I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the (...) spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition. (shrink)

Leibniz frequently uses the notion of expression, but it is not easy to see just how he understood that relation. This paper focuses on the particular case of the expression of God, which is prominent in the 'Discourse on Metaphysics'. The treatment of expression there suggests several questions. Which substances did Leibniz believe expressed God? Why did Leibniz believe those substances expressed God? And did he believe that all substances expressed God in the same way and for the same reasons? (...) In answering those questions the paper distinguishes two views about expression in the 'Discourse', considers Leibniz's reasons for holding that substances express their causes, and argues that Leibniz's views about emanative causation are important for understanding the unity of his apparently distinct views here. The paper concludes by looking briefly at how the 'Discourse' fits into the evolution of Leibniz's views on this issue over time. (shrink)

In this paper we focus on Deleuze’s interpretation of small perceptions in Leibniz’s thought, as well as on the supposed abandon of this notion in Kant. In connection with the two issues we contend that the way both authors deal with them makes sense within the framework of the Enlightenment.

ArgumentAt the end of the seventeenth and beginning of the eighteenth century, ageing was specifically a medical issue. Indeed, on the one hand, ageing is a normal process of living; on the other hand, old age often entails specific pathologies. Is it really possible to dissociate old age from pathology? If so, how can we think of old age and explain both the necessity and the normality of it? If not, what is the cause of this dysfunction? Modern medical controversies (...) argue along the lines of the respective partisans ofiatromecanism, empirical medicine, and animist medicine. Furthermore, it progressively appears that the issue of aging must also be addressed within the social field, where old age is affected by sanitary, economic, and strategic conditions. Indeed, doctors, economists, and philosophers even tried to assess old age quantitatively with new methods of arithmetic. Thus, in this paper, we want to draw what constitutes the systems of knowledge of old age as a medical category located at the borderlines between epistemological, practical, and social challenges. (shrink)

This paper argues for two claims. (1) In his biological views, Kenelm Digby tries to reconcile aspects of an Aristotelian theory of composite substance with early modern corpuscularianism. (2) From a methodological point of view, he uses the Stoic-Epicurean epistemology of common notions in order to show the adequacy of his conciliatory approach. The first claim is substantiated by an analysis of Digby’s views on the role of mixture and homogeneity in the process of animal generation. The second claim is (...) substantiated by an analysis of Digby’s views on the role of the concept of quantity in the evaluation of scientific hypotheses. Both arguments make use of the context of Digby’s philosophy: the first argument draws on his background in the work of early modern corpuscularian Aristotelians such as Daniel Sennert; the second argument draws on his background in the epistemology of Pierre Gassendi. (shrink)

Leibniz’s claim that this is the best of all possible worlds has been subject to numerous criticisms, both from his contemporaries and ours. In this paper I investigate a cluster of such criticisms based on the existence, abundance or character of worldly evil. As several Leibniz-inspired versions of optimism have been advanced in recent years, the aim of my investigation is to assess not just how Leibniz’s brand of optimism fares against these criticisms, but also whether optimism as a philosophy (...) has the resources to meet these challenges. I show that none of the criticisms considered has sufficient force to pose a threat to Leibniz’s version of optimism or to one modelled on it. (shrink)

Peu connue à cause de l’absence d’ouvrage de référence qui la présenterait dans toute son étendue, la pensée politique de Leibniz présente cependant un intérêt non négligeable pour l’histoire de la philosophie politique. En concevant l’homme comme sociable par nature, Leibniz ne fait pas pour autant de l’État l’aboutissement des sociétés naturelles, mais plutôt un moment passager dans la réalisation du monde moral au sein du monde naturel. Dès lors, le meilleur régime pour un tel État, ne résultant pas d’un (...) contrat social bien que sujets et souverain y soient dans un rapport mutuel d’obligation, serait celui qui permettrait d’allier le mieux puissance et sagesse. Refusant tout pouvoir arbitraire, et insistant sur la nécessité de distinguer les pouvoirs, Leibniz considère la monarchie comme le meilleur régime en ce qu’elle serait plus facilement amendable : assisté d’un parlement, le puissant monarque ne pourrait qu’être sage.Little-known because of the lack of a work of reference that would present it in all its extent, Leibniz’s political thought is however of significant interest for the history of political philosophy. By conceiving humans has sociable by nature, Leibniz doesn’t depict the State as the outcome of natural societies, but rather as a passing moment in the realization of the moral world within the natural world. Therefore, the best regime for such a State, not resulting from a social contract although subjects and sovereign are there in a mutual relationship of obligation, would be the one uniting best power and wisdom. Refusing every arbitrary power and emphasizing on the necessity of distinguishing powers, Leibniz considers monarchy as the best regime for it would be more easily improvable: assisted by a parliament, a potent monarch could only be wise[1]. (shrink)

