Leibniz desenvolve uma intensa actividade filosófico-científica ao longo de um período de mais de cinquenta anos, na procura de uma via da modernidade mais complexa do que o mecanicismo vulgar, que reduz significativamente o campo do saber. A correspondência com Jacob Thomasius, seu professor mais influente, permitiu ao jovem Filósofo uma cuidada reflexão sobre dois tópicos nucleares da sua elaboração teórica – o da continuidade e o da forma –, que são, simultaneamente, motivo de afinidade e de divergência entre ambos. (...) De facto, tal como Thomasius, Leibniz assume a tarefa de conciliar antigos e modernos, mas, diferentemente do seu Mestre, entende que a matriz dessa ciência eclética é a ciência moderna e não a aristotélica. No que diz respeito à forma e mais precisamente à forma subs­tancial, Leibniz concorda com Thomasius que ela é imprescindível na filosofia natural, mas explica a sua génese de modo mecânico, através do movimento. Por seu lado, em virtude do estatuto fenomenal do movimento, a sua causa primordial não poderá ser outra que o próprio espírito. Por conseguinte, a primeira filosofia de Leibniz conjuga mecanicismo e espiritualismo. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Symbolic Mathematics and the Intellect Militant: On Modern Philosophy’s Revolutionary SpiritCarl PageWhat makes modern philosophy different? My question presupposes the legitimacy of calling part of philosophy “modern.” That presupposition is in turn open to question as regards its meaning, its warrant, and the conditions of its applicability. 1 Importance notwithstanding, such further inquiries all start out from the phenomenon upon which everyone agrees: philosophy running (...) through Plato and Aristotle looks significantly different from philosophy running from Descartes to Kant.My concern in this essay is with the phenomenon of the difference itself, rather than with the second-order questions associated with how properly to assign it historical meaning. I take the difference between ancient and modern philosophy to be as significant as differences in philosophy’s history can be: modern philosophy rests on a new interpretation of the nature and fulfillment of human reason, and disputes about the nature of human reason are the ultimate battles of philosophy. But the general thesis is not my main point. 2 The focus of this essay falls on what may be called the integrity of the phenomenon, on the specific interpretation of human reason that lends modern philosophy its peculiar face. [End Page 233]Modern philosophy’s strikingly revolutionary spirit is my point of departure. When Descartes writes in the first of his Meditations that “it was necessary, once in the course of my life, to demolish everything completely and start again right from the foundations if I wanted to establish anything at all in the sciences that was stable and likely to last,” 3 he reveals the same enthusiasm for total reform later found in Kant: “This attempt to alter the procedure which has hitherto prevailed in metaphysics, by completely revolutionizing it in accordance with the example set by the geometers and physicists, forms indeed the main purpose of this critique of pure speculative reason.” 4 How exactly did philosophy become so convinced that its central tradition—a sprawling, disorganized, ugly city, as Descartes has it in the Discourse (I:116)—needed razing to the ground in the interest of some rational town-planning? Moreover, the calls for revolution have not abated, despite contemporary disillusionment with both Cartesian rationalism and Enlightenment philosophy in general; they have grown more shrill. The confidence with which rationalism, foundationalism, universalism, logocentrism, Platonism, and so on are currently set at naught for the sake of contingency, particularity, and difference reveals the same revolutionary and totalizing spirit that marks the earlier phase of philosophy’s modernity. Such enthusiasm is reason’s freedom taken to an extreme. 5 What inspires this march of the intellect militant? What, if anything, justifies its hubristic self-assertions in the domain of philosophy? These are the questions I address.Descartes is commonly identified as the father of modern philosophy. While the full story of modern philosophy’s parentage is more complicated than this, it is fair to say that in Descartes self-consciousness of a new mode of doing philosophy emerges with a focus and revolutionary sense of purpose that caught philosophical imagination in his own time and continues to do so in ours. 6 Motifs of modern philosophy may be found in many places—Machiavelli, Hobbes, Francis Bacon, Nicholas of Cusa, Giordano Bruno, Jakob Boehme—nonetheless, Descartes’s intensely single-minded, even jealous advocacy commends itself to all but the most stubborn antiquarian mentality as modernity’s almost perfect philosophical representative. [End Page 234]That Descartes stands on a remarkable philosophical cusp is apparent in the contrast between the title and the subject matter of his most influential philosophical work: Meditationes de Prima Philosophiae (1641). To that point prima philosophia or First Philosophy had been construed as the metaphysics. It was not concerned with the critical question of how metaphysical sciences are possible and was not directly related to any doctrine of the human soul—except perhaps on the one point of the divinity of nous, the human soul’s highest part. In Descartes’s Meditations, on the other hand, the landscape has altered. Doubt, certainty, knowledge, the ego cogitans and its stream of representations are the new subject matter. What is first in philosophy is no longer what... (shrink)

Although Leibniz's writing forms an enormous corpus, no single work stands as a canonical expression of his whole philosophy. In addition, the wide range of Leibniz's work--letters, published papers, and fragments on a variety of philosophical, religious, mathematical, and scientific questions over a fifty-year period--heightens the challenge of preparing an edition of his writings in English translation from the French and Latin.

Leibniz construit, teste et vérifie sans cesse la pertinence et la cohérence de sa philosophie en la rapportant aux conclusions des autres disciplines. Cette méthode heuristique nourrit son dialogue avec les sciences mathématiques et physiques; moins connus, les enjeux révélés par la réforme moderne de la médecine et la chimie suscitent une interrogation sur la vie et la qualité. Ces sciences expérimentales s'avèrent en effet cruciales pour une philosophie de la nature qui cherche à concilier le mécanisme et le finalisme (...) à travers les concepts d'entéléchie et de monade. Elles obligent en outre à préciser la logique de l'expérience, la fonction de la raison, le statut des principes explicatifs (loi, cause, éléments, analogie). Enfin, elles exigent un fondement qui permette de rapporter les phénomènes organiques à leur véritable origine: la vie. Ce programme se réalise de façon systématique dans la controverse qu'entretiennent Leibniz et Stahl au sujet d'une philosophie de la nature capable de prendre acte des découvertes modernes de la médecine et de la chimie, tout en fondant ces connaissances sur une théorie générale de la substance et de la vie. (shrink)

Avec les innombrables inedits, la volumineuse correspondance de Leibniz represente l'indispensable complement a l'etude de son oeuvre publiee. La correspondance avec Jakob Thomasius (Professeur a l'Universite de Leipzig et premier maitre de Leibniz), presentee pour la premiere fois de maniere exhaustive, s'etend de 1663 a 1672. Elle revele les principales preoccupations du jeune philosophe et permet d'apprecier le point de depart de ses reflexions, specialement en physique. Nourri d'un aristotelisme eclaire, en rupture avec la scolastique, Leibniz esperait jeter les bases (...) d'une Reforme de la philosophie naturelle, analogue a celle que Luther, au siecle precedent, avait realisee en theologie. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Abraham, Planter of Mathematics":Histories of Mathematics and Astrology in Early Modern EuropeNicholas PopperFrancis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be (...) created devoted to "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical." He continued:And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts, or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings, their Oppositions, Decayes, Depressions, Oblivions, Removes, with the causes, and occasions of them, and all other events concerning learning, throughout the ages of the world; I may truly affirme to be wanting.2Bacon thus positioned himself not only as a Father of Modern Science, but also a Father of the History of Science.Following Bacon's suggestion, I will examine the "small memorials" of the history of mathematics—and particularly the mathematical art of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras... (shrink)

