This chapter argues that the standard conception of Spinoza as a fellow-travelling mechanical philosopher and proto-scientific naturalist is misleading. It argues, first, that Spinoza’s account of the proper method for the study of nature presented in the Theological-Political Treatise (TTP) points away from the one commonly associated with the mechanical philosophy. Moreover, throughout his works Spinoza’s views on the very possibility of knowledge of nature are decidedly sceptical (as specified below). Third, in the seventeenth-century debates over proper methods in the (...) sciences, Spinoza sided with those that criticized the aspirations of those (the physico-mathematicians, Galileo, Huygens, Wallis, Wren, etc) who thought the application of mathematics to nature was the way to make progress. In particular, he offers grounds for doubting their confidence in the significance of measurement as well as their piece-meal methodology (see section 2). Along the way, this chapter offers a new interpretation of common notions in the context of treating Spinoza’s account of motion (see section 3). (shrink)

This book attempts to provide a general interpretation of the history of philosophy in the seventeenth-century Dutch Republic.

Willem Jacob ’s Gravesande is widely remembered as a leading advocate of Isaac Newton’s work. In the first half of the eighteenth century, ’s Gravesande was arguably Europe’s most important proponent of what would become known as Newtonian physics. ’s Gravesande himself minimally described this discipline, which he called «physica», as studying empirical regularities mathematically while avoiding hypotheses. Commentators have as yet not progressed much beyond this view of ’s Gravesande’s physics. Therefore, much of its precise nature, its methodology, and (...) its relation to Newton’s actual work remains unclear. This article discusses one particular methodological element that ’s Gravesande himself often stressed in detail, namely the use of mathematics in philosophy and physics. In doing so, it takes exception to the claim that mathematics played only a minor role in ’s Gravesande’s work, a view put forward in recent historiography. Besides that, this article casts new light on the interpretation of ’s Gravesande’s philosophical notion of «mathematical reasoning», a notion that has remained somewhat obscure thus far. (shrink)

According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. When this grand narrative was brought into question, our perspectives on the question of mathematization should have changed. It seems, however, that they were instead set aside, both because of a general distrust towards sweeping narratives that are always subject to the suspicion that they overlook the unyielding complexity of real history, (...) and because of a shift in our interests. The more obscure and idiosyncratic they are, an alchemist, a patron of the sciences or a lunatic collector is nowadays honored in journals of the history of sciences. As for the general issues involved in the question of mathematization, they are rejected as obsolete, or reserved for specialized journals in the history of mathematics. The article « Forms of mathematization » examines in general the notion of mathematization, distinguishes different forms of mathematization and defends a renewed study of the forms of mathematization in the history of the early sciences. (shrink)

Spinoza's Ethics is one of the most remarkable, important, and difficult books in the history of philosophy: a treatise simultaneously on metaphysics, knowledge, philosophical psychology, moral philosophy, and political philosophy. It presents, in Spinoza's famous 'geometric method', his radical views on God, Nature, the human being, and happiness. In this wide-ranging 2006 introduction to the work, Steven Nadler explains the doctrines and arguments of the Ethics, and shows why Spinoza's endlessly fascinating ideas may have been so troubling to his contemporaries, (...) as well as why they are still highly relevant today. He also examines the philosophical background to Spinoza's thought and the dialogues in which Spinoza was engaged - with his contemporaries, with ancient thinkers, and with his Jewish rationalist forebears. His book is written for the student reader but will also be of interest to specialists in early modern philosophy. (shrink)

In this essay, I will bring several hitherto neglected sources, which pertain to Petrus van Musschenbroek’s unpublished manuscripts, to the fore. The folios at hand show that Musschenbroek read and actively engaged with Spinoza’s Ethica. More precisely, it will be shown that Musschenbroek held clear-cut anti-Spinozistic convictions.

Alexander X. Douglas situates Spinoza's philosophy in its immediate historical context, and argues that much of his work was conceived with the aim of rebutting the claims of his contemporaries. In contrast to them, Spinoza argued that philosophy reveals the true nature of God, and reinterpreted the concept of God in profound and radical ways.