The topic of disinterested love became fashionable in 1697 due to the famous amour pur dispute between Fénelon (1651-1715) and Bossuet (1627-1704). It soon attracted the attention of Electress Sophie of Hanover (1630-1714) and she asked for an opinion about the dispute from her trusted friend and correspondent, the Hanoverian councilor Gottfried Wilhelm Leibniz (1646-1716). This gave Leibniz an opportunity to present his views on the matter, which he had developed earlier in his career (for example, in Elementa juris naturalis (...) of 1671 and Codex iuris gentium of 1693). In his 1697 letter to Sophie he did not explicitly take sides in the dispute, but formulated his own views on the topic in a theological manner, aiming to provide an account of disinterested love which would surpass the doctrines of both French theologians. In addition to presenting Leibniz’ early views on disinterested love and examining this alternative formulation of his views on love, I will show that after the letter Leibniz gave this alternative perspective up and returned to his earlier, more philosophical views on the topic, which suggests that he regarded them to be superior to the theological version, where the virtue of charity was related to the virtue of hope. (shrink)

Im Rahmen seines Projektes eines calculus universalis entwarf Leibniz Anfang 1679 in neun Texten drei unterschiedliche Modelle der aristotelischen Logik mit Hilfe von Zahlen. Durch diese von ihm erfundenen charakteristischen Zahlen wollte Leibniz die Schlussweisen der aristotelischen Logik auf rein arithmetische Rechnungen reduzieren. In der vorliegenden Arbeit zeigen wir genau, wie die drei Modelle untereinander zusammenhängen bzw. aufeinander aufbauen. Zu diesem Zweck geben wir drei Kriterien an, mit Hilfe derer sich Modelle der aristotelischen Logik klassifizieren lassen. Zum einen können wir (...) dadurch die Leibniz' sehen Definitionen leicht nachvollziehen sowie auch die Stärken und Schwächen der einzelnen Modelle präzise beschreiben. Besonders für das ausgefeilte letzte Modell, dessen Grundbereich aus Paaren natürlicher Zahlen besteht, liefert unsere Methode einen ganz natürlichen Zugang zu den Leibniz'sehen Definitionen, die im Original recht sperrig wirken. Wir zeigen insbesondere -was Leibniz nicht herausgestellt hat -, dass allein aus der universell-positiven alle anderen drei » aristotelischen Relationen' herleitbar sind. Ein Grund für manche Schwierigkeiten mit dem Verständnis der Leibniz'sehen charakteristischen Zahlen ist die von ihm verwendete Nomenklatur. Der problematischen Schreibweise mit Vorzeichen + und -, die in der Vergangenheit manchen Kommentator auf die falsche Fährte gelockt hat, geben wir eine neue Deutung: Dadurch entpuppt sich das letzte Modell als ganz natürliche Erweiterung des vorangehenden vom Grundbereich der natürlichen in den Bereich der positiven rationalen Zahlen. -Mit der vorliegenden Arbeit hoffen wir, der Verwendung charakteristischer Zahlen als theoretisches Instrument für die Untersuchung der aristotelischen Logik einen neuen Impuls geben zu können. Deshalb diskutieren wir am Schluss der Arbeit noch die aus der Literatur bekannten Stärken und Schwächen des Leibniz'sehen Modells und formulieren zwei offene Fragen zu diesem Komplex. (shrink)

