie. This chapter evaluates that claim by examining two distinct lineages of Leibniz’s metaphysical conception of dynamic appetition. On one hand, by demonstrating the existence of a “vis viva” in inanimate objects and by ascribing two distinct powers—perception and appetition—to all plants and animals as well as to his incorporeal “monads,” Leibniz seemed to restore force to physics and experience and intentionality to (...) animals. On the other hand, on account of the publication history of his writings, Leibniz’s pre-established harmony and preformation theory were seen by most philosophers before Herder and Schelling as reducing humans as well as animals to machines without free-will and their development to a mechanically predetermined succession of states. While appreciation of Leibniz’s views on activity and creativity in nature did increase towards the end of the century, other philosophical antecedents for the “drive” motif in German philosophy should be considered. (shrink)

In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with (...) Leibniz's modal metaphysics of complete individual concepts. The fundamental theorem of Leibniz's modal metaphysics of concepts is proved, namely, whenever an object x has F contingently, then (i) the individual concept of x contains the concept F and (ii) there is a (counterpart) complete individual concept y which doesn't contain the concept F and which `appears' at some other possible world. Finally, the author shows how the concept containment theory of truth can be made precise and made consistent with a modern conception of truth. (shrink)

In this article I argue that Hutcheson has a theory of obligation that is different in important ways from the views of his predecessors and that his theory may not be as problematic as critics have claimed. In section (I) I sketch a brief picture of the rich conceptual landscape surrounding the concept of obligation in the Early Modern period. I focus on the five figures Hutcheson explicitly references: Hugo Grotius, Samuel Pufendorf, their French translator and commentator Jean (...) Barbeyrac, as well as G. W. Leibniz and Richard Cumberland. In section (II) I offer an account of Hutcheson’s theory of obligation and illustrate that not only does Hutcheson have a view on what previous figures called the source, end, and object of obligation, he also focuses on the epistemological question of the origin of our idea of obligation as opposed to the metaphysical question of the efficient cause of obligation. Furthermore, although Hutcheson shares with his predecessors the idea that obligation implies a certain kind of necessity, he conceives of this necessity in a unique way, namely in terms of the necessity of a perception. In section (III) I defend Hutcheson’s theory of obligation against three objections: 1. that it makes a sham of obligation by locating its source within the human being, 2. that it is reducible to divine command theory, and 3. that, in the end, Hutcheson has no real or meaningful theory of obligation. My hope is that, at the very least, appraising these objections helps further clarify the theory of obligation that Hutcheson presents in his works. (shrink)

Leibniz uses the concept of probability in both epistemic and non-epistemic contexts, as do many of his contemporaries. Some commentators have claimed that this dual-use is inexact or confused. In this paper, I describe Leibniz’s understanding of the concept of probability and discuss its dual usage in his work. Then, building on Leibniz’s creation theory, in conjunction with Russell’s interpretation of the Principle of Sufficient Reason, I endeavor to justify this dual usage and to show that this (...) justification is also valuable for the contemporary discussion of the concept of probability. Published on 2022-12-28 10:04:03. (shrink)

Cherchant à refonder l’édifice euclidien, Leibniz a formulé une Caractéristique géométrique qui annonce les concepts géneraux de la théorie des ensembles. Dans ce cadre, il a pu en particulier formaliser sa conception du continu. L’intérêt du Pacidius Philalethi (1676) est de montrer qu’en choisissant la conception intensionnelle du continu -position qu’il ne dementira jamais- il sélectionne parmi les images duales celle dont se déduit le changement qualitatif, base d’une philosophie naturelle qui soutiendra encore la dynamique ultérieure. Une tâche se (...) dessine maintenant, soit déduire la nécessité d’un mouvement universei et infiniment varié à partir de ses conditions topologiques.We know that Leibniz intended to bring new foundations to the euclidean geometry and he has according to this view formulate a Characteristica geometrica which announces few general concepts of set theory. Parlicularly he tried to formalise his conception of continuity. Before the main interest of the Pacidius Philalethi (1676) is here: showing us that Leibniz when he chooses an intensional conception of continuity he chooses in the same time the dual image from which be can deduce the qualitative variation. We reckon again these conception at the grounds of his later philosophy of nature. But now we have to follow Leibniz demostrating how universal and infinite variations flow from its topological conditions. (shrink)

Cherchant à refonder l’édifice euclidien, Leibniz a formulé une Caractéristique géométrique qui annonce les concepts géneraux de la théorie des ensembles. Dans ce cadre, il a pu en particulier formaliser sa conception du continu. L’intérêt du Pacidius Philalethi (1676) est de montrer qu’en choisissant la conception intensionnelle du continu -position qu’il ne dementira jamais- il sélectionne parmi les images duales celle dont se déduit le changement qualitatif, base d’une philosophie naturelle qui soutiendra encore la dynamique ultérieure. Une tâche se (...) dessine maintenant, soit déduire la nécessité d’un mouvement universei et infiniment varié à partir de ses conditions topologiques.We know that Leibniz intended to bring new foundations to the euclidean geometry and he has according to this view formulate a Characteristica geometrica which announces few general concepts of set theory. Parlicularly he tried to formalise his conception of continuity. Before the main interest of the Pacidius Philalethi (1676) is here: showing us that Leibniz when he chooses an intensional conception of continuity he chooses in the same time the dual image from which be can deduce the qualitative variation. We reckon again these conception at the grounds of his later philosophy of nature. But now we have to follow Leibniz demostrating how universal and infinite variations flow from its topological conditions. (shrink)