In the wake of the Scientific Revolution, the late seventeenth and eighteenth centuries saw the complete demolition of traditional structures of authority, scientific thought, and belief by the new philosophy and the philosophes, including Voltaire, Diderot, and Rousseau. The Radical Enlightenment played a part in this revolutionary process, which effectively overthrew all justification for monarchy, aristocracy, and ecclesiastical power, as well as man's dominance over woman, theological dominance of education, and slavery. Despite the present day interest in the revolutions of (...) the eighteenth century, the origins and rise of the Radical Enlightenment have received limited scholarly attention. The greatest obstacle to the movement finding its proper place in modern historical writing is its international scope: the Racial Enlightenment was not French, British, German, Italian, Jewish or Dutch, but all of these at the same time. In this wide-ranging volume, Jonathan Israel offers a novel interpretation of the Radical Enlightenment down to La Mettie and Diderot, two of its key exponents. Particular emphasis is placed on the pivotal role of Spinoza and the widespread underground international philosophical movement known before 1750 as Spinozism. (shrink)

In this "Dictionary," more than four hundred biographical entries encompass all the Dutch thinkers who exercised a major influence on the intellectual life of the Golden Age, as well as those who developed their ideas and beliefs through interaction with other scholars. Additional entries describe foreign philosophers who lived in the country temporarily and whose work was influenced by their stay. These include John Locke, Rene Descartes and Pierre Bayle.

Readers of Spinoza's philosophy have often been daunted, and sometimes been enchanted, by the geometrical method which he employs in his philosophical masterpiece the Ethics. In Meaning in Spinoza's Method Aaron Garrett examines this method and suggests that its purpose, in Spinoza's view, was not just to present claims and propositions but also in some sense to change the readers and allow them to look at themselves and the world in a different way. His discussion draws not only on Spinoza's (...) works but also on those of the philosophers who influenced Spinoza most strongly, including Hobbes, Descartes, Maimonides and Gersonides. This controversial book will be of interest to historians of philosophy and to anyone interested in the relation between form and content in philosophical works. (shrink)

This study explores several arguments against Spinoza's philosophy that were developed by Henry More, Samuel Clarke, and Colin Maclaurin. In the arguments on which I focus, More, Clarke, and Maclaurin aim to establish the existence of an immaterial and intelligent God precisely by showing that Spinoza does not have the resources to adequately explain the origin of motion. Attending to these criticisms grants us a deeper appreciation for how the authority derived from the empirical success of Newton's enterprise was used (...) to settle debates within philosophy. What I emphasize is that in the progression from More to Clarke to Maclaurin, key Newtonian concepts from the Principia (1687), such as motion, atomism, and the vacuum, are introduced and exploited in order to challenge the account of matter and motion that is presented in Spinoza's Ethics (1677). Building on this treatment, I use the arguments from More and Clarke especially to help discern the anti-Spinozism that can be detected in Newton's General Scholium (1713). Ultimately, the Newtonian criticisms that I detail offer us a more nuanced view of the problems that plague Spinoza's philosophy, and they also challenge the idea that Spinoza seamlessly fits into a progressive narrative about the scientific revolution. (shrink)

This study on the reception of Cartesianism is the result of a four-year fellowship as assistant-in-training at the Faculty of Philosophy of the University of Groningen. Zie: Preface.

Baruch Spinoza’s (1632–77)Tractatus theologico-politicus (1669 or 1670) caused outrage across the Dutch Republic, for it obliterated the carefully installed separation between philosophy and theology. The posthumous publication of Spinoza’s Ethica, which is contained in his Opera posthuma (1677), caused similar consternation. It was especially the mathematical order in which the Ethica was composed that caused fierce opposition, for its mathematical appearance gave the impression that Spinoza’s heretical teachings were established demonstratively. In this essay, I document how the Dutch physician, local (...) politician, and amateur mathematician and experimenter Bernard Nieuwentijt (1654–1718) attempted to physico-mathematically and methodologically counter the threats posed by Spinoza’s program. Nieuwentijt tried to defend the authority of the scriptures in times at which they came under attack by the new philosophy and by the emerging sciences that were gradually winning terrain. The crux of his defense consisted in delineating a modest epistemology, a “learned ignorance,” that would cure Spinoza’s followers of their pansophical aspirations, on the one hand, and remove the conflict between the Bible and reason, on the other. The specific way in which he sought to accomplish this distinguished him from Dutch Reformed thought, or so I will argue. (shrink)