In 1675, Burchard de Volder (1643–1709) was the first professor to introduce the demonstration of experiment into a university physics course and built the Leiden Physics Theatre to accommodate this new pedagogy. When he requested the funds from the university to build the facility, he claimed that the performance of experiments would demonstrate the “truth and certainty” of the postulates of theoretical physics. Such a claim is interesting given de Volder’s lifelong commitment to Cartesian scientia. This chapter will examine de (...) Volder’s views on experiment and show that they are not Newtonian or inductivist, as is sometimes claimed. While de Volder thinks we need deductive reasoning from first principles to provide evidence of the certainty of the content of our physical theories, he also contends that we need experiment to provide evidence of the certainty of the existence of the particular bodies those theories discuss. This approach to experiment is based on a distinction between rational certainty and the certainty of material bodies in the actual world. While this account is deeply influenced by Descartes, it is importantly different than Descartes’ distinction between absolute and moral certainty. De Volder’s “Cartesian Empiricism” is best understood as a continuation and further development of a long tradition of teaching through observation at Leiden. (shrink)

This paper examines the origin, range and meaning of the Principle of Action and Reaction in Kant’s mechanics. On the received view, it is a version of Newton’s Third Law. I argue that Kant meant his principle as foundation for a Leibnizian mechanics. To find a ‘Newtonian’ law of action and reaction, we must look to Kant’s ‘dynamics,’ or theory of matter. I begin, in part I, by noting marked differences between Newton’s and Kant’s laws of action and reaction. I (...) argue that these are explainable by Kant’s allegiance to a Leibnizian mechanics. I show (in part II) that Leibniz too had a model of action and reaction, at odds with Newton’s. Then I reconstruct how Jakob Hermann and Christian Wolff received Leibniz’s model. I present (in Part III) Kant’s early law of action and reaction for mechanics. I show that he devised it so as to solve extant problems in the Hermann-Wolff account. I reconstruct Kant’s views on ‘mechanical’ action and reaction in the 1780s, and highlight strong continuities with his earlier, pre-Critical stance. I use these continuities, and Kant’s earlier engagement with post-Leibnizians, to explain the un-Newtonian features of his law of action and reaction. (shrink)

Thomas Hobbes was, rather famously, a nominalist. The core of that nominalism is the belief that the only universal things are universal names: there are no universal objects, or universal ideas. This paper looks at what Hobbes's views about universal names were, how they evolved over time, and how Hobbes argued for them. The remainder of the paper considers two objections to Hobbes's view: a criticism made by several of Hobbes's contemporaries, that Hobbes's view could not account for people saying (...) the same thing in different languages; and a more recently popular criticism of Hobbes, that his nominalism's reliance on similarity implicitly (and inconsistently) involves reliance on a universal. (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)

Russell’s critique of substance monism is an ideal starting point from which to understand some main concepts in Spinoza’s difficult metaphysics. This paper provides an in-depth examination of Spinoza’s proof that only one substance exists. On this basis, it rejects Russell’s interpretation of Spinoza’s theory of reality as founded upon the logical doctrine that all propositions consist of a predicate and a subject. An alternative interpretation is offered: Spinoza’s substance is not a bearer of properties, as Russell implied, but an (...) eternally active, self-actualizing creative power. Eventually, Spinoza the Monist and Russell the Pluralist are at one in holding that process and activity rather than enduring things are the most fundamental realities. (shrink)

According to the received view (Bocheński, Kneale), from the end of the fourteenth to the second half of nineteenth century, logic enters a period of decadence. If one looks at this period, the richness of the topics and the complexity of the discussions that characterized medieval logic seem to belong to a completely different world: a simplified theory of the syllogism is the only surviving relic of a glorious past. Even though this negative appraisal is grounded on good reasons, it (...) overlooks, however, a remarkable innovation that imposes itself at the beginning of the sixteenth century: the attempt to connect the two previously separated disciplines of logic and mathematics. This happens along two opposite directions: the one aiming to base mathematical proofs on traditional (Aristotelian) logic; the other attempting to reduce logic to a mathematical (algebraical) calculus. This second trend was reinforced by the claim, mainly propagated by Hobbes, that the activity of thinking was the same as that of performing an arithmetical calculus. Thus, in the period of what Bocheński characterizes as ‘classical logic’, one may find the seeds of a process which was completed by Boole and Frege and opened the door to the contemporary, mathematical form of logic. (shrink)

In a famous critique, Goodman dismissed similarity as a slippery and both philosophically and scientifically useless notion. We revisit his critique in the light of important recent work on similarity in psychology and cognitive science. Specifically, we use Tversky’s influential set-theoretic account of similarity as well as Gärdenfors’s more recent resuscitation of the geometrical account to show that, while Goodman’s critique contained valuable insights, it does not warrant a dismissal of similarity.