In his well-known Discourse on Metaphysics , Leibniz puts individual substance at the basis of metaphysical building. In so doing, he connects himself to a venerable tradition. His theory of individual concept, however, breaks with another idea of the same tradition, that no account of the individual as such can be given. Contrary to what has been commonly accepted, Leibniz’s intuitions are not the mere result of the transcription of subject-predicate logic, nor of the uncritical persistence of some (...) old metaphysical assumptions. They grow, instead, from an unprejudiced inquiry about our basic ontological framework, where logic of truth, linguistic analysis, and phenomenological experience of the mind’s life are tightly interwoven. Leibniz’s struggle for a concept capable of grasping concrete individuals as such is pursued in an age of great paradigm changes – from the Scholastic background to Hobbes’s nominalism to the Cartesian ‘way of ideas’ or Spinoza’s substance metaphysics – when the relationships among words, ideas and things are intensively discussed and wholly reshaped. This is the context where the genesis and significance of Leibniz’s theory of ‘complete being’ and its concept are reconstrued. The result is a fresh look at some of the most perplexing issues in Leibniz scholarship, like his ideas about individual identity and the thesis that all its properties are essential to an individual. The questions Leibniz faces, and to which his theory of individual substance aims to answer, are yet, to a large extent, those of contemporary metaphysics: how to trace a categorial framework? How to distinguish concrete and abstract items? What is the metaphysical basis of linguistic predication? How is trans-temporal sameness assured? How to make sense of essential attributions? In this ontological framework Leibniz’s further questions about the destiny of human individuals and their history are spelt out. Maybe his answers also have something to tell us. This book is aimed at all who are interested in Leibniz’s philosophy, history of early modern philosophy and metaphysical issues in their historical development. (shrink)

Hegel’s Philosophy of Nature begins with the concepts of space and time, and all of the concepts and phenomena that follow in the text are spatio-temporal. But the actual content of Hegel’s theory of space and time has remained obscure despite two centuries of interpretation, and obscure for at least two reasons. First, it is unclear how Hegel’s theory relates to those of his immediate predecessors (Newton, Leibniz, Kant) as well as other theories in the history (...) of philosophy. Second, the theoretical function to be played by this theory of space and time has remained unclear. In this paper, we clarify the first issue by interpreting Hegel’s theory as a theory of space-time, and we clarify the second issue by interpreting that theory as securing the theoretical possibility of motion. Of course, it will not be the same theory of space-time as the one that proceeds from modern relativistic physics; but designating Hegel’s theory as a theory of space-time helps to mark it out from its most prominent predecessors and helps to make sense of some of its most distinctive features—particularly Hegel’s insistence that time has three dimensions just as space does. This latter feature—the three-dimensionality of time—serves to distinguish Hegel’s view both from the classical mechanics of Newton and Kant (in which time does not interact with the spatial directions) and from contemporary relativistic physics (in which there is such interaction but time is only a single dimension added to the spatial dimensions). In Hegelian space-time, three-dimensional time is the flip side of three-dimensional space—it is this conception that makes Hegel’s view so distinctive. (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)

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)

Three different notions of concepts are outlined: one derives from Leibniz, while the other two derive from Frege. The Leibnizian notion is the subject of his "calculus of concepts" (which is really an algebra). One notion of concept from Frege is what we would call a "property", so that when Frege says "x falls under the concept F", we would say "x instantiates F" or "x exemplifies F". The other notion of concept from Frege is that of the (...) notion of sense, which played various roles within Frege's theory. This notion of concept can be generalized and, as such, accounts for our intuitive talk of "x's concept of ...", where the ellipsis can be filled in with a name for individual, a property, or a relation, etc. After outlining these three notions, I then discuss how (axiomatic) object theory offers a distinct, precise regimentation of each of the three notions. (shrink)

In the second edition of Hermann Cohen’s Kant’s Theory of Experience, he abandons the interpretation of Kant’s Anticipations of Perception that he gave in the first edition, in favourof a radically different one. On his early interpretation, the Anticipations is largely of psychological interest for its influence on, and continuing significance for, physiological psychology and psychophysics. But on his mature interpretation, it defends the superiority of a dynamic conception of nature over a mechanical conception. Further, on his early interpretation, (...) Cohen thought the Anticipations was not a central part of Kant’s critical theory of knowledge. But on his mature interpretation, he thinks it is absolutely central to that project. What is more, Cohen seems to have revised his interpretation in a relatively short period of time, in 1880-1. This paper argues that Cohen’s change in views about Kant’s Anticipations is explained by his reception of Leibniz in the very early 1880s, and specifically Cohen’s reception of Leibniz’s arguments against Descartes’ view that extension is the essence of matter. (shrink)

