Leibniz: Philosophy of Science

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

The disciplinary differentiation of sciences attracted Leibniz’s attention for a long period of time. From nowadays prospects it looks very well grounded as soon as in Leibniz’s manuscripts a modern scholar finds clue ideas of any research field which would tempt him to consider Leibniz as one of the founders of this particular discipline. We argue that this is possible only in retrospection and would significantly distort the essence of Leibniz’s epistemology. Our approach implies, in contrary, the investigation of the (...) Leibniz doctrine of signs on the background of the related philosophical problem, that of expression. The choice of semiotics is justified by the fact that it took a central place in his theoretical constructions, both those of natural sciences and of philosophy. In Leibniz system of knowledge the concept of notes and sings served a theoretical foundation of his most important and long-life aspiration to build up practical science of universal characteristics. In his eyes this practical science was the science of sciences, and we can consider it as the matrix for all possible scientific knowledge. (shrink)

This article centers on Hume’s position on the intelligibility of natural philosophy. To that end, the controversy surrounding universal gravitation shall be scrutinized. It is very well-known that Hume sides with the Newtonian experimentalist approach rather than with the Leibnizian demand for intelligibility. However, what is not clear is Hume’s overall position on the intelligibility of natural philosophy. It shall be argued that Hume declines Leibniz’s principle of intelligibility. However, Hume does not eschew intelligibility altogether; his concept of causation itself (...) stipulates mechanical intelligibility. (shrink)

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, (...) requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz. (shrink)

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

This volume tells the story of the legacy and impact of the great German polymath Gottfried Wilhelm Leibniz (1646-1716). Leibniz made significant contributions to many areas, including philosophy, mathematics, political and social theory, theology, and various sciences. The essays in this volume explores the effects of Leibniz’s profound insights on subsequent generations of thinkers by tracing the ways in which his ideas have been defended and developed in the three centuries since his death. Each of the 11 essays is concerned (...) with Leibniz’s legacy and impact in a particular area, and between them they show not just the depth of Leibniz’s talents but also the extent to which he shaped the various domains to which he contributed, and in some cases continues to shape them today. With essays written by experts such as Nicholas Jolley, Pauline Phemister, and Philip Beeley, this volume is essential reading not just for students of Leibniz but also for those who wish to understand the game-changing impact made by one of history’s true universal geniuses. (shrink)

Recently we proposed "quantum language" (or, the linguistic Copenhagen interpretation of quantum mechanics"), which was not only characterized as the metaphysical and linguistic turn of quantum mechanics but also the linguistic turn of Descartes=Kant epistemology. We believe that quantum language is the language to describe science, which is the final goal of dualistic idealism. Hence there is a reason to want to clarify, from the quantum linguistic point of view, the following problems: "brain in a vat argument", "the Cogito proposition", (...) "five-minute hypothesis", "only the present exists", "Copernican revolution", "McTaggart's paradox", and so on. In this paper, these will be discussed and clarified in quantum language. That is, these are not in quantum language. Also we emphasize that Leibniz's relationalism in Leibniz-Clarke correspondence is regarded as one of the most important parts of the linguistic Copenhagen interpretation of quantum mechanics. This paper is the revised version of the paper: Open Journal of Philosophy, 2018 Vol.8, No.5, 466-480). (shrink)

This article aims to interpret Leibniz’s dynamics project through a theory of the causation of corporeal motion. It presents an interpretation of the dynamics that characterizes physical causation as the structural organization of phenomena. The measure of living force by mv2 must then be understood as an organizational property of motion conceptually distinct from the geometrical or otherwise quantitative magnitudes exchanged in mechanical phenomena. To defend this view, we examine one of the most important theoretical discrepancies of Leibniz’s dynamics with (...) classical mechanics, the measure of vis viva as mv2 rather than ½ mv2. This “error”, resulting from the limits of Leibniz’s methodology, reveals the systematic role of this quantity mv2 in the dynamics. In examining the evolution of the quantity mv2 in the refinement of the force concept from potentia to actio, I argue that Leibniz’s systematic limitations help clarify dynamical causality as neither strictly metaphysical nor mechanical but a distinct level of reality to which Leibniz dedicates the “dynamica” as “nova scientia”. (shrink)

I argue that the key dynamical concepts and laws of Newton's Principia never gained a solid foothold in Germany before Kant in the 1750s. I explain this absence as due to Leibniz. Thus I make a case for a robust Leibnizian legacy for Enlightenment science, and I solve what Jonathan Israel called “a meaningful historical problem on its own,” viz. the slow and hesitant reception of Newton in pre-Kantian Germany.