This paper employs the revised conception of Leibniz emerging from recent research to reassess critically the ‘radical spiritual revolution’ which, according to Alexandre Koyré’s landmark book, From the closed world to the infinite universe was precipitated in the seventeenth century by the revolutions in physics, astronomy, and cosmology. While conceding that the cosmological revolution necessitated a reassessment of the place of value-concepts within cosmology, it argues that this reassessment did not entail a spiritual revolution of the kind assumed by Koyré, (...) in which ‘value-concepts, such as perfection, harmony, meaning and aim’ were shed from the conception of the structure of the universe altogether. On the contrary, thanks to his pioneering intuition of the distinction between physical and metaphysical levels of explanation, Leibniz saw with great clarity that a scientific explanation of the universe which rejected the ‘closed world’ typical of Aristotelian cosmology did not necessarily require the abandonment of key metaphysical doctrines underlying the Aristotelian conception of the universe. Indeed the canon of value-concepts mentioned by Koyré—meaning, aim, perfection and harmony—reads like a list of the most important concepts underlying the Leibnizian conception of the metaphysical structure of the universe. Moreover, Leibniz’s universe, far from being a universe without God—because, as Clarke insinuated, it does not need intervention from God—is a universe which in its deepest ontological fabric is interwoven with the presence of God.Author Keywords: Leibniz; Koyré; Clarke; Universe; Cosmology; Harmony. (shrink)

The reflections recorded in this paper arise from three moments in the theory of definition and of conceptual analysis. The moments are: Frege’s review of Husserl’s Philosophy of Arithmetic, the discussion there of the paradox of analysis, and the division that Frege marks, ensuing upon his distinction of Sinn/sense from Bedeutung/reference, between two different conceptions of definition; Leibniz’s still serviceable account of a distinction between the clarity and the distinctness of ideas---a distinction that prompts the suggestion that the guiding purpose (...) of lexical definition is Leibnizian clarity whereas that of real definition is inseparable from the pursuit of Leibnizian distinctness; Leibniz’s speculations concerning the limit or terminus of analysis. The apparent failure of these speculations, casting doubt as it does upon the aspirations that give rise to them, points to the long-standing need to reconfigure the philosophical business of enquiry into concepts. (shrink)

In his groundbreaking work of 1969, Spinoza's Metaphysics: An Essay in Interpretation, Edwin Curley attacked the traditional understanding of the substance-mode relation in Spinoza, according to which modes inhere in substance. Curley argued that such an interpretation generates insurmountable problems, as had already been claimed by Pierre Bayle in his famous Dictionary entry on Spinoza. Instead of having modes inhere in substance Curley suggested that the modes’ dependence upon substance should be interpreted in terms of (efficient) causation, i.e., as committing (...) Spinoza to nothing over and above the claim that substance is the (efficient) cause of the modes. These bold and fascinating claims generated one of the most important scholarly controversies in Spinoza scholarship of the past thirty-five years. In this paper I argue against Curley’s interpretation and attempt to reestablish the traditional understanding of Spinozistic modes as inhering in God and as predicated of God. I also criticize Curley’s philosophical motivation for suggesting this interpretation. In order to show that, for Spinoza, modes are predicated of - and inhere in - substance, I will proceed in the following manner. First, I will summarize Curley’s arguments against substance-mode inherence and present his alternative interpretation of the substance-mode relation. I will then present what I consider to be the most compelling arguments against Curley’s interpretation. Some of these arguments have already been suggested in the literature of the past thirty years (and by Bayle); however, as far as I know, most of the arguments I will be making are new. In the subsequent section I will respond to objections that Curley and Bayle advance against Spinoza’s view of God as the substratum in which all things inhere. Finally, I will address whether Spinozistic modes are predicated of (and not only inhere in) substance, and whether Spinoza considered modes to be particular properties (or “tropes,” in the jargon of contemporary metaphysics). Since Bayle’s claims will be used both in support of and against Curley’s interpretation, it would be appropriate to say a few introductory words on Bayle’s stance. In his Spinoza entry, Bayle criticizes Spinoza’s claim that all things are modes of God, claiming that it “is the most monstrous hypothesis that could be imagined, the most absurd, and the most diametrically opposed to the most evident notions of our mind.” Bayle, however, has no doubt that when Spinoza claims that all things are modes of God, Spinoza means that all things inhere in God. Curley embraces Bayle’s arguments against Spinoza, but uses them in order to claim that we should not ascribe to Spinoza a view which is allegedly shown by Bayle to be absurd. What we should do, Curley argues, is to reinterpret the substance-mode relation as a relation of causal dependence, which would set Spinoza free from Bayle’s hook. Interestingly, as we shall soon see, Bayle himself discusses and rejects a very similar revisionary interpretation of the substance-mode relation. (shrink)