The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmatic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with (...) the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics. (shrink)

In _Regimens of the Mind_, Sorana Corneanu proposes a new approach to the epistemological and methodological doctrines of the leading experimental philosophers of seventeenth-century England, an approach that considers their often overlooked moral, psychological, and theological elements. Corneanu focuses on the views about the pursuit of knowledge in the writings of Robert Boyle and John Locke, as well as in those of several of their influences, including Francis Bacon and the early Royal Society virtuosi. She argues that their experimental programs (...) of inquiry fulfill the role of regimens for curing, ordering, and educating the mind toward an ethical purpose, an idea she tracks back to the ancient tradition of _cultura animi_. Corneanu traces this idea through its early modern revival and illustrates how it organizes the experimental philosophers’ reflections on the discipline of judgment, the study of nature, and the study of Scripture. _ _ _ _ It is through this lens, the author suggests, that the core features of the early modern English experimental philosophy—including its defense of experience, its epistemic modesty, its communal nature, and its pursuit of “objectivity”—are best understood. (shrink)

In the eighteenth century, Newton's ideas were an important element of the dominant world view, but it was not immediately clear that they could play such a role. What made them seem philosophically relevant is investigated in the case of the Dutch Republic. At the universities people initially were rather sceptical about Newton's theories. Support came mainly from scientific amateurs who tried to place their religious feelings on a scientific footing. The Spinozists' claim that religion was refuted by mathematics created (...) the need for a scientific answer, which would demonstrate the fallaciousness of Spinoza's geometrical method and uphold revealed religion. In this article, it is shown in some detail how Newtonian ideas were put to such use among mathematical amateurs in Amsterdam, mainly under the influence of informal contacts with David Gregory and his circle. Physico-theology appeared not so much as a fresh start as a transformation of the older mathematical approach of philosophical and religious questions. (shrink)