This paper tackles the question of whether the order of concepts was still a relevant aspect of scientific rigour in the 19th and 20th centuries, especially in the case of authors who were deeply influenced by the Leibnizian project of a universal characteristic. Three case studies will be taken into account: Hermann Graßmann, Giuseppe Peano and Kurt Gödel. The main claim will be that the choice of primitive concepts was not only a question of convenience in modern hypothetico-deductive (...) investigations, but sometimes also the result of philosophical investigations onto the foundation of scienti­fic disciplines. The question of the "right" order of concepts is an ideal to be followed rather than a task that can be fulfilled, but remains nonetheless an essential part of the axiomatic enterprise. This paper aims to question whether there is in fact such a stark contrast, as there is often claimed to be in the literature, between the debates relating to the right order of concepts and the foundational questions concerning modern axiomatics. The scientific rupture determined by the appearance of hypothetico-deductive systems in mathema­tics and logic should thus not be dissociated from some relevant continuities concerning the ideal of knowledge as the search for a general theory of concepts deriving from some fundamental elements. (shrink)

This paper tackles the question of whether the order of concepts was still a relevant aspect of scientific rigour in the 19th and 20th centuries, especially in the case of authors who were deeply influenced by the Leibnizian project of a universal characteristic. Three case studies will be taken into account: Hermann Graßmann, Giuseppe Peano and Kurt Gödel. The main claim will be that the choice of primitive concepts was not only a question of convenience in modern hypothetico-deductive (...) investigations, but sometimes also the result of philosophical investigations onto the foundation of scienti­fic disciplines. The question of the "right" order of concepts is an ideal to be followed rather than a task that can be fulfilled, but remains nonetheless an essential part of the axiomatic enterprise. This paper aims to question whether there is in fact such a stark contrast, as there is often claimed to be in the literature, between the debates relating to the right order of concepts and the foundational questions concerning modern axiomatics. The scientific rupture determined by the appearance of hypothetico-deductive systems in mathema­tics and logic should thus not be dissociated from some relevant continuities concerning the ideal of knowledge as the search for a general theory of concepts deriving from some fundamental elements. (shrink)

This paper develops a valid reconstruction in first-order predicate logic of Leibniz’s argument for his complete concept definition of substance in §8 of the Discours de Métaphysique. Following G. Rodriguez-Pereyra, it construes the argument as resting on two substantial premises, the “merely verbal” Aristotelian definition and Leibniz’s concept containment theory of truth, and it understands the resulting “real” definition as saying not that an entity is a substance iff its complete concept contains every predicate of that entity, (...) but iff its complete concept contains every predicate of any subject to which that concept is truly attributable. An account is suggested of why Leibniz criticises the Aristotelian definition as merely nominal and how he takes his own definition to overcome this shortcoming: while on the Aristotelian basis the predication relation could generate endless chains, so that substances as endpoints of predication would be impossible, Leibniz’s definition reveals lowest species as such endpoints, which he therefore identifies with individual substances. Since duplicate lowest species make no sense, the Identity of Indiscernibles for substances follows. The reading suggests a Platonist interpretation according to which substances do not so much have but are individual essences, natures or forms. (shrink)

The analysis of identity as coreference is strongly associated with Frege ; it is the view in Begriffsschrift, and, some have argued, henceforth throughout his work. This thesis is incorrect: Frege never held that identity is coreference. The case is made not by interpretation of “proof-quotes”, but rather by exploring how Frege actually deploys the concept. Two cases are considered. The first, from Grundgesetze, are the definitions of the core concepts, zero and truth; the second, from Begriffsschrift, is the (...) validity of Leibniz's Law. In both cases, if identity is coreference, results ensue that would be unacceptable to Frege. (shrink)

This work makes the revisionist claim that "the theory of mind in the Critique [of Pure Reason] is much more traditional and rationalistic than it at first appears, but that it is also more defensible than is generally recognized". Specifically, Ameriks aims to show that "Kant can be seen as wanting, above all else, to put... into a respectable form" the "core of the rationalist commitment" "to the idea that we have a special kind of identity that can withstand (...) all the kinds of change that ordinarily spell the end of ordinary objects". But, first, Ameriks's account of the "core of the rationalist commitment" is maddeningly vague and unstable--indeed, Ameriks's conception of rationalism is so ill-defined that at one point skepticism about the external world is treated as a part of rationalism rather than as the very much undesired consequence of certain Cartesian premises which Kant thought it to be!--and the discussion is damagingly ahistorical. Ameriks does emphasize the developmental dimension within Kant's own work, ranging over the whole of Kant's published corpus and mining the various lecture courses on metaphysics which have now been gathered together as volume 28 of the Berlin edition of Kants gesammelte Schriften. But his picture of rationalism itself and its characteristic arguments is undifferentiated and undocumented, and this leads to the misconception that Kant thought that some theoretical defense of rationalist theses could still be maintained while what are merely some possible arguments in their behalf were criticized; but some review of Leibniz, Wolff, Baumgarten and Meier would surely have shown that Kant was criticizing all of the chief arguments for the rationalist conception of the soul known to him, and attention to Kant's own claim for the completeness of his presentation of these natural and inevitable illusions of human reason could have suggested only that Kant himself thought that these were all the theoretical arguments for a rationalist philosophy of mind there could be. Second, it is questionable whether Ameriks's view really revises our standard reading of Kant's conclusions at all. The gist of Ameriks's argument is that in spite of Kant's specific criticism of the paralogistic arguments of pure psychology, Kant retained a favorable attitude toward the theoretical and not just practical postulation of such properties as immateriality and transcendental freedom at the noumenal level--but this turns out to mean little more than that Kant accepted his own transcendental idealism. This is hardly revolutionary, and the interest of the point is far from strengthened by Ameriks's own conclusion that transcendental idealism cannot be fully proved. (shrink)