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

In this paper I argue that Leibniz's ethics is a kind of virtue ethics where virtues of the agent are explanatorily primary. I first examine how Leibniz obtained his conception of justice as a kind of love in an early text, Elements of Natural Law. I show that in this text Leibniz's goal was to find a satisfactory definition of justice that could reconcile egoism with altruism, and that this was achieved through the Aristotelian virtue of friendship where friends treat (...) each other as “other selves.” Following this decisive moment, Leibniz adopted an Aristotle‐inspired ethical framework where the virtuous agent is central for moral evaluations. I then show that, despite certain developments, Leibniz's ethics retained this essential feature throughout his career. In Leibniz's later writings, God constitutes the foundation of the moral realm, and the fundamental moral endeavor of human beings consists in the imitation of God. (shrink)

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

Pierre-Sylvain Régis’s Cartesianism is quite singular in seventeenth-century French philosophy. Though, can we speak of a form of experimental science in Régis’s work? After exploring his notions of ‘system’ and ‘hypothesis’, I will define his position in relation to Claude Perrault, Jacques Rohault, and the Royal Society. I argue, first, that the contrasts which traverse French science are not so much about the use of experiments but about whether or not observational data can be traced back to hypotheses and to (...) a coherent system. Secondly, that we can detect a significant similarity between Boyle’s positions and the views expressed by Perrault and also by Régis. Lastly, that French science, even in its Cartesian version, is much more probabilistic than English experimental philosophy. (shrink)

According to veridicalism, your beliefs about the existence of ordinary objects are typically true, and can constitute knowledge, even if you are in some global sceptical scenario. Even if you are a victim of Descartes’ demon, you can still know that there are tables, for example. Accordingly, even if you don’t know whether you are in some such scenario, you still know that there are tables. This refutes the standard sceptical argument. But does it solve the sceptical problem posed by (...) that argument? I argue that it does not, because we do not know substantively more about the external world according to veridicalism than we do according to the sceptical argument. Rather, veridicalism merely reformulates what little knowledge we have. I then draw some general conclusions about the nature of the sceptical problem, the formulation of the standard argument, and the significance of this for some other, non-veridicalist strategies. (shrink)

This volume takes cue from the idea that the thought of no philosopher can be understood without considering it as the result of a constant, lively dialogue with other thinkers, both in its internal evolution as well as in its reception, re-use, and assumption as a starting point in addressing past and present philosophical problems. In doing so, it focuses on a feature that is crucially emerging in the historiography of early modern philosophy and science, namely the complexity in the (...) production of knowledge. The book explores the applicability of this approach to a long-considered armchair philosopher, namely René Descartes, who is now more and more understood as a full-blown scientist, networker, and intellectual éminence grise rather than as the mere philosopher of the cogito, as well as the originator of different ‘Cartesianisms’ which encompassed many ideas and approaches for long captured by dichotomic historiographical categories as rationalism and empiricism, or speculative and experimental philosophy. The essays gathered in the volume aim to address the ways in which Descartes’s philosophy evolved and was progressively understood by scientists, philosophers, and intellectuals from different contexts and eras, either by considering direct interlocutors of Descartes such as Isaac Beeckman and Elisabeth of Bohemia, early modern thinkers who developed upon his ideas and on particular topics as Nicolas Malebranche or Thomas Willis, those who adapted his overall methodology in developing new systems of knowledge as Johannes Clauberg and Pierre-Sylvain Régis, and contemporary thinkers from continental and analytic traditions like Emanuele Severino and Peter Strawson. (shrink)