According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. This grand narrative began with the exhibition of quantitative laws that these heroes, Galileo and Newton for example, had disclosed: the law of falling bodies, according to which the speed of a falling body is proportional to the square of the time that has elapsed since the beginning of its fall; the (...) law of gravitation, according to which two bodies are attracted to one another in proportion to the sum of their masses and in inverse proportion to the square of the distance separating them -- according to his own preferences, each narrator added one or two quantitative laws of this kind. The essential feature was not so much the examples that were chosen, but, rather, the more or less explicit theses that accompanied them. First, mathematization would be taken as the criterion for distinguishing between a qualitative Aristotelian philosophy and the new quantitative physics. Secondly, mathematization was founded on the metaphysical conviction that the world was created pondere, numero et mensura, or that the ultimate components of natural things are triangles, circles, and other geometrical objects. This metaphysical conviction had two immediate consequences: that all the phenomena of nature can be in principle submitted to mathematics and that mathematical language is transparent; it is the language of nature itself and has simply to be picked up at the surface of phenomena. Finally, it goes without saying that, from a social point of view, the evolution of the sciences was apprehended through what has been aptly called the "relay runner model," according to which science progresses as a result of individual discoveries. Grand narratives such as this are perhaps simply fictions doomed to ruin as soon as they are clearly expressed. In any case, the very assumption on which this grand narrative relies can be brought into question: even in the canonical domain of mechanics, the relevant epistemological units crucial to understanding the dynamics of the Scientific Revolution are perhaps not a few laws of motion, but a complex set of problems embodied in mundane objects. Moreover, each of the theses just mentioned was actually challenged during the long period of historiographical reappraisal, out of which we have probably not yet stepped. Against the sharp distinction between a qualitative Aristotelian philosophy and the new quantitative physics, numerous studies insist that Rome wasn't built in a day, so to speak. Since Antiquity, there have always been mixed sciences; the emergence of pre-classical mechanics depends on both medieval treatises and the practical challenges met by Renaissance engineers. It is indeed true that, for Aristotle, mathematics merely captures the superficial properties of things, but the Aristotelianisms were many during the Renaissance and the Early Modern period, with some of them being compatible with the introduction of mathematics in natural philosophy. In addition, the gap between the alleged program of mathematizing nature and its effective realization was underlined as most natural phenomena actually escaped mathematization; at best they were enrolled in what Thomas Kuhn began to rehabilitate under the appellation of the "Baconian sciences," i.e., empirical investigations aiming at establishing isolated facts, without relating them to any overarching theory. Hence, mathematization of nature cannot pretend to capture a historical fact: at most, it expresses an indeterminate task for generations to come. On top of these first two considerations, and against the thesis of the neutrality of the mathematical language, it was urged that mathematics is not "only a language" and that, exactly as other symbolic means or cognitive tools, it has its own constraints. For example, it has been thoroughly explained that the Euclidean theory of proportions both guides and frustrates the Galilean analysis of motion; its shortages were particularly clear with respect to the expression of continuity, which is crucial in the case of motion. Consequently, when calculus was invented and applied to the analysis of motion, it was not a transposition that left things as they stood. Even more clearly than in the case of a translation from one natural language to another, the shift from one symbolic language to another entails that certain possibilities are opened while others are closed. The cognitive constraints imposed by established mathematical theories, as seen in the theory of proportions or calculus, were not the only ones to be studied in relation to mathematization. Certain schemes dependent on the grammar of natural languages, e.g., the scheme of contrariety, or certain symbolic means of representation, e.g. geometrical diagrams and numerical tables, were also subject to such scrutiny. Lastly, it was insisted that, even if we concede the existence of scientific geniuses, mathematics is largely produced by intellectual communities and embedded within social practices. More attention was consequently paid to the forms of communication in given mathematical networks, or to the teaching of the discipline in, for example, Jesuit colleges and universities. The set of mathematical practices specific to specialized craftsmen, highly-qualified experts and engineers began to be studied in its own right. All these reflections may have helped us change our perspectives on the question of mathematization. It seems, however, that they were instead set aside, both because of a general distrust towards sweeping narratives that are always subject to the suspicion that they overlook the unyielding complexity of real history, and because of a shift in our interests. The more obscure and idiosyncratic they are, an alchemist, a patron of the sciences or a lunatic collector is nowadays honored in journals of the history of sciences. As for the general issues involved in the question of mathematization, they are rejected as obsolete, or reserved for specialized journals in the history of mathematics. Consequently, before presenting the essays of this fascicle, I would like to say a few words in favor of a renewed study of the forms of mathematization in the history of the early sciences. (shrink)

Francis Bacon and the art of direction -- An art of tempering the mind -- The distempered mind and the tree of knowledge -- A comprehensive culture of the mind -- The end of knowledge -- The study of nature as regimen -- Cultura and medicina animi: an early modern tradition -- The physician of the soul -- Sources -- Genres -- Utility: practical versus speculative knowledge -- Self-love and the fallen/uncultured mind -- The office of reason -- Passions, errors, (...) and assent -- The discipline, the virtues, and habituation -- Virtuoso discipline -- The cure of the mind and Solomon's house -- Passions, errors, and method -- Idols and diseases of the mind -- Epistemic modesty -- The way of inquiry -- A 'union of eyes and hands': the community and objectivity revisited -- Robert Boyle: experience as paideia -- The limits and the 'perfection' of reason -- The weak mind and the virtues of a free inquiry -- Reason and experience -- The Christian philosopher -- John Locke and the education of the mind -- Limits of reason, useful knowledge, and the duty to search for truth -- A natural history of the distempered mind -- The regulation of assent: a perfecting exercise -- The discourse with a friend -- Studying nature -- Lived physics -- The appropriateness of disproportion -- Experience, history, and speculation -- Affective cognition -- Studying 'God's contrivances' -- The study of theology and the growth of the mind -- Worlds and angels -- Reading scripture -- Conclusion. (shrink)

This book attempts to provide a general interpretation of the history of philosophy in the seventeenth-century Dutch Republic. It concentrates on the heritage of Humanism, and on the rise of Dutch Cartesianism and Spinozism.