Over the past decades a number of scholars have identified Johann Heinrich Bisterfeld as one of the most decisive early influences on Leibniz. In particular, the impressive similarity between their conceptions of universal harmony has been stressed. Since the issue of relations is at the heart of both Bisterfeld and Leibniz’s doctrines of universal harmony, the extent of the similarity between their doctrines will depend, however, on Bisterfeld and Leibniz’s respective theories of relations, and especially on their ontologies (...) of relations. This paper attempts to determine in more detail whether Bisterfeld’s ontology of relations contains at least the germ of the defining features of the ontology of relations later developed by Leibniz. It comes to the conclusion that, although Bisterfeld’s theory of relations is not as fully developed and explicit as that of Leibniz, it does contain all the key “ingredients” of it. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:119. THE IMPORT OF HUME'S THEORY OF TIME In this paper I examine the significance of Hume's theory of time for some of the more famous of the doctrines in the Treatise, and how it works as a basis for his peculiar brand of scepticism, a basis that is at least as important in this regard as his principle that all ideas are derived from some original (...) impression. To bring into relief some of the peculiarities of Hume's theory of time we may observe that it was not uncommon in the seventeenth and eighteenth centuries to distinguish between space and extension and between time and duration, to say, as does for example Leibniz, that "in some way extension is to space as duration is to time", and perhaps also to agree with him "that duration and extension are attributes of things, but time and space are taken to be something outside of things and serve to measure them. " Duration taken as an attribute of things or substantives connotes the permanence, or perseverance, or continuation of the existence of such substantives. Thus Descartes says, "the duration of each thing is a mode [he subsequently calls it an 'attribute'] under which we consider the thing in so far as it continues to exist" (French version) or "perseveres 2 in existence" (Latin version). Or Spinoza: "Duration is the attribute under which we conceive the existence of created things in so far as they persevere in their own 3 actuality". But though duration refers to things as persevering or continuing in existence, it applies equally, as Descartes indicates, to both changing and unchanging things. In order to comprehend the duration of all things under the same measure we usually compare their duration with the duration of the greatest and most regular motions, which are those which create years and days, and these we call time.4 Spinoza's account of duration and time are much the same. Duration is the primary notion and time presupposes it. Going beyond Hume to Kant we find that in distinguishing 120. three modes of time, namely duration, succession and coexistence, Kant argues that succession presupposes duration and that all time determinations of change (or succession) presuppose substance as that which is permanent or continuant through change. In Hume, however, we find no distinction between space and extension, nor between time and duration. These are merely two pairs of synonyms. In the case of space Hume seems to prefer on the whole to talk about extension, probably because extension lends itself more easily to discussion of divisibility. In the case of time, however, which he, defines as succession, he is indeed aware of the view which we have just been considering, according to which duration is referred primarily to an object qua con-. tinuing or persevering or enduring, whether or not undergoing successive changes. This concept of duration, he says, I take to be the common opinion of philosophers as well as of the vulgar. (T37) Duration in this common philosophical and vulgar sense is not a synonym of Humean time or succession, and it is for Hume, a "fiction", something falsely attributed to objects. Why is this so? 'Tis evident, that time or duration [Hume is here taking the two terms as synonyms] consists of different parts... 'Tis also evident, that these parts are not co-existent: For that quality of the co-existence of parts belongs to extension, and is what distinguishes it from duration. Now as time is compos 'd of parts, that are not co-existent; an unchangeable object, since it produces none but co-existent impressions, produces none that can give us the idea of time; and consequently that idea must be deriv'd from a succession of changeable objects, and time in its first appearance can never be sever 'd from such a succession (T35,36) Although Hume maintains that there is no idea which is not derived from some original impression, it would appear that this is not strictly so with the idea of time [or, for that matter with the idea of space]. Rather time is the manner or way in which impressions appear to the mind, namely... (shrink)

Larry Jorgensen aims to show that "Leibniz offers a fully natural theory of mind", recommending Leibniz to our contemporary discussion of naturalism. Readers of Leibniz will, however, hesitate to call him a naturalist. After all, he considered natural laws to be subordinated rules below general divine laws and rejected explaining the soul's action by bodily motion. Jorgensen does have a point, though, when he refers to Leibniz's frequent pleas for natural explanations and his continuity principle.Jorgensen's project unfolds in four (...) parts. The first offers a discussion of Leibniz's concept of nature and a clear presentation of Leibniz's principles, above all the... (shrink)

This book presents a systematic reconstruction of Leibniz’s dynamics project (c. 1676-1700) that contributes to a more comprehensive understanding of the concepts of physical causality in Leibniz’s work and 17th century physics. It argues that Leibniz’s theory of forces privileges the causal relationship between structural organization and physical phenomena instead of body-to-body mechanical causation. The mature conception of Leibnizian force is not the power of one body to cause motion in another, but a kind of (...) structural causation related to the configuration of integral systems of bodies in physical evolution. By treating the immanent philosophy of Leibniz’s dynamics, this book makes explicit the systematic aims and inherent limits of Leibniz's physical project, in addition to providing an alternative vision of the scientific understanding of the physical world in the late 17th and early 18th century. (shrink)