In recent years, there has been renewed interest in Pyrrhonism among both philosophers and historians of philosophy. This skeptical tradition is complex and multifaceted, since the Pyrrhonian arguments have been put into the service of different enterprises or been approached in relation to interests which are quite distinct. The diversity of conceptions and uses of Pyrrhonism accounts for the diversity of the challenges it is deemed to pose and of the attempts to meet them. The present volume brings together twelve (...) essays by leading specialists which explore the history and philosophical significance of this form of skepticism: they discuss some thorny questions concerning ancient Pyrrhonism, explore its influence on certain modern thinkers, and examine it in relation to contemporary analytic philosophy. The essays combine historical and exegetical analysis with an assessment of the philosophical merits of the Pyrrhonian outlook, with the aim of understanding it both in its historical context and in connection with contemporary concerns. This volume, the first entirely devoted to a detailed study of the Pyrrhonian tradition, is intended to open up new exegetical and philosophical perspectives on Pyrrhonism and to motivate further examination of certain difficult issues. It will be a valuable resource for scholars of ancient philosophy, historians of modern philosophy, and epistemologists, as well as for graduate students interested in skepticism. (shrink)

The point of this study is to reconsider the roots of German idealism in pre-Kantian German modern philosophy of the seventeenth and early eight eenth centuries, or in pre-Enlightenment philosophy, which paved the way for the Enlightenment. Considered for far too long as depending solely on Leibniz and stigmatized as dogmatic—all too often it is referred to and summed up as “Leibnizo-Wolffian”—modern German philosophy appears, under close examination, to bear the mark of scepticism. This scepticism is precisely embodied (...) by Thomasius, who is in many ways the father of German modern philosophy and a contemporary opponent of Leibniz. The aim of this paper is to reconsider the important series of philosophical transformations from Leibniz to Kant. I will be arguing that the pervasive nature of scepticism in the thought of Thomasius and his followers enabled the striking spread of Hume’s philosophy in modern German philosophy, Wolff included. In this way, I hope to contribute to understanding the sources of modern philosophy through what can be called, with Foucault in mind, an archaeology of the Aufklärung, with the aim of rethinking Kant’s own contribution. (shrink)

Newton composed several mathematical tracts which remained in manuscript form for decades. He chose to print some of his mathematical tracts in their entirety only after 1704. In this paper I will give information on the dissemination of Newton’s mathematical manuscripts before the eighteenth-century printing stage. I will not consider another important vehicle of dissemination of Newton’s mathematical discoveries, namely his correspondence with other mathematicians or with intermediaries such as Collins and Oldenburg.In a first stage, Newton’s mathematical manuscripts were rendered (...) available to a group of acolytes, who copied and transmitted them, sometimes in mutilated form. The practice of scribal publication helped Newton to establish his mathematical reputation and to form around himself a group of followers.One can divide Newton’s mathematical activity into two periods: an early analytical and modernist period in which he developed a Cartesian and Wallisian ‘new analysis’, followed by a mature synthetic period, beginning in the 1670s, in which he distanced himself from analysis in favour of geometry, from infinitesimals in favour of limits, from the analysis of the moderns in favour of the geometry of the ancients. Newton came to the conclusion that the ‘new analysis’ was not a mathematical language fit for publication.Newton, however, could not restrict himself to scribal publication of his mathematical manuscripts for too long. The priority dispute with Leibniz, the new status of Newton as undisputed master of British mathematicians and the changing canons of mathematical publication introduced by the funding of scientific academies favoured Newton’s option for the printing of his mathematical manuscripts. However, when Newton decided to print his early analytical mathematical work, he tried to modify and present it to bring it in line with the values that characterise the methodological shift of the 1670s, values that he wished to promote among his followers.Author Keywords: Isaac Newton; Manuscripts; Scribal publication; Analysis; Synthesis. (shrink)

The point of this study is to reconsider the roots of German idealism in pre-Kantian German modern philosophy of the seventeenth and early eight eenth centuries, or in pre-Enlightenment philosophy, which paved the way for the Enlightenment. Considered for far too long as depending solely on Leibniz and stigmatized as dogmatic—all too often it is referred to and summed up as “Leibnizo-Wolffian”—modern German philosophy appears, under close examination, to bear the mark of scepticism. This scepticism is precisely embodied (...) by Thomasius, who is in many ways the father of German modern philosophy and a contemporary opponent of Leibniz. The aim of this paper is to reconsider the important series of philosophical transformations from Leibniz to Kant. I will be arguing that the pervasive nature of scepticism in the thought of Thomasius and his followers enabled the striking spread of Hume’s philosophy in modern German philosophy, Wolff included. In this way, I hope to contribute to understanding the sources of modern philosophy through what can be called, with Foucault in mind, an archaeology of the Aufklärung, with the aim of rethinking Kant’s own contribution. (shrink)

The article presents philosophical views on music in the context of the transformations of the worldview from Antiquity to the Modern Time. In this research author also mentions the contemporary issues, and uses her own philosophical concept of the music, which can be described as following: the value of music as a substance and the way of the valuable interaction of a person with the world affirm the essence of musical being, in which the invariable principle of Harmony, the (...) principle of Chaos-Form movement, is preserved. Music expresses the fluid essence of the world and changes of being in space and time. Philosophy of music as a field of philosophical knowledge considers music from ontological-epistemological and phenomenological-axiological prospectives, as something more than just a form of art. It explores the deep, ultimate foundations of the existence of music as such and the philosophical and aesthetic foundations of musical art. Since ancient times music has been a representation of the world in the human conscience and served as the harmonic equivalent of cosmological philosophy, mathematics, astronomy, and astrophysics. The scientific view on music was enriched in the Modern Time by the expanded view on the cosmo-sound space reflected in musical art, which at the same time transforms the mathematical ideas of geometricity, squareness etc. The tendency to create integral world music in the musical practice of the XX-XXI centuries explains the attempt of mankind to present music by modern methods of composing musical art as an expression of fear towards the secret Harmony of universal existence, and, on the other hand - as a form of search for salvation and mental balance, intuitively reflecting what is happening in natural science, which more and more points to the abyss of unknowable universe, and the unstable place of man in the world. (shrink)

The appellation “Western” is, in my view, inappropriate when applied to Ancient Hellas and its greatest product, the Hellenic philosophy. For, as a matter of historical fact, neither the spirit of free inquiry and bold speculation, nor the quest of perfection via autonomous virtuous activity and ethical excellence survived, in the purity of their Hellenic forms, the imposition of inflexible religious doctrines and practices on Christian Europe. The coming of Christianity, with the theocratic proclivity of the Church, especially the (...) hierarchically organized Catholic Church, sealed the fate of Hellenic philosophy in Europe for more than a millennium. Since the Italian Renaissance, several attempts primarily by Platonists to revive the free spirit and other virtues of Hellenic philosophy have been invariably frustrated by violent reactions from religious movements, the Reformation and the Counter-Reformation, and the bloody wars which followed their appearance in Europe. Modern science succeeded to a certain extent, after struggle with the Catholic Church, in freeing itself from the snares of medieval theocratic restrictions. Thus, it managed to reconnect with the scientific spirit of late antiquity and its great achievements, especially in the fields of cosmology, physics, mathematics, and medicine, which enabled modern science to ad-vance further. But it seems that the mainstream European philosophy has failed to follow the example of science and to liberate itself, too. As in the Middle Ages, so in modern and post-modern times the “European philosophy” has continued to play the undignified and servile role of handmaiden of something. In addition to the medieval role of “handmaiden of theology” (ancilla theologiae), since the seventeenth century philosophy in Europe assumed the role of “handmaiden of science” (ancilla scientiae) and, with the coming of the Marxist “scientific socialism,” the extra role of ‘handmaiden of ideology” (ancilla ideologiae). In this respect, the so-called “Western philosophy,” as it has been historically practiced in Christian and partially Islamized Europe, is indeed a very different kind of product from the autonomous intellectual and ethical human activity, which the Ancient Hellenes named philosophia and honored as “the queen of arts and sciences.” In this historical light, Hellenic philosophy would appear to be closer to the Asian philosophies of India, China, Japan, and Korea than to Western or “European philosophy.” So as we stand at the post-cold war era, witnessing the collapse of Soviet-style Socialism and the coming of the post-modern era; as we look at the dawn of a new millennium and dream of a new global order of freedom and democracy, the moment seemspropitious for reflection. We may stop and reflect upon our philosophical past as exemplified in the free spirit of Hellenic philosophy and its misfortunes, its great “passion” in Christian Europe in the last two millennia or so. (shrink)