Perceptual similarity is one of the most fiercely debated topics in the philosophy and psychology of perception. The documented history of the issue spans all the way from Plato – who regarded similarity as a key factor for human perceptual experience and cognition – through to contemporary psychologists – who have tried to determine whether, and if so, how similarity relationships can be established between stimuli both within and across the senses. Recent research on cross-sensory associations, otherwise known as crossmodal (...) correspondences – that is, the existence of observable consensual associations, or mappings, between stimuli across different senses – represents an especially interesting field in which to study perceptual similarity. In fact, most accounts of crossmodal association that have been put forward in the literature to date evoke perceptual similarity as a key explanatory factor mediating the underlying association. At the same time, however, these various accounts raise several important theoretical questions concerning the very nature of similarity, with, for example, the sensory, affective, or cognitive underpinnings of similarity judgements remaining unclear. We attempt to shed light on these questions by examining the various accounts of crossmodal associations that have been put forward in the literature. Our suggestion is that perceptual similarity varies from being phenomenologically-based to conceptually-based. In particular, we propose that the nature of the associations underlying similarity judgements – whether these associations are phenomenologically-, structurally-, emotionally-, or conceptually-based – may be represented in a two-dimensional space with associative strength on one axis, and cognitive penetrability on the other. (shrink)

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

Early modern Protestant scholars closely engaged with Islamic thought in more ways than is usually recognized. Among Protestants, Lutheran scholars distinguished themselves as the most invested in the study of Islam and Muslim culture. Mehmet Karabela brings the neglected voices of post-Reformation theologians, primarily German Lutherans, into focus and reveals their rigorous engagement with Islamic thought. Inspired by a global history approach to religious thought, Islamic Thought Through Protestant Eyes offers new sources to broaden the conventional interpretation of the Reformation (...) beyond a solely European Christian phenomenon. -/- Based on previously unstudied dissertations, disputations, and academic works written in Latin in the seventeenth and eighteenth centuries, Karabela analyzes three themes: Islam as theology and religion; Islamic philosophy and liberal arts; and Muslim sects (Sunni and Shi‘a). This book provides analyses and translations of the Latin texts as well as brief biographies of the authors. -/- These texts offer insight into the Protestant perception of Islamic thought for scholars of religious studies and Islamic studies as well as for general readers. Examining the influence of Islamic thought on the construction of the Protestant identity after the Reformation helps us to understand the role of Islam in the evolution of Christianity. (shrink)

The eighteenth-century German rationalist tradition is, broadly speaking, committed to (what I call) ‘the principle of rational cognition’: the grounded must be rationally cognizable from its sufficient ground. Whereas the prevailing view takes the fundamental challenge to rationalist paradise to stem from the principle of sufficient reason, I argue that it instead stems from this principle: How is it possible to rationally cognize anything at all from its ground? By investigating the opposing responses of two of Leibniz’s most influential immediate (...) successors, Christian Wolff and Christian Crusius, we find no easy way to remain in rationalist paradise. (shrink)

In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converg-ing series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz’s various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper answers the (...) question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world. (shrink)

Kant’s moral proof of the postulate of immortality in the Critique of Practical Reason is often dismissed as a failed argument that trades on illicit conceptual shifts. I argue that Kant’s argument is more interesting and less problematic than is usually thought. I first examine its role in the second Critique’s Dialectic. I then point out that the standard interpretation, according to which the argument presupposes God’s intuitive grasp of the moral equivalence between the disposition to pursue holiness and its (...) attainment, faces a number of philosophical and textual problems. I offer an alternative reading that avoids these problems. In particular, I stress the importance of Kant’s mathematized conception of the relationship between infinite progress towards an ideal goal and its attainment and argue that appealing to this conception allows Kant to meet a well-known criticism that his proof illegitimately substitutes the endless progress towards holiness for holiness itself. (shrink)

Christian Wolff’s attitude towards Leibniz’s legacy is a notoriously vexed question in the history of eighteenth-century German philosophy. In reaction against the untenable traditional depiction o...