This paper examines the Leibnizian influence in Deleuze's theory of the spatium. Leibniz's critique of Cartesian extension and Newtonian space leads him to a conception of space in terms of internal determination and internal difference. Space is thus understood as a structure of individual relations internal to substances. Making some Nietzschean corrections to Leibniz, Deleuze understands the spatium in terms of individuating differences instead of individual relations. Leibnizian space is thus transformed into a genetic space producing both extension (quantity) (...) and quality. (shrink)

This paper explores the development of Leibniz’s metaphysics of the Incarnation in the context of his philosophy. In particular it asks to what extent Leibniz’s repeated endorsement of the traditional analogy between the union in humankind of soul (mind) and body, and the union in Christ of divine and human natures, could be accommodated by his more general metaphysical doctrines. Such an investigation highlights some of the deepest commitments in Leibniz’s theory of substance as well as (...) detect in it some unresolved tensions. The paper comes to the conclusion that puzzling points of Leibniz’s metaphysics of the Incarnation, rather than being problems specific to his theology, uncover tensions in his theory of substance as such – tensions converging on the vexed question of whether there can or cannot be genuine corporeal substances in Leibniz’s mature philosophy. (shrink)

This paper re-assesses the place of theology in Leibniz’s thought focusing on the relationship between theory and praxis. It takes as its point of departure a general conclusion established in previous work, namely that Leibniz’s key formulations of his overarching plan for the reform and advancement of all the sciences, are devoted to a set of objectives which is both shaped by broadly theological concerns and ultimately practical. Against this backdrop, the discussion will then turn to an (...) exploration of how Leibniz thought of theology as such. I argue that Leibniz was committed to the elaboration of a robust Christian dogmatic which was rationally defensible, and that this commitment resulted in a genuine engagement with Christian theology which took very seriously its theoretical content. The key additional thesis argued for in this paper is that this theoretical engagement was in the service of a science which he conceived as ultimately practical. For Leibniz, the ultimate aim of theology was to lead to the love of God above all things and, in so doing, to salvation and eternal happiness. It is in the light of this practical end that his theological pragmatism should be evaluated. When this is done, it becomes apparent that, beneath Leibniz’s efforts at theological reconciliation in the context of his Kirchenpolitik, there lies a deeper, fundamental and properly theological emphasis on praxis, grounded in Leibniz’s epistemology and driven by his conception of salvation as ultimately dependent on a practical attitude – the love of God above all things. Leibniz’s theological pragmatism was remarkably -- perhaps even surprisingly -- close to the family of prudential approaches to religious belief proposed by Pascal and later authors such as William James. The paper concludes that Leibniz’s conception of theology as ultimately practical is very much in line with the whole thrust of Leibniz’s intellectual programme as expressed in the over-arching plans discussed in the first section. These plans too were driven by a practical end: the promotion of the common good and of human happiness as the celebration of the glory of God in his creation. At the same time, the end of happiness – whether worldly or eternal -- should not be regarded as competing with Leibniz’s theoretical endeavours – whether in the sciences or in theology -- but as directly supported by them. (shrink)

In this paper I will discuss the doctrine of substance which emerges from Leibniz’s unpublished early memoir De affectibus of 1679. The memoir marks a new stage in Leibniz’s views of the mind. The motivation for this change can be found in Leibniz’s rejection of the Cartesian theory of passion and action in the 1670s. His early Aristotelianism and some features of Cartesianism persisted to which Leibniz added influences from Hobbes and Spinoza. His nascent dynamical concept (...) of substance is seemingly a combination of old and fresh influences, representing a characteristically eclectic approach, but I will argue that the influence of Hobbes is especially important in the memoir. To do that, I will examine Leibniz’s development in the 1670s up to the De affectibus and consider the nature of affects in the memoir, especially the first affect which starts the thought sequence. This first affect of pleasure or pain is the key to Leibniz’s theory of active substances and in this way to the whole of Leibniz’s moral psychology and ethical metaphysics. (shrink)

Much of the scholarship on Kant’s theory of concept formation has focused on the question of whether his theory suffers from circularity, i. e., whether it presupposes the very concepts whose origin it should explain. In this article, I defend Kant against a well-known objection raised by Hannah Ginsborg. Ginsborg, I argue, overlooks the relatively narrow aim of Kant’s theory of concept formation. Kant explicitly frames it as an account of a concept’s inherent generality, or form. (...) However, Ginsborg’s objection is not about a concept’s form; it concerns the concept’s content. Moreover, Kant addresses the issue that she raises in his theory of definitions, which explains how a concept’s content can be revised and perfected. Kant considered all empirical concepts to be incomplete and imprecise. For this reason, he denied that they can be properly defined. Kant also did not regard the content of empirical concepts as fixed or permanent. Indeed, he expected that we would continually expand and revise their content on the basis of experience. I argue that these facts, along with the narrow scope of Kant’s theory of concept formation, effectively defuse Ginsborg’s objection. (shrink)