The work of David R. Lachterman, The Ethics of Geometry, subtitled A Genealogy of Modernity, concerns essentially the status of geometry in Euclid’s Elements and in Descartes’s Geometry. It is a remarkable work, at once by the declared breadth of its ambitions and by the very great precision of its analyses, which are always supported by a prodigious philosophical culture. David Lachterman’s concern is to grasp, by way of an in-depth commentary of certain, particularly crucial passages of these two foundational (...) works, the change in geometry’s status from the one to the other, and this, as a sort of symptom of what the Moderns, since Descartes, will always experience as a necessary, inaugural rupture with regard to tradition. This change is underlaid, according to the author, by a profound change in the philosophical ethos, and in particular, in the geometer’s ethos. One must understand ethos, Lachterman explains, in the manner of Aristotle: those characteristic means that human beings have by which to act in the world or to behave in relation to one another, or to themselves. There is thus an “ethics” of geometry, namely, in the manner and the style of doing geometry, of behaving as a mathematician both toward apprentices and toward the veritable nature of the “entities” which are to be taught or learnt, and which give their discipline its name. That there is a difference of ethos between Euclid and Descartes implies, according to Lachterman, that there is also a difference in the source of intelligibility of the “mathematical,” understood in the most general sense. This in turn implies a deeper difference in the mode of being in general: it suffices to note that, in the ancient case, the source of intelligibility of the geometric figure lies in the nature of the figure itself, and that in the modern case, the same source is found in the “strategies” and “tactics” suited to bringing the figure to its visibility or to its embodiment, 315 in order to notice that this change in the mode of access to intelligibility must have had profound repercussions upon philosophical thought. It is in this sense that the author’s design is also, at the same time, not genetic, but genealogical. The break between ancient and modern mathematics pleas in favor of a consideration of the rupture of modern thought relative to ancient thought; thus, implicitly—and it is one of the great merits of this book that it shows this—against all homogenizing levelling, in Heidegger’s fashion, of the history of thought down to the history of “the” discipline of metaphysics. If there is something Heideggerian, in the best sense of the term, in Lachterman’s way of considering ethos as coextensive with modes of being, there is, on the other hand, and we ought to be very glad of it, something anti-Heideggerian in his original manner of bringing out the effective novelty of modern thought. For, according to him, modern thought is no longer to be defined, explicitly or exclusively, by the so-called “metaphysics of subjectivity.” Instead, it is defined by a self-regulated, operative, and constructive productivity of thought—and this as much with regard to itself as to its objects. To put it briefly, whereas ancient thought is rather polarized by the logico-eidetic, modern thought is polarized by a sort of methodical constructivism, the status of which is, in reality, very complex. If Descartes speaks of “the construction of a problem,” while Leibniz speaks of the “construction of an equation,” and Kant of the “construction of a concept,” everything depends—as we might guess—upon the multiple meanings that the term ‘construction’ may take on. Is it to be taken in the sense of an absolute creation, a quasi ex nihilo creation, which would render mathematics divine? Is it the creation of artefacts, or again, is it the methodical exploration of problems posed to thought by the existence of objects or corresponding ideas, themselves supposed to be somewhere in the divine understanding? We already discern the breadth and the depth of the debate, and we sense that the essential will be played out in Lachterman’s commentaries on the famous Cartesian solution of the problem of Pappus—the birth certificate, as we know, of analytic geometry. (shrink)

Scientific observation has led to the discovery of recurring patterns in nature. Symmetry is the property of an object showing regularity in parts on a plane or around an axis. There are several types of symmetries observed in the natural world and the most common are mirror symmetry, radial symmetry, and translational symmetry. Symmetries can be continuous or discrete. A discrete symmetry is a symmetry that describes non-continuous changes in an object. A continuous symmetry is a repetition of an object (...) an infinite number of times. A consequence of continuous symmetry is the existence of conservation laws. A natural system with discrete and continuous symmetries displays several physical properties, such as the existence of long-range order. Geometric shapes exhibit symmetry as mirror reflections of each other. Symmetry in nature has been a model of beauty since the beginning of civilization. Since the earliest times, nature itself has manifestly been a model, evincing regularity in sundry forms and occurrences–from minerals and plants to the anatomy of living beings, to the regularly recurring stellar constellations. For Ancient Greek philosophers, proportion, symmetry, and harmony, were the basics to determine whether something is beautiful or not. Ancient Greek philosophers were known for bringing logic and rational thinking to phenomena that were previously explained by mythology and Gods. They observed the natural world around them and used their knowledge to answer questions about the proportion in observable objects and the origin of Earth. The Greek words _summetria_ and _summetros_ appear frequently in the Timaeus, defined as parts with each other and with the whole. Plato has a very rough concept of symmetry, and when he uses “beauty” to characterize the so-called Platonic Solids in the Timaeus, he seems to be emphasizing their regularity and indirectly their symmetry. Plato believes the four elements (earth, air, fire, water) have been constructed by the Demiurge, or a divine craftsman who appoints order in an otherwise chaotic universe. Minerals are representative examples of beauty, order, and symmetry in inorganic materials. Well-formed minerals (crystals) are a collection of equivalent faces related by symmetry. The goal of this paper is to relate the perspective of symmetry in ancient Greek philosophy with the modern scientific evidence of the geometric description of crystal structures. The five Platonic solids are ideal models of geometrical patterns that occur throughout the world of minerals. In this paper, minerals serve as a model of connecting the symmetry theory in Plato’s philosophy and modern advances in mineralogy. (shrink)