It is easier to work out the age of the world than to work out how old Flavius Josephus thought it was. Since the nineteenth century, the former has been the concern of scientists and is now estima...

If I see, hear, or touch a sparrow, the sparrow seems real to me. Unlike Bigfoot or Santa Claus, it seems to exist; I will therefore judge that it does indeed exist. The “sense of existence” refers to the kind of awareness that typically grounds such ordinary judgments of existence or “reality.” The sense of existence has been invoked by Humeans, Kantians, Ideologists, and the phenomenological tradition to make substantial philosophical claims. However, it is extremely controversial; its very existence has (...) been called into question. This paper aims to clarify the nature and reality of the sense of existence by studying a psychiatric condition in which the sense appears to be disrupted: depersonalization disorder (DPD). (shrink)

In our contribution to this special issue on thought experiments and mathematics, we aim to insert theology into the conversation. There is a very long tradition of substantial inquiries into the relationship between theology and mathematics. Platonism has been provoking a consolidation of that tradition to some extent in recent decades. Accordingly, in this paper we look at James R. Brown’s Platonic account of thought experiments. Ultimately, we offer an analysis of some of the merits and perils inherent in framing (...) the use of thought experiments in mathematics and theology in terms of Platonism. (shrink)

Leibniz famously argues that there must be simple substances, since there are composites, and a composite is nothing but a collection of simples. I reconstruct Leibniz’s argument, showing that it relies on a commitment to mereological nihilism (i.e., the view that composites cannot be true beings). I show further that Leibniz endorses mereological nihilism as early as the 1680s and offers both direct and indirect support for this commitment: indirect support via the notion of unity and direct support via the (...) notion of persistence. I then assess the alignment of Leibniz’s mereological nihilism with his other commitments during the 1680s, including his potential commitment to corporeal substances. I argue that any viable interpretation of Leibniz’s commitment to corporeal substances is compatible with mereological nihilism, which provides a new perspective both on Leibniz’s developing theory of substance and on his mature theory of simple substance. (shrink)

Today, many philosophers write on topics of contemporary interest, such as emerging technologies, scientific advancements, or major political events. However, many of these reflections, while philosophically valuable, fail to contribute to those who may benefit the most from them. In this article, we discuss our own experience of engaging with nursing researchers and practicing nurses. By drawing on the field of philosophical phenomenology, we intervene in a longstanding debate over the meaning of “empathy” in nursing, which has important implications for (...) nursing research, training, and practice. However, our intention is not only to introduce and discuss this philosophical intervention. Rather, we present this intervention as a model for how philosophers might successfully engage with the field of nursing, and perhaps with other fields as well, with the aim of effecting positive change in research or practice. The article proceeds in five parts. First, we introduce the problem of conceptual clarity in nursing and explain why many nursing concepts are still in need of refinement. Second, we discuss the origins of the concept of empathy in nursing and outline the challenges associated with borrowing theory from other fields. Third, we explain how nurses tend to conceptualize empathy today, drawing upon the psychological distinction between cognitive and emotional empathy. Fourth, we discuss our intervention in this debate and explain how we attempt to resolve existing conceptual confusions by developing the concept of empathy from the ground up. Fifth, we conclude by briefly reflecting upon some of the challenges of interdisciplinary engagement and providing some recommendations based upon our own experience. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

Leibniz claims that Berkeley “wrongly or at least pointlessly rejects abstract ideas”. What he fails to realize, however, is that some of his own core views commit him to essentially the same stance. His belief that this is the best (and thus most harmonious) possible world, which itself stems from his Principle of Sufficient Reason, leads him to infer that mind and body must perfectly represent or ‘express’ one another. In the case of abstract thoughts he admits that this can (...) happen only in virtue of thinking of some image that, being essentially a mental copy of a brain state, expresses (and is expressed by) that state. But here he faces a problem. In order for a thought to be genuinely abstract, its representational content must differ from that of any mental image, since the latter can represent only particular things. In that case, however, an exact correspondence between the accompanying mental image and the brain state would not suffice to establish a perfect harmony between mind and body. Even on Leibniz’s own principles, then, it appears that Berkeley was right to dismiss abstract ideas. (shrink)