Many historians of the calculus deny significant continuity between infinitesimal calculus of the seventeenth century and twentieth century developments such as Robinson’s theory. Robinson’s hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his (...) Leibnizian sympathies, Robinson regards Berkeley’s criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley’s criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz’s infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz’s defense of infinitesimals is more firmly grounded than Berkeley’s criticism thereof. We show, moreover, that Leibniz’s system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz’s strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 41.1 (2003) 131-132 [Access article in PDF] Christia Mercer. Leibniz's Metaphysics: Its Origins and Development. New York: Cambridge University Press, 2001. Pp. xiii + 528. Cloth, $80.00. Christia Mercer's massive study is aimed at unearthing the hidden roots of Leibniz's metaphysics by placing the German philosopher back in the intellectual context within which his thought first took shape. In so doing she stresses (...) the fundamental importance of Leibniz's early years for the development of his philosophy. In particular she convincingly argues for the key role played by Leibniz's early exposure to the thought of eclectic thinkers (including his teachers) who were trying to build a new philosophical synthesis centered around the key tenets of Christian theology and combining elements of Aristotelianism, Platonism, and (in at least some cases) the new mechanical philosophy of nature.One of Mercer's central theses is that the methodological and metaphysical commitments that Leibniz developed during his youth formed the bedrock of his mature philosophy (23). More precisely, her bold claim is that Leibniz's core metaphysics (including the complete concept account of substance) was constructed in 1668-71, re-examined and slightly developed in 1672-79, and then used for the rest of his long philosophical career (18, 470). The key inspirational forces driving the development of Leibniz's philosophy, in her view, had even earlier origins. In the mid-1660s Leibniz did not yet have a fully formulated metaphysics; but he already possessed very definite philosophical objectives which were to guide the development of his metaphysics and form the unstated assumptions underlying his mature thought (40). Mercer identifies these unstated assumptions as a "Metaphysics of Method," a "Metaphysics of Substance," and a "Metaphysics of Divinity," all of which she finds fully developed in his early thought (468-9).According to Leibniz's "Metaphysics of Method" (examined in part I), there exists a truth beneath the prominent philosophical schools which can and ought to be discovered. This conciliatory methodology was Leibniz's answer to the political, religious, and philosophical chaos around him. He was deeply convinced that his brilliantly original eclectic metaphysics would provide the foundation of philosophical, theological, and even political peace. Leibniz's "Metaphysics of Substance," Mercer argues in part II, melded an Aristotelian approach to substance with a mechanical physics and originated at the very outset of his intellectual carrier in an attempt to solve specific theological problems (e.g., those of the incarnation and resurrection). Platonism in turn offered the material for Leibniz's "Metaphysics of Divinity" (explored in part III), that is, for his conception of the relationship between God and creatures. The fourth and final part of Mercer's book takes her analysis of Leibniz's writings up to 1679 and describes the laying of the foundations of his mature metaphysics. She concludes not only that Leibniz proposed the doctrine of pre-established harmony prior to his departure for Paris in March 1672, but also, more generally, that the other tenets of Leibniz's mature thought, including his theory of truth, grew naturally out of his early metaphysics (see, in particular, 2, 15-8, 47, 52, 169-70, 250-2, 300-1, 472).Throughout the book Mercer describes her interpretation as "startling," "unfamiliar," "dramatic," and "surprising," and fears that "readers may balk" at her conclusions since "so much of Leibniz's thought has escaped us for so long" (see, for instance, 1, 9, 471). Some readers may feel, on the contrary, that she has underestimated the extent to which several of her central theses—such as the importance of the earliest stages of Leibniz's philosophical development in general and of eclecticism, theological problems, and Platonism, as well as Aristotelianism within that development in particular—are already reflected in the [End Page 131] best recent traditions of international Leibniz scholarship. But her book undoubtedly breaks new ground and remains an important contribution to an exciting field which cannot and will not be ignored. While international Leibniz scholarship may not absorb some of this book's more... (shrink)

It is well known that a central issue in the famous debate between Gottfried Wilhelm Leibniz and Samuel Clarke is the nature of space. They disagreed on the ontological status of space rather than on its geometrical or physical structure. Closely related is the disagreement on the existence of vacuums in nature: while Leibniz denies it, Clarke asserts it. In this paper, I shall focus on Leibniz's position in this debate. In part one, I shall reconstruct the theory of (...) physical space which Leibniz presents in his letters to Clarke. This theory differs from Leibniz's ultimate metaphysics of space, but it is particularly interesting for systematic reasons, and it also gave rise to a lively discussion in modern philosophy of science. In part two, I shall examine whether the existence of vacuums is ruled out by that theory of space, as Leibniz seems to imply in one of his letters. I shall confirm the result of E. J. Khamara that Leibniz's theory of space rules out the existence of a certain kind of vacuum, namely extramundane vacuums, although it does not rule out vacuums within the world. (shrink)

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

The doctrine of natural machines, of organisms, of composite substances, assumes a marked consistency in Leibniz starting from his mature years (let us say, from the publishing of New System in 1965 onwards). There is no doubt, therefore, that for a full explanation of the conceptual content of the reflection of Leibniz on the nature of living substances we must turn to the “classic” places in which it took form: from the letters to De Volder and Lady Masham of the (...) early 1700s, to the Nouveaux Essais, to Animadversiones contra Stahl and, naturally to Princìpes de la Nature et de la Grace and to the Monadologie. We can in any case ask what are the elements of specific difference are that emerge in this vast doctrinal corpus regarding those elements of the theory of the living being that had already appeared with a certain frequency in the texts of the early 1780s. Put in other words: what link of continuity subsists between the proto-theory of the living being of the ‘80s and that of the mature years (let us say from New System on)? Or, overturning the formulation of the problem: what elements of discontinuity suddenly break into Leibniz’s reflections from the second half of the ‘90s compared to the immediately preceding phases of his thought? Certainly, the monads, the machines of nature. But is it possibile to focus even more clearly the lens of our observations? I mean: after a decade of intense theoretical debate on the nature of corporeal substances, on organisms, on machines of nature, is it possibile to sketch a historical picture that accounts in a coherent manner for the development of Leibniz's thought in relation to the questions raised here? (shrink)