David Hume is the most influential precursor of modern empiri cism. By modern empiricism, I intend a belief that all cognitive conflicts can be resolved, in principle, by either appeal to matters offact, via scientific procedure, or by appeal to some sets of natural or conventional standards, whether linguistic, mathematical, aes thetic or political. This belief itself is a consequent of an old appre hension that all synthetic knowledge is based on experience, and that the rest can be (...) reduced to a set of self-evident truths. In this broad sense, Modern Empiricism encompasses classes, such as Logi cal Empiricism, Logical Atomism and Philosophical Analysis, and unique individuals such as Russell and Moore. It excludes, thereby, the present day continental philosophies, such as Thomism, Exist entialism, and Dialectical Materialism. Modern empiricists, to be sure, are influenced by many other phi losophers. Locke, Berkeley, and Mill, among the classical empiri cists, and Leibniz and Kant, among the rationalists (the former especially on the logico-mathematical side) in one way or other are responsible for the appearance of empiricism in its new form. But none of them were as influential as Hume. This, by itself is not news. Weinberg, in his well-known book, An Examination of Logical Positivism, observes that: Many, if not all, of the principal doctrines of contemporary positivism derive from Hume. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns by Arkady PlotnitskyNoam CohenPLOTNITSKY, Arkady. Logos and Alogon: Thinkable and Unthinkable in Mathematics, from the Pythagoreans to the Moderns. Cham: Springer, 2023. xvi + 294 pp. Cloth, $109.99The limits of thought in its relations to reality have defined Western philosophical inquiry from its very beginnings. The shocking discovery of the incommensurables in (...) Greek mathematics not only reintroduced these limits with greater force but also instigated two different forms of coping with the unthinkable in Western philosophy, mathematics, and science. As Arkady Plotnitsky sets forth, in response to the incommensurability crisis in the ancient Greek intellectual world, there appeared two different attitudes toward the alogon, that is, the unthinkable or irrational. Plato and his followers sought to overcome the unthinkable, of which the incommensurables in mathematics are only an example, through philosophy. In contrast, the Pythagoreans continued to hold on to mathematics as the primary means of knowing the world, but put a larger emphasis on geometry. Plotnitsky [End Page 359] claims that by not putting aside the primacy of mathematics, the Pythagorean shift from arithmetic to geometry established in Western thought a certain tolerance toward the unthinkable within the realm of the thinkable, “a possibility of the alogon in the logos.” Until modern times this remained no more than a possibility. However, in modern mathematics and mathematical physics Plotnitsky identifies a certain fulfillment of this potential, a “radical Pythagorean mathematics.” In his comprehensive and thought-provoking study, Plotnitsky recounts the development of such radical modern Pythagoreanism, not only to tell its history but also to suggest that the unthinkable is a condition of possibility for thought, and that a proper recognition of this role it plays is crucial for the advancement of mathematical thinking and thinking in general.Plotnitsky begins by portraying in broad strokes the two defining characteristics of radical Pythagorean mathematics: the presence of the unthinkable within mathematical thought itself, and the interplay of algebra and geometry. Relying on an extensive knowledge of the history of modern mathematics and physics, in the first two chapters of the book Plotnitsky gradually demonstrates the key role that the alogon plays in some theories of modern mathematical thought, such as Gödel’s incompleteness theorems and quantum mechanics. He also presents and clarifies his own conception of the history of Western thought as a creative process of concept-forming. By creating rather than discovering concepts, great mathematicians break new ground for thinking. The book as a whole argues in length for these two main theses.In chapter 3, the author addresses the thought of Bernhard Riemann to make the case that Riemann’s mathematical thought puts an emphasis on creative conceptual thinking and is not defined merely by calculations or logic. Such thinking is problem-posing rather than axiomatic. Riemann’s central innovation in this respect is the concept of manifold (Mannigfaltigkeit), which enabled him to think anew space and geometry in a radical non-Euclidean fashion, implying an infinite number of possible geometries. Plotnitsky argues—borrowing Deleuze and Guattari’s terminology—that this opened up a “plane of immanence,” which is to say that Riemann created a concept-generating movement of thought. However, we cannot grasp the generation of concepts in modern mathematics without giving proper attention to the interplay of algebra and geometry that defines it. Chapter 4 demonstrates this interweaving of the two fields by recounting the history of the idea of the curve in modernity, from the analytic geometry and calculus of Fermat and Descartes to its modification in the concept of a Riemann surface, up to its more recent developments in the algebraic geometry of Weil and Grothendieck. It gives a historical account of the algebraization of the curve that at the same time brings into relief the irreducible geometrical aspect, continuity, of all modern mathematical conceptualizations of the curve.The next two chapters provide further case studies. Chapter 5 expands and solidifies the argument of chapter 2. It discusses three examples of mathematical practice, each displayed by a pair of important [End Page 360] mathematicians: Abel and Galois, Lobachevsky and Riemann, Weil and Grothendieck. Each case... (shrink)

This volume is a critical edition of the ten-year correspondence between Gottfried Wilhelm Leibniz, one of Europe’s most influential early modern thinkers, and Bartholomew Des Bosses, a Jesuit theologian who was keen to bring together Leibniz’s philosophy and the Aristotelian philosophy and religious doctrines accepted by his order. The letters offer crucial insights into Leibniz’s final metaphysics and into the intellectual life of the eighteenth century. Brandon C. Look and Donald Rutherford present seventy-one of Leibniz’s and Des Bosses’s letters (...) in the original Latin and in careful English translation. Few of the letters have been translated into English before. The editors also provide extensive annotations, deletions, and marginalia from Leibniz’s various drafts, and a substantial introduction setting the context for the correspondence and analyzing the main philosophical issues. (shrink)

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

This volume is a critical edition of the eight-year correspondence between Gottfried Wilhelm Leibniz and Burcher de Volder, professor of philosophy and mathematics at Leiden University. Containing the surviving correspondence between Leibniz and De Volder, the volume also presents a generous selection from the letters between Leibniz and his friend Johann Bernoulli, through whose intercession the correspondence began. Bernoulli acted as intermediary throughout, and the often candid discussions between Leibniz and Bernoulli provide illuminating background to the correspondence proper. Each (...) of the selections appears both in the original Latin and in English translation. (shrink)

François Viète is often regarded as the first modern mathematician on the grounds that he was the first to develop the literal notation, that is, the use of two sorts of letters, one for the unknown and the other for the known parameters of a problem. The fact that he achieved neither a modern conception of quantity nor a modern understanding of curves, both of which are explicit in Descartes’ Geometry, is to be explained on this view (...) “by an incomplete symbolization rather than by any obstacle intrinsic in the system.” Descartes’ Geometry provides only a “clearer expression” of themes already sounded in Viète’s work, one that perfects Viète’s literal calculus and gives it “its modern form”; it merely continues the “‘new’ and ‘pure’ algebra which Viète first established as the ‘general analytic art’.” It can seem, furthermore, that this must be right, that had there been some obstacle intrinsic to Viète’s system that barred the way to a modern conception of quantity and a modern understanding of curves, then Descartes’ Geometry would have had to have taken a very different form than it did. As it was, Descartes had only to improve Viète’s symbolism, free himself of the last vestiges of the ancient view of geometrical and arithmetical objects, and apply the new symbolism to the study of curves in order to achieve what Viète did not but could have. But what, really, is the status of this “could have”; what would it actually have taken for Viète to achieve Descartes’ results in the Geometry? The interest of the question lies in its potential to better our understanding of the nature of modern mathematics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Method in Ancient PhilosophyDavid K. GliddenJyl Gentzler, editor. Method in Ancient Philosophy. Oxford: Clarendon Press, 1998. Pp. viii + 398. Cloth, $72.00.The fifteen papers in this collection constitute revisions of conference proceedings and reflect the varied interests of participants. The ensemble exhibits a thoroughly modern methodology. Whatever and however various ancient methods of philosophy may have been, in Anglo-American scholarship it is standard practice (...) to first address established scholarly interpretations as the primary entry point to critical discussionóoften displacing antiquity with a critical vocabulary of philosophical modernity. Scholars may come to understand each other better, but at the risk of asking the wrong questions or sacrificing ancient texts themselves as mere means of producing papers.Most scholars are progressives. They believe philosophy has advanced past the comparatively primitive wisdom of antiquity, and so such scholars feel perfectly entitled to make better sense of ancient texts, by patiently explaining what the ancients would have meant had they only been able to get it right. There are, of course, exceptions. And some papers in this collection suggest deeper faith in our philosophic fathers. So, the battle between the ancients and the moderns is joined once more, between those who would adorn their papers with footnotes for their peers and those who would attempt more anthropological an inquiry into ancient philosophic practices.Ian Mueller and Robert Bolton each address the same passage in Plato's Phaedo, both beginning with an article from Vlastos, first published in 1969. Mueller thoughtfully explores three different yet related accounts of what we might call scientific method in explaining Plato's views on natural change. Bolton wonders whether scholars are asking the wrong questions. Patricia Curd attempts a progressivist account of Eleatic thought, notwithstanding her recognition of the paucity of ancient sources. Complete with elaborately numbered sentences, Gail Fine focuses primarily on Burnyeat (1976) on Plato on Protagoras. Constance Meinwald presents a rather near-sighted account of two passages in the Philebus that employ the peras-apeiron distinction, with a view toward Plato's allegedly modernist mathematization of understanding. Lesley Brown revisits five pages of the Sophist that were hotly debated in the 1960s. With charity and elegance, she offers several plausible solutions to puzzles posed by previous scholars. Sometimes time smoothes over differences.A. A. Long's essay on Plato's presentation of Socrates in the Theaetetus might appear more philosophically anthropological. Yet Long reveals progressive sympathies, suggesting that Plato dispatches Socrates in the Theaetetus, so as to prepare the way for a more rigorously academic form of philosophizing, such as that exhibited in the Sophist. [End Page 111] In this way, Long speculates, Plato abandoned practical ethics for the academic life of research, so familiar to university professors and conference participants. It might be hard to square such speculation with Plato's Laws and the reception of Plato's writings among his own contemporaries. Still, Socrates' shifting role in Plato's dialogues is well worth pondering.By comparison, T. H. Irwin's contribution is wonderfully old-fashioned. His paper addresses the background knowledge to be presumed by ancient readers of Plato's dialogues and how that knowledge is artfully put to use in Plato's depiction of Socrates' reflections on the unity of virtue. By speculating on Plato's relation to his ancient readers, Irwin displaces many modernist preoccupations, though not without himself falling victim to that peculiar scholarly obsession of dating Plato's dialogues by their doctrines.With characteristic conservatism, Gisela Striker cautions scholars not to over-read Aristotle's Prior Analytics. While that extraordinary work may have deep implications for the history of formal logic, it probably was instead intended to be part of a general account of argument. In a similar vein, Charlotte Witt attempts to rescue Aristotle from scholars who would delimit Aristotle's multifarious uses of the "for the sake of" explanation, which altogether pervade his metaphysics, physics, biology and ethics. Yet, Witt soon finds herself competing in a contest over interpretive distinctions, a sport that will certainly never capture Aristotle's own authorial intentions.Facing another mass of scholarship, in this case on Aristotle's dialectic, C. D. C. Reeve sensibly attempts to... (shrink)