This essay proposes a new interpretation of a central, and yet overlooked, argument Leibniz offers against Descartes’s power-free ontology of the corporeal world. Appealing to considerations about the successiveness of motion, Leibniz attempts to show that the reality of motion requires force. It is often assumed that the argument is driven by concerns inspired by Zeno. Against such a reading, this essay contends that Leibniz’s argument is instead best understood against the background of an Aristotelian view of the priority of (...) real being over time. The essay also shows how this alternative interpretation can help to shed new light on the difference between Leibnizian forces and Aristotelian powers, as well as on Leibniz’s famous claim that accounting for force leads us beyond the mechanistic corporeal realm. (shrink)

Gottfried Wilhelm Leibniz endorses a version of the guise of the good thesis: he holds that whenever we do something intentionally, we do it because it seems good to us. This paper explores Leibniz...

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)

Leibniz's principle of sufficient reason is the claim that everything has a sufficient reason. But is Leibniz committed to the necessity or to the contingency of his great principle? I argue that Leibniz is committed to its contingency, given that he allows for the absolute possibility of entities that he claims violate the PSR. These are all cases of qualitatively indiscernible entities, such as indiscernible atoms, vacua, and bodies. However, Leibniz's commitment to the contingency of the PSR seems to stand (...) in tension with his inference of the PSR from his theory of truth. I argue that this apparent tension can be resolved satisfactorily. When it comes to his modal views on the PSR, Leibniz's position is entirely consistent. (shrink)

Leibniz’s claim that this is the best of all possible worlds has been subject to numerous criticisms, both from his contemporaries and ours. In this paper I investigate a cluster of such criticisms based on the existence, abundance or character of worldly evil. As several Leibniz-inspired versions of optimism have been advanced in recent years, the aim of my investigation is to assess not just how Leibniz’s brand of optimism fares against these criticisms, but also whether optimism as a philosophy (...) has the resources to meet these challenges. I show that none of the criticisms considered has sufficient force to pose a threat to Leibniz’s version of optimism or to one modelled on it. (shrink)

Studie se věnuje otázce po ontologickém statusu ideálního, potažmo fenomenálního prostoru v pojetí Gottfrieda Wilhelma Leibnize. Nejprve bude ujasněno, v jakém smyslu lze podle Leibnize za prostor v pravém slova smyslu považovat primárně pouze prostor ideální, sekundárně však rovněž prostor fenomenální. Posléze se vymezím zejména vůči takovým interpretacím leibnizovského ideálního prostoru, které v něm spatřují předzvěst prostoru kantovského. Leibnizův ideální, matematický prostor zde totiž bude přirovnán spíše k prostoru suárezovskému, případně hobbesovskému, nikoli však kantovskému.

This paper addresses Peter Sloterdijk’s optimistic ‘attitude’. I show that it is a philosophical posture based on pragmatic speculation and spiritual exercise. By situating it in a tradition that passes from Leibniz’s meliorism to Whitehead’s ecology of propositions, I argue that optimism is an essential component of a public use of reason of which the finality is no longer the good sense of critique but of the care for common sense. At stake is the cosmological and cosmopolitical care for the (...) possibility of rationalization processes in a ‘monstruous world’ of ever denser feedback mechanisms. (shrink)

Leibniz is unclear about the nature of pleasure. In some texts, he describes pleasure as a perception of perfection, while in other texts he describes pleasure as being caused by a perception of perfection. In this article, I disambiguate two senses of “perception of perfection”, which clarifies Leibniz’s considered position. I argue that pleasure is a perception of an increase in a substance’s power which is caused by a substance’s knowledge of a perfection of the universe or God. This reading (...) helps clarify the nature of Leibnizian happiness. Happiness is a cognitive process (akin to a mood), constituted fundamentally out of pleasure, which is grounded in increases in a substance’s power. A rational substance will sustain its happiness so long as it is more powerful than it is weak, and it is engaging in activities that increase its power. (shrink)