Traditionally the modern theory of ideas has been discussed primarily in reference to its alleged introduction of a veil of mental items between the mind and the world, which leads, through the empiricists, to radical skepticism about the existence of an external world. Here I propose to emphasize an entirely different aspect of the Cartesian theory of ideas which, in my view, is more fundamental in opening the empiricist path that leads to Hume’s radical skepticism. I argue that (...) what I call the “phenomenological presentation” model of ultimate justification is rooted in a fundamental ambiguity between sensible and intellectual apprehension insinuated by Descartes’s view of “clear and distinct” ideas together with his emphasis on the priority of intuition over logical inference. Sensible apprehension relies on immediate acquaintance with items pheno-menologically and ostensively present before the mind as given particulars. The phenomenological presentation model takes its clues from sensible apprehension, although the items present before the mind might themselves be either ideas of the understanding, images of the imagination, sensory impressions, or material external objects. Intellectual apprehension, by contrast, as I illustrate with Leibniz’s model of our knowledge of concepts and truths of reason, consists in the discursive, non-ostensive grasping of the generality of abstract concepts and of formal structures . For Leibniz, all intellectual apprehension is unambiguously “logical discursive apprehension” as opposed to “direct ostensive apprehension.” Thus, Leibniz unmistakably disambiguates Descartes’s model in favor of a precise intellectual model. The empiricists, by contrast, correspondingly disambiguate Descartes’s conception in favor of an entirely sensible model.Tradicionalmente, a teoria moderna das idéias foi discutida principalmente em conexão com a sua suposta introdução de um véu de itens mentais entre a mente e o mundo que leva, por meio dos empiristas, ao ceticismo radical sobre a existência de um mundo externo. Aqui eu proponho enfatizar um aspecto completamente diferente da teoria Cartesiana das idéias que, na minha visão, é mais fundamental no que diz respeito a abrir o caminho empirista que conduz ao ceticismo radical de Hume. Eu argumento que o que eu chamo de o modelo de “apresentação fenomenológica” de justificação última está baseado em uma ambigüidade fundamental entre apreensão sensível e intelectual insinuada pela visão de Descartes de idéias “claras e distintas” junto com a sua ênfase na prioridade da intuição sobre inferência lógica. A apreensão sensível confia no contato imediato com itens presentes fenomenologicamente e ostensivamente perante a mente como particulares dados. O modelo de apresentação fenomenológica está inspirado na apreensão sensível, embora os itens que se apresentam perante a mente poderiam ser eles mesmos idéias do entendimento, figuras da imaginação, impressões sensórias, ou objetos externos materiais. A apreensão intelectual, por contraste, como eu ilustro com o modelo de Leibniz de nosso conhecimento de conceitos e verdades da razão, consiste na compreensão discursiva e não-ostensiva da generalidade de conceitos abstratos e de estruturas formais . Para Leibniz, toda a apreensão intelectual é claramente “apreensão discursiva lógica” por oposição a “apreensão ostensiva direta”. Assim, Leibniz claramente desfaz a ambigüidade do modelo de Descartes em favor de um modelo intelectual preciso. Os empiristas, por contraste, desfazem a ambigüidade da concepção de Descartes em favor de um modelo completamente sensível. (shrink)

I have developed an informational interpretation of Leibniz’s metaphysics and dynamics, but in this paper I will concentrate on his theory of time. According to my interpretation, each monad is an incorporeal automaton programed by God, and likewise each organized group of monads is a cellular automaton governed by a single dominant monad. The activities of these produce phenomena, which must be “coded appearances” of these activities; God determines this coding. A crucially important point here is that we (...) have to distinguish the phenomena for a monad from its states. Both are a kind of representation: a state represents the whole world of monads, and phenomena for a monad “result” from the activities of monads. But the coding for each must be different; R for the first, Ph for the second, where W is a state of the monadic world. The reason for this is that no monadic state is in space and time, but phenomena occur in space and time. Now, the basis of the phenomenal time must be in the timeless realm of monads. This basis is the order of state-transition of each monads. All the changes of these states are given at once by God, and these do not presuppose time. The coded appearances of this order occur in time, and its metric must depend on God’s coding for phenomena. For humans, in particular, this metric time is derived from spatial distance via the laws of dynamics. Thus there may well be an interrelation between spatial and temporal metric. This means that the Leibnizian frame allows relativistic metric of space-time. I will show this after outlining Leibniz’s scenario. (shrink)