C'est en janvier 1678 que Leibniz a adopté la formule mv2 comme mesure de la force et a identifié en elle l'invariant d'un principe général de conservation, évinçant le principe cartésien de conservation de la quantité de mouvement. Leibniz a caractérisé comme " réforme " cette nouvelle formulation qui rendait possible d'appréhender dans une systématicité originale les lois du mouvement. Le De corporum concursu est publié ici pour la première fois, avec d'autres documents entièrement inédits qui en éclairent les antécédents (...) et les suites. L'Introduction restitue l'état des problèmes qui ont soutenu la formation des idées fondatrices de la philosophie de la nature leiblizienne. Un Commentaire suivi, faisant place à la traduction de larges extraits, restitue la signification historique et épistémologique d'un document qui apporte une information entièrement nouvelle sur un moment essentiel dans la constitution de la pensée de Leibniz. (shrink)

The novel use of symbolism in early modern mathematics poses both philosophical and historical questions. How can we trace its development and transmission through manuscript sources? Is it intrinsically related to the emergence of symbolic algebra? How does symbolism relate to the use of diagrams? What are the consequences of symbolic reasoning on our understanding of nature? Can a symbolic language enable new forms of reasoning? Does a universal symbolic language exist which enable us to express all knowledge? (...) This book brings together a collection of papers that address all these and related questions which were initially posed at a conference held in Ghent (Belgium) in August 2009. Scholars working on philosophy of science, history of philosophy and history of mathematics provide an insight into the role and function of symbolic representations in the development of early modern mathematics. The papers cover the period from early abbaco arithmetic and algebra (14h century) up to Leibniz (early 18th century). (shrink)

This volume presents two Leibnizian writings, the Specimen of Philosophical Questions Collected from the Law and the Dissertation on Perplexing Cases. These works, originally published in 1664 and 1666, constitute, respectively, Leibniz's thesis for the title of Master of Philosophy and his doctoral dissertation in law. Besides providing evidence of the earliest development of Leibniz's thought and amazing anticipations of his mature views, they present a genuine intellectual interest, for the freshness and originality of Leibniz's reflections on a striking variety (...) of logico-philosophical puzzles drawn from the law. The Specimen addresses puzzling issues resulting from apparent conflicts between law and philosophy (the latter broadly understood as comprising also mathematics, as well as empirical sciences). The Dissertation addresses cases whose solution is puzzling because of the convoluted logical form of legal dispositions and contractual clauses, or because of conflicting priorities between concurring parties. In each case, Leibniz dissects the problems with the greatest ingenuity, disentangling their different aspects, and proposing solutions always reasonable and sometimes surprising. And he does not refrain from peppering his intellectual acrobatics with some humorous comments. bbbbbb. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Causation Debate in Modern Philosophy: 1637–1739J. A. CoverKenneth Clatterbaugh. The Causation Debate in Modern Philosophy: 1637–1739. New York and London: Routledge, 1999. Pp. xi + 239. Cloth, $75.00. Paper, $21.00.Over the scholastics and earliest moderns, Hume had an advantage of hindsight in declaring that "There is no question, which on account of its importance, as well as difficulty, has caus'd more disputes both among ancients (...) and modern philosophers, than this concerning the efficacy of causes, or that quality which made them be followed by their effects" (Treatise I.iii.14). Between the scholastics and Hume fell (i) Descartes, (ii) classical mechanists such as Hobbes and Gassendi, (iii) the Cartesians Le Grand and Malebranche, (iv) the explanatory rationalists Spinoza and Leibniz, (v) later experimental mechanists such as Boyle, Rohault and Newton, and (vi) the so-called empiricists Locke and Berkeley. This book presents an accessible and admirably broad overview of the modern debate about causation, without sacrificing serious attention to textual details. With two chapters on (i) and one apiece on (ii) - (vi), Clatterbaugh earns for himself and his reader a helpfully synoptic picture of philosophical shifts in the causation debate in the hundred years separating Descartes' Discourse and Hume's Treatise. By the end of the (modern) day, (1) the four-fold causes of Aristotelian-Scholasticism have given way to efficient causation alone; (2) no pre-existing forms in efficient causes are to be found, nor indeed any substantial active powers whatever; (3) there is no deep sense in which causes communicate reality to effects; (4) necessary connection has gone by the board; (5) divine causation has no place in a natural philosophy of causation. No surprises there, but Clatterbaugh's effort reminds us afresh of the varied and torturous routes to such shifts, helping advanced students better (or newly) appreciate them in the comfortable space of 200 pages.Of those pages, a third are devoted to Descartes and the Cartesians. That's not inappropriate, given the importance and difficulty of Descartes's response to Aristotelian-Scholastic accounts of causation, and its influence on occasionalist sentiments on the Continent. The tenor and value of this book may be illustrated by reflecting on the first of these—a rich and frustrating business, both in Descartes's texts and in Clatterbaugh's book. Suppose we grant Descartes the back of his hand to substantial forms and active formal causes as at best "unexplanatory" (counseling Regius): his "at-least-as-much-reality-in-the-cause-as-in-the-effect" principle might be treated as the basis of "an alternative" metaphysical account of causation (19-32). Well, it might be so-treated: but three versions of the principle later, the reader will be excused for judging it little more than a necessary condition for some event-pair x,y counting as a cause-effect pair. If the scholastic appeal to active forms is unexplanatory, then Descartes's [End Page 600] principle—which isn't Descartes's principle at all but a scholastic commonplace—can scarcely fill the explanatory gap. Glossed as a predictable consequence of some strong form of influxus physicus, it is embarrassed by Foucher's objection (that mind bears no likeness to body) and by the weight of texts urging that accidents are individual to their bearers. Having offered us no deep metaphysical story about what in the world answers to 'vis,' Descartes is at best a bungling "interactionist" (here appropriating Clatterbaugh's word for someone whose apparent talk of secondary causes we are asked to respect as expressing a strict and considered philosophical commitment). One can only side with Voetius in reckoning Descartes's replacement of forms by purely quantitative, mechanical principles of motion as expressing a mere "disposition of the movable to move... not an activity of an efficient cause, but merely a necessary condition and a causa sine qua non" (my emphasis: Selectarum Disputationum I [1648-59], 873). Descartes has no deep theory about the nature of causation.Is that too harsh? Had this book a different target, one could fairly complain that the author too infrequently steps away from the texts and commentators to offer and defend a... (shrink)

Gottfried Wilhelm Leibniz, who was born in 1646 just before the end of the Thirty Years War and who died 1716, is surely one of the most bizarre and interesting of the early modern philosophers. He was an astonishing polymath, and responsible for some of the most advanced work in the sciences of his day—he was, for instance, the co-inventor along with Newton, of differential calculus, and is generally recognized as the greatest logician of the early modern period, (...) responsible for advances in logic not rivaled until the mid-nineteenth century. But this progressive aspect of Leibniz’s thought is paired by one that was more backward looking, deeply engaged with premodern forms of thinking that referred back through Medieval culture to the philosophy of ancient times. And alongside of his scientific advances, he is known for having created one of the most baroque and puzzling metaphysical systems in the history of philosophy—the so-called “Monadology”. For much of his life he was also absorbed in theological disputes that have now been long been forgotten, and generally thought of as alien to modern scientific modes of thought. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Hellenistic and Early Modern PhilosophyChristopher S. CelenzaJon Miller and Brad Inwood, editors. Hellenistic and Early Modern Philosophy. New York: Cambridge University Press, 2003. Pp. xii + 330. Cloth, $60.00.There are at least two ways of writing the history of philosophy: the first and most common among those self-identified as "philosophers" treats philosophers of the past as if they were in live dialogue with the present. Only (...) the text is dissected, studied, and analyzed as the interpreter attempts to reconstruct, examine, and occasionally challenge the arguments under consideration. Practitioners of this first way assume that systematic and seemingly internally coherent styles of thought are most worthy of the name "philosophy." These thinkers believe that the term "philosophy," as Richard Rorty pointed out long ago, has an "honorific" sense: philosophy as such stands above other forms of thought, it is regulative in scope, and it serves as something that examines the conclusions of other, necessarily less rigorous fields. The second way is more explicitly contextualist, seeking to understand what a past thinker may have meant in his own time, what outside factors may have shaped his arguments, and how his thought may be part of broader historical currents that are none the less worthy of being remembered and studied now. Practitioners of this way are more likely to believe that ambiguities or seeming deficiencies of clarity that we find in the work of a past thinker are unlikely to be resolved by hypothetical, propositional reconstruction; rather the ambiguities are apparent to us because we are differently situated, so that the study of history is a more powerful tool in helping us satisfactorily access the work of a past thinker than rationalistic reconstruction. (Full disclosure: I am an advocate of the second way.) This volume presents studies that fall into both of the two camps, as Jerome Schneewind points out in his cogent introduction.The volume has a manifest unity: almost all of the articles are concerned in some way with different Hellenistic schools of thought and the way early modern thinkers used, re-imagined, and interpreted them. The studies are often meticulous and all are stimulating. Anthony Long offers a wonderfully synthetic presentation of ancient Stoicism as a coherent system, after which he examines the way Spinoza, Justus Lipsius, and the eighteenth-century Anglican bishop Joseph Butler measure up; unsurprisingly, they don't measure up that well. Margaret Osler seeks to illuminate the way Gassendi appropriated certain aspects of Epicureanism. Philip Mitsis argues that modern scholarship on Locke has not taken Locke's interest in Cicero's De officiis as a tool for teaching morality seriously. Donald Rutherford studies Leibniz's critique of Stoicism, which "centers," he writes, on their "failure to offer an adequate explanation of the nature of moral progress and of the dependence of human happiness on the hope for such progress" (62-63). Catherine Wilson presents a study of the corpuscular aspect of Epicurean natural philosophy among Leibniz and his contemporaries. Jon Miller eloquently and thoughtfully discusses the way Grotius and Spinoza worked with the natural law theory of the Stoics. Among a number of excellent articles, perhaps the most interesting is Stephen Menn's. Menn makes a compelling case that Descartes's intellectual autobiography in the Discourses may be seen as part of a tradition. In it, the writer presents himself as reaching a moment of dissatisfaction with the intellectual customs with which he has come into contact and as needing to strike off into new directions, unencumbered by the vestiges of those customs. While others, most notably Dan Garber, have shown that, as Menn puts it, "none of Descartes's contemporaries seem to have thought in 1637 that they were witnessing a revolution" (142), Menn's study is striking because it shows the depth of the tradition within which Descartes was working. Next, Gail Fine finds that the Cyrenaics, as presented by Sextus Empiricus, seem to have [End Page 207] endorsed "the view that there are truths, beliefs, and knowledge about the subjective" (214). Steven Nadler seeks to show that there is no mysticism in Spinoza's thought, even though it was not uncommon in Spinoza's own day to... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 40.1 (2002) 121-122 [Access article in PDF] Book Review Humanism and Early Modern Philosophy Jill Kraye and M. W. F. Stone, editors. Humanism and Early Modern Philosophy. New York: Routledge, 2000. Pp. xii + 270. Cloth, $75.00 Early-modern philosophy begins in the seventeenth century. This book, based on a colloquium at the Warburg Institute, London in 1997, strives at extending (...) the limits of this period into the sixteenth and fifteenth centuries. Thus "the long-standing exclusion of the Renaissance from the standard philosophical curriculum" (xii) should come to an end by acknowledging its being an integral part of early modern philosophy and its relevance for an understanding of modern thought. The distinctive element of the Renaissance was, according to the editors, humanism, understood as the revival of ancient sources from the fourteenth century on, and its impact on the shaping of modern thought by these sources.One can identify the following types of argument offered in the twelve contributions to this book: (1) Renaissance humanists mediated classical sources into the seventeenth and following centuries either by translating Greek texts into Latin (Lohr on Aristotle commentaries) or by offering new interpretations that were to become standard (Hankins on Ficino and Galileo, and Mercer on the German Platonists). (2) Ancient modes of thought, mediated through the Renaissance, shaped modern philosophy (Stone on Aristotelian and Reformed ethics, Levi on Stoicism in Justus Lipsius, Kraye on Marcus Aurelius editions, and Osler on Gassendi and Aristotle). (3) Humanist literary forms and mentalities survived in modern thought (Bianchi on dialogue, Vickers on rhetoric in Bacon, and James on 'grandeur' and scientific argument).Two papers do not fit into this scheme: in "The Theology of Lorenzo Valla," the only paper dealing directly with a Renaissance humanist, Monfasani wants to prove that "Valla was no theologian." Monfasani does this on the basis of a very narrow concept of dogmatic correctness, blaming Valla continuously for being banal, to the effect that the paper does not contribute to the topic of the book. One could well connect Valla's theological issues (free will, summum bonum, trinity, etc.) with his provocative stirring up of philosophy in general and show his influence on Protestant theology and on modern ethics.The other paper is by J. R. Milton, which is enlightening because it summarizes the prejudices against humanism in modern philosophy ("'Delicate learning,' erudition and the enterprise of philosophy"). He endorses "one of the most familiar narratives in European philosophy" (161), namely that Descartes's breakthrough was due to his total rupture [End Page 121] with the philosophical tradition, especially with contemporary humanist and scholastic thought. Thus Descartes's triumph was that of the myth of the irrelevance of history to philosophy as evident in Galileo, Locke, and even Hume. If antecedents are acknowledged, e.g., in Berkeley, then accepting that they "provide us either with an irreplaceable source of wisdom or with equally irreplaceable models for imitation, or indeed both" (167), still fails to recognize that the history of a philosophical problem is a part of that problem rather than just some general "wisdom" or a model for imitation. Of course, Milton repeats the myth of Bacon's anti-humanism, masterly refuted in this very book by Brian Vickers, and Milton believes that Valla "enthroned" "custom and example" and therefore for him "it would be difficult if not impossible to state Hempel's Raven Paradox" (169). One might wonder whether the conclusion: "All ravens are black --all non-black things are non-ravens," is the paramount of modern philosophy. But a thorough reader of Valla's logic might discover similarities to pragmatism, which are fostered by his deep criticism of language with the tools of Renaissance humanism. However, Descartes's indebtedness to Renaissance method and rhetoric is handbook knowledge today.The audience for this collection of samples are specialists either in seventeenth- or eighteenth-century philosophy, or in Renaissance thought, or even philosophers in the narrow sense of the disciplines. The latter are difficult to convince of the usefulness of historic studies or "erudite activity" (Milton... (shrink)