Between Wolff and Kant: Merian's Theory of Apperception UDO THIEL IT IS WELL KNOWN that the nodon of apperception or self-consciousness is central to Kant's theoretical philosophy. Kant introduces the notion in one of the crucial parts of the Critique of Pure Reason, the Transcendental Deduction of the Categories, and assigns it an important role in his critique of traditional metaphysics of the soul in the Transcendental Dialectic.' It is also well known that Kant did not invent the term (...) "apperception." Leibniz had introduced the French 'Tapperception" into philosophical terminology early in the eigh- teenth century. Kant scholars generally stress, rightly, that Kant's notion of apperception differs significandy from that of his predecessors. However, the precise relation between Kant's concept of apperception and earlier accounts has not been considered in any detail. Wolfgang Carl, for example, simply states that the main difference is that, prior to Kant, apperception was under- stood as relating only to mental acts and their contents, and not to the subject that thinks and has ideas, whereas in Kant apperception relates essentially to the thinking subject. 2 This very general thesis is questionable even in regard to some of the philosophers that Carl cites in this context . It is clearly not true of some other pre-Kantian philoso- phers who deal with self-consciousness. ' References to the Critique of Pure.. (shrink)

This paper casts doubt on a recent criticism of Frege's theory of concepts and extensions by showing that it misses one of Frege's most important contributions: the derivation of the infinity of the natural numbers. We show how this result may be incorporated into the conceptual structure of Zermelo- Fraenkel Set Theory. The paper clarifies the bearing of the development of the notion of a real-valued function on Frege's theory of concepts; it concludes with a (...) brief discussion of the claim that the standard interpretation of second-order logic is necessary for the derivation of the Peano Postulates and the proof of their categoricity. (shrink)

The object of this article is the scholastic inspirations found in the metaphysical disputation De principio individui by Gottfried Wilhelm Leibniz. The purpose ofthis study was, on one hand, a reconstruction of Leibniz’s theory concerning the principle of individuation, and on the other hand, a presentation of some texts by medieval scholastic authors (Henry of Ghent, Peter of Falco, Thomas Aquinas, Aegidius of Rome, Robert Kilwardby, William of Ockham) to whose ideas Leibniz refers in the named work, even (...) though he had, for the most part, only second-hand information concerning them. In his juvenile treatise, Leibniz states that the individuating principle has to be universal, which means relevant to all kinds of being; it has to be metaphysical in character and not merely epistemological. He regards individuality as synonymous with unity combined with difference. He resolutely takes sides with nominalism and rejects the reality of all kinds of universal beings and beings whose unity is weaker than numerical unity. As a consequence of this assumption, he rejects the conceptions in which the principle of individuation is formed by: double negation, existence or the haecceity. By contrast, he embraces the solution (close to the tradition originated by Ockham and also related to Suarez), according to which the whole entity (tota entitas) of an individual thing is the principle of individuation. In effect, for Leibniz, any real thing is simply singular, which comes down to the thesis that a thing is singular owing to its own metaphysical subcomponents, which are singular by themselves. (shrink)

Il est une opinion fort répandue que la théorie leibnizienne de l'identité personnele dans les Nouveaux Essais est contradictoire car elle renferme deux thèses incompatibles, à savoir, que 1) comme persone, je suis mon esprit, et que 2) je pourrais continuer, sans mon esprit. Dans cette étude, par une interprétation nouvelle de la pensée leibnizienne sur l'identité personnelle dans les Nouveaux Essais, je soutiens que pour Leibniz est vrai mais est faux, et que par conséquence sa théorie est consistante.

Resumen El objetivo principal de este artículo es analizar la distinción leibniziana entre apercepción sensible y consáentia a la luz de su ontología monadológica, con la intención de esclarecer las diferencias constitutivas entre los tres tipos de mónadas que Leibniz postula, esto es, entre las mónadas simples, las meras almas y los espíritus. Con esto, además de argumentar en contra de la concepción estándar de la apercepción, la cual termina por confinarla al caso específico de los espíritus, sitúo la propuesta (...) del hannoveriano entre dos lecturas contemporáneas: por un lado, aquella que comprende la apercepción como un acto de orden superior reflexivo, esto es, una percepción de la percepción; y, por otro lado, aquella que, al distinguir entre apercepción sensible y consáentia, privilegia una teoría de primer orden para hablar de la primera, reservando los actos reflexivos para la segunda. Aunque la evidencia textual es más afín con la segunda, hay elementos de la primera que permiten matizarla.The main aim of this article is to analyze Leibniz’s distinction between sensitive apperception and ‘conscientia’ through his monadological ontology, with the intention of lighten the constitutive differences between the three types of monads that Leibniz state, that is, between bare monads, souls and spirits. By proving this, my approach not only argues against the standard conceptions of Leibniz's notion of apperception, which ends attributing apperception only to the specify case of spirits, but it abo places the Hanoverian proposal between two contemporary lectures: on one side, an approach that understand apperception as a high order reflexive act, that is, a perception of a perception; on the other side, an approach that distinguishes sensible apperception from ‘conscientia’ in order to privilege a first order theory for the first one, reserving the reflective acts only for the second. Even when the textual evidence is closer to the last one, there are some elements of the first approach that allow us to improve it. (shrink)

Uygar Abaci's Kant's Revolutionary Theory of Modality starts with a helpful and illuminating historical contextualization of Kant's theory of modality. It sets out the ontotheological debates that form the backdrop of Kant's pre-Critical modal theorizing. Abaci covers the proofs of the existence of God by Anselm and Descartes, as well as Leibniz and Wolff. The first two start from the idea of God as the ens perfectissimum and then try to establish the existence of God by arguing that (...) existence is a perfection. The last two, by contrast, consider God to be the ens necessarium, such that God exists necessarily, provided the concept of God is not self-contradictory; they then attempt to establish the possibility of... (shrink)