In Plato’s eponymous dialogue, Timaeus, the main character presents the universe as an (almost) perfect sphere filled by tiny, invisible particles having the form of four regular polyhedrons. At first glance, such a construction may seem close to an atomistic theory. However, one does not find any text in Antiquity that links Timaeus’ cosmology to the atomists, while Aristotle opposes clearly Plato to the latter. Nevertheless, Plato is commonly presented in contemporary literature as some sort of atomist, sometimes as supporting (...) a form of so-called ‘mathematical atomism’. However, the term ‘atomism’ is rarely defined when applied to Plato. Since it covers many different theories, it seems that this term has almost as different meanings as different authors. The purpose of this article is to consider whether it is correct to connect Timaeus’ cosmology to some kind of ‘atomism’, however this term may be understood. Its purpose is double: to obtain a better understanding of the cosmology of the Timaeus, and to consider the different modern ‘atomistic’ interpretations of this cosmology. In short, we would like to show that such a claim, in any form whatsoever, is misleading, an impediment to the understanding of the dialogue, and more generally of Plato’s philosophy. (shrink)

Le corps entier des sciences peut estre consideré comme l’ocean, qui est continué partout, et sans interruption ou partage, bien que les hommes y conçoivent des parties, et leur donnent des noms selon leur commodité. Et comme il y a des mers inconnues, ou qui n’ont esté navigeés que par quelques vaisseaux que le hazard y avoir jettés: on peut dire,[10] de même qu’il y a des sciences dont on a connu quelque chose par rencontre seulement et sans dessein. L’art (...) des combinaisons est de ce nombre; elle signifie chez moy, autant que la science des formes ou formules ou bien des variations en general. En un mot, c’est la Specieuse universelle ou la Characteristique. De sorte qu’elle traite de eodem et diverso; de simili et dissimili; de absoluto et relato; comme la Mathematique ordinaire traite de [15] uno et multis, de magno et parvo, de toto et parte. On peut même dire que la Logistique ou bien l’Algebre luy est sousordonnée en un certain sens. Car lorsqu’on se sert de plusieurs notes indifferentes, ou qui au commencement du calcul pouvoient estre echangées et substituées mutuellement sans faire tort au raisonnement, en quoy les lettres d’Alphabet sont fort propres; et lors que ces lettres ou notes signifient des grandeurs, ou [20] des nombres generaux, il en vient l’Algebre ou plus tost la Specieuse de Viete. Et c’est justement en cela que consiste l’avantage de l’Algebre de Viete et de Descartes sur celle des anciens, qu’en se servant des lettres au lieu des nombres tant connus, qu’inconnus, on vient a des formules, ou il y a quelque liaison et ordre, qui donne moyen à nostre esprit de. (shrink)

Le corps entier des sciences peut estre consideré comme l’ocean, qui est continué partout, et sans interruption ou partage, bien que les hommes y conçoivent des parties, et leur donnent des noms selon leur commodité. Et comme il y a des mers inconnues, ou qui n’ont esté navigeés que par quelques vaisseaux que le hazard y avoir jettés: on peut dire,[10] de même qu’il y a des sciences dont on a connu quelque chose par rencontre seulement et sans dessein. L’art (...) des combinaisons est de ce nombre; elle signifie chez moy, autant que la science des formes ou formules ou bien des variations en general. En un mot, c’est la Specieuse universelle ou la Characteristique. De sorte qu’elle traite de eodem et diverso; de simili et dissimili; de absoluto et relato; comme la Mathematique ordinaire traite de [15] uno et multis, de magno et parvo, de toto et parte. On peut même dire que la Logistique ou bien l’Algebre luy est sousordonnée en un certain sens. Car lorsqu’on se sert de plusieurs notes indifferentes, ou qui au commencement du calcul pouvoient estre echangées et substituées mutuellement sans faire tort au raisonnement, en quoy les lettres d’Alphabet sont fort propres; et lors que ces lettres ou notes signifient des grandeurs, ou [20] des nombres generaux, il en vient l’Algebre ou plus tost la Specieuse de Viete. Et c’est justement en cela que consiste l’avantage de l’Algebre de Viete et de Descartes sur celle des anciens, qu’en se servant des lettres au lieu des nombres tant connus, qu’inconnus, on vient a des formules, ou il y a quelque liaison et ordre, qui donne moyen à nostre esprit de. (shrink)

Le corps entier des sciences peut estre consideré comme l’ocean, qui est continué partout, et sans interruption ou partage, bien que les hommes y conçoivent des parties, et leur donnent des noms selon leur commodité. Et comme il y a des mers inconnues, ou qui n’ont esté navigeés que par quelques vaisseaux que le hazard y avoir jettés: on peut dire,[10] de même qu’il y a des sciences dont on a connu quelque chose par rencontre seulement et sans dessein. L’art (...) des combinaisons est de ce nombre; elle signifie chez moy, autant que la science des formes ou formules ou bien des variations en general. En un mot, c’est la Specieuse universelle ou la Characteristique. De sorte qu’elle traite de eodem et diverso; de simili et dissimili; de absoluto et relato; comme la Mathematique ordinaire traite de [15] uno et multis, de magno et parvo, de toto et parte. On peut même dire que la Logistique ou bien l’Algebre luy est sousordonnée en un certain sens. Car lorsqu’on se sert de plusieurs notes indifferentes, ou qui au commencement du calcul pouvoient estre echangées et substituées mutuellement sans faire tort au raisonnement, en quoy les lettres d’Alphabet sont fort propres; et lors que ces lettres ou notes signifient des grandeurs, ou [20] des nombres generaux, il en vient l’Algebre ou plus tost la Specieuse de Viete. Et c’est justement en cela que consiste l’avantage de l’Algebre de Viete et de Descartes sur celle des anciens, qu’en se servant des lettres au lieu des nombres tant connus, qu’inconnus, on vient a des formules, ou il y a quelque liaison et ordre, qui donne moyen à nostre esprit de. (shrink)

Discourse on Metaphysics and Other Essays contains complete translations of the two essays that constitute the best introductions to Leibniz's complex thought: Discourse on Metaphysics of 1686 and Monadology of 1714. These are supplemented with two essays of special interest to the student of modern philosophy, On the Ultimate Origination of Things of 1697 and the Preface to his New Essays of 1703-1705. The translations are taken from Leibniz, Philosophical Essays, edited and translated by Roger Ariew and Daniel Garber (...) (Hackett, 1989). (shrink)

Vorwort, von R. Loosen und F. Vonessen.--Leibniz und das binäre Zahlensystem, von F. Vonessen.--Das Geheimnis der Schöpfung; Neujahrsbrief an Herzog Rudolph August von Braunschweig-Lüneburg-Wolfenbüttel, von G. W. Leibniz.--Leibniz und die chinesische Philosophie, von R. Loosen.--Lettre sur la philosophie chinoise à Nicolas de Remond. Abhandlung über die chinesische Philosophie. Von G. W. Leibniz. Anhang: Anmerkungen, Abkürzungen (bibliographical: p. [133-153]--Nachwort: Zur fünftausendjährigen Geschichte des binären Zahlensystems: Fuh-Hi, G. W. Leibniz, Norbert Wiener, von J. Gebser.

The article is devoted to the comparison of two types of proofs in mathematical practice, the methodological differences of which go back to the difference in the understanding of the nature of mathematics by Descartes and Leibniz. In modern philosophy of mathematics, we talk about conceptual and formal proofs in connection with the so-called Hilbert Thesis, according to which every proof can be transformed into a logical conclusion in a suitable formal system. The analysis of the arguments (...) of the proponents and opponents of the Thesis, “conceptualists” and “formalists”, is presented respectively by the two main antagonists – Y. Rav and J. Azzouni. The focus is on the possibility of reproducing the proof of “interesting” mathematical theorems in the form of a strict logical conclusion, in principle feasible by a mechanical procedure. The argument of conceptualists is based on pointing out the importance of other aspects of the proof besides the logical conclusion, namely, in introducing new concepts, methods, and establishing connections between different sections of meaningful mathematics, which is often illustrated by the case of proving Fermat’s Last Theorem (Y. Rav). Formalists say that a conceptual proof “points” to the formal logical structure of the proof (J. Azzouni). The article shows that the disagreement is based on the assumption of asymmetry of mutual translation of syntactic and semantic structures of the language, as a result of which the formal proof loses important semantic factors of proof. In favor of a formal proof, the program of univalent foundations of mathematics In. Vojevodski, according to which the future of mathematical proofs is associated with the availability of computer verification programs. In favor of conceptual proofs, it is stated (A. Pelc) that the number of steps in the supposed formal logical conclusion when proving an “interesting” theorem exceeds the cognitive abilities of a person. The latter circumstance leads the controversy beyond the actual topic of mathematical proof into the epistemological sphere of discussions of “mentalists” and “mechanists” on the question of the supposed superiority of human intelligence over the machine, initiated by R. Penrose in his interpretation of the Second Theorem of Goedel, among whose supporters, as it turned out, was Goedel himself. (shrink)

« Que l’on étudie donc la nécessité des phénomènes matériels et l’ordre des causes efficientes, on trouvera que rien ne se passe sans une cause qui satisfait l’imagination, que rien n’échappe aux lois mathématiques du mécanisme. Que l’on contemple d’autre part la chaîne d’or des fins et la sphère des formes qui constituent comme un monde intelligible, et l’on reconnaîtra que, grâce à la perfection de l’Auteur suprème, les sommets de l’éthique et de la métaphysique se confondent, de sorte que (...) rien ne se fait sans la plus haute raison. Car le même Dieu est à la fois la forme éminente et la cause efficiente première et la fin ou l’ultime raison des choses. Il sied que nous adorions ses traces dans les choses et que non seulement nous contemplions les moyens par lesquels il agit et le mécanisme des causes matérielles, mais qu’encore nous méditions sur les fins sublimes de cette admirable habileté; que nous reconnaissions en Dieu, en même temps que l’architecte du monde matériel, aussi et surtout le Roi des esprits, dont l’intelligence a tout ordonné pour le mieux et créer l’univers comme l’État le plus parfait possible sous le gouvernement du plus puissant et du plus sage des monarques. ». (shrink)

In this book G. W. Leibniz presents not only his reflections on predestination and election but also a more detailed account of the problem of evil than is found in any of his other works apart from the _Theodicy_. Surprisingly, his _Dissertation on Predestination and Grace_ has never before been published in any form. Michael J. Murray's project of translating, editing, and providing commentary for the volume will therefore attract great interest among scholars and students of Leibniz's philosophy and theology. (...) Leibniz addresses such topics as free will, moral responsibility, divine causation, justice, punishment, divine foreknowledge, and human freedom, revealing crucial aspects of the genesis of his mature metaphysics and the theological motivations behind it. (shrink)

Leibniz’s De incerti aestimatione, which contains his solution to the division problem, has not received much attention, let alone much appreciation. This is surprising because it is in this work that the definition of probability in terms of equally possible cases appears for the first time. The division problem is used to establish and test probability theory; it can be stated as follows: if two players agree to play a game in which one has to win a certain number of (...) rounds in order to win the pool, but if they break the game off before either of them has won the required number of rounds, how should the pool be distributed? Our article has two aims: it provides the readers with the first published English translation of De incerti aestimatione, and it also gives them a brief commentary that explains Leibniz’s philosophical and mathematical concepts necessary in order to understand this work. The translation is as literal as possible throughout; it shows how Leibniz struggled at times to find a solution to the division problem and how he approached it from different angles. The commentary discusses Leibniz’s views on four key concepts: fairness, hope, authority and possibility. The commentary then outlines how Leibniz attempted to solve the problem of division. (shrink)

Tout au long de sa vie Leibniz remettra sur le metier le projet d'un calcul geometrique qui exprime directement, et non par le biais des equations de l'analyse, les relations purement geometriques et leur degre zero, la situation ou situs. Dans cet echantillon de caracteristique universelle il n'est guere difficile d'identifier les premisses de la topologie moderne. Nous trouvons ici un apercu quasi complet (et en grande partie inedit) de la premiere phase des travaux leibniziens, dont l'objectif initial est a (...) lui seul une gageure, la reforme de l'axiomatique euclidienne. (shrink)

Despite his significance in early modern Germany, where he was well-known as a political and moral philosopher, jurist, lay-theologian, social and educational reformer, Christian Thomasius (1655-1728) is little known in the world of Anglophone scholarship. 1 Unlike those of his mentor, Samuel Pufendorf, none of Thomasius's works was translated into English, when, at the end of the seventeenth century, English thinkers were searching for a final settlement to the religious question. None has been translated since. Moreover, while Thomasius has (...) been subject to increasing scholarly attention in Germany since the 1970s, where he has been treated largely as a representative of the "early Enlightenment," there is very little secondary literature on him in English. 2 Things are however beginning to change in this regard, with recent research already giving rise to important new Anglophone books and essays. 3 Knud Haakonssen's article on [End Page 595] Thomasius for the new Routledge Encyclopedia of Philosophy might well be a straw in the wind. (shrink)

The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility in nature, rather than in mathematics. In line with this distinction, we offer a reading of the fictionality of infinitesimals. The letter has been claimed to support a reading of infinitesimals according to which they are (...) logical fictions, contradictory in their definition, and thus absolutely impossible. The advocates of such a reading have lumped infinitesimals with infinite wholes, which are rejected by Leibniz as contradicting the part–whole principle. Far from supporting this reading, the letter is arguably consistent with the view that infinitesimals, as inassignable quantities, are mentis fictiones, i.e., (well-founded) fictions usable in mathematics, but possibly contrary to the Leibnizian principle of the harmony of things and not necessarily idealizing anything in rerum natura. Unlike infinite wholes, infinitesimals—as well as imaginary roots and other well-founded fictions—may involve accidental (as opposed to absolute) impossibilities, in accordance with the Leibnizian theories of knowledge and modality. (shrink)