This book presents new research into key areas of the work of German philosopher and mathematician Gottfried Wilhelm Leibniz (1646-1716). Reflecting various aspects of Leibniz's thought, this book offers a collection of original research arranged into four separate themes: Science, Metaphysics, Epistemology, and Religion and Theology. With in-depth articles by experts such as Maria Rosa Antognazza, Nicholas Jolley, Agustín Echavarría, Richard Arthur and Paul Lodge, this book is an invaluable resource not only for readers just beginning to discover Leibniz, but (...) also for scholars long familiar with his philosophy and eager to gain new perspectives on his work. (shrink)

This paper explores the question of Leibniz’s contribution to the rise of modern ‘science’. To be sure, it is now generally agreed that the modern category of ‘science’ did not exist in the early modern period. At the same time, this period witnessed a very important stage in the process from which modern science eventually emerged. My discussion will be aimed at uncovering the new enterprise, and the new distinctions which were taking shape in the early modern period under the (...) banner of the old Aristotelian terminology. I will argue that Leibniz begins to theorize a distinction between physics and metaphysics that tracks our distinction between the autonomous enterprise of science in its modern meaning, and the enterprise of philosophy. I will try to show that, for Leibniz, physics proper is the study of natural phenomena in mathematical and mechanical terms without recourse for its explanations to metaphysical notions. This autonomy, however, does not imply for Leibniz that physics can say on its own all that there is to be said about the natural world. Quite the opposite. Leibniz inherits from the Aristotelian tradition the view that physics needs metaphysical roots or a metaphysical grounding. For Leibniz, what is ultimately real is reached by metaphysics, not by physics. This is, in my view, Leibniz’s chief insight: the new mathematical physics is an autonomous enterprise which offers its own kind of explanations but does not exhaust what can (and should) be said about the natural world. (shrink)

Do theories of quantum mechanics and quantum gravity require spacetime to be a basic, ground level feature, or can spacetime be seen as an emergent element of these theories? While several commentators have raised serious doubts about the prospects of forgoing the standard spacetime backdrop, it will be argued that a defense of these emergent spacetime interpretations of quantum mechanics and quantum gravity hypotheses can be made, whether as an inference to the best explanation or using another strategy. Furthermore, the (...) idea that space and time can arise from a quite different, non-spatiotemporal level of reality will be shown to have various historical precedents, especially in the seventeenth and eighteenth centuries, a realization that may help dispel some of the mystery associated with these types of hypotheses. (shrink)

This essay examines the relationship between monads and space in Kant’s early pre-critical work, with special attention devoted to the question of ubeity, a Scholastic doctrine that Leibniz describes as “ways of being somewhere”. By focusing attention on this concept, evidence will be put forward that supports the claim, held by various scholars, that the monad-space relationship in Kant is closer to Leibniz’ original conception than the hypotheses typically offered by the later Leibniz-Wolff school. In addition, Kant’s monadology, in conjunction (...) with God’s role, also helps to shed light on further aspects of his system that are broadly Leibnizian, such as monadic activity and the unity of space. (shrink)

An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple (...) and being informative. (shrink)

This paper attempts to resolve the puzzle associated with the non-spatiality of monads by investigating the possibility that Leibniz employed a version of the extension of power doctrine, a Scholastic concept that explains the relationship between immaterial and material beings. As will be demonstrated, not only does the extension of power doctrine lead to a better understanding of Leibniz’ reasons for claiming that monads are non-spatial, but it also supports those interpretations of Leibniz’ metaphysics that accepts the real extension of (...) bodies. (shrink)

Although the historical reputation of Gottfried Wilhelm Leibniz (1646–1716) largely rests on his philosophical and mathematical work, it is widely known that he made important contributions to many of the emerging but still inchoate branches of natural science of his day. Among the many scientific papers Leibniz published during his lifetime are ones on the nascent science we now know as hydrology. While Leibniz’s other scientific work has become of increasing interest to scholars in recent years, his thinking about hydrology (...) has been neglected, despite being relatively broad in extent, including as it does papers on the ‘raising of vapours’ and the formation of ice, as well as the separation of salt and fresh water. That list can now be extended still further following the discovery of a previously unpublished letter of Leibniz’s on the causes of the devastating Lombardy flood of October and November 1705. This letter, which will be the focus of our paper, reveals the depth of Leibniz’s understanding of key hydrological processes. In it, he considers various mechanisms for the flood, such as heavy rains on high ground, underwater earthquakes, and a mountain collapse. Over the course of the paper we examine each of these mechanisms in depth, and show that Leibniz was in the vanguard of hydrological thinking. We also show that the letter contains one of the first scholarly attempts to apply aspects of the still-forming notion of the hydrological cycle to account for a flood event. (shrink)

We investigate the structure common to causal theories that attempt to explain a (part of) the world. Causality implies conservation of identity, itself a far from simple notion. It imposes strong demands on the universalizing power of the theories concerned. These demands are often met by the introduction of a metalevel which encompasses the notions of 'system' and 'lawful behaviour'. In classical mechanics, the division between universal and particular leaves its traces in the separate treatment of cinematics and dynamics. This (...) analysis is applied to the mechanical theories of Newton and Leibniz, with some surprising results. (shrink)

Extension is probably the most general natural property. Is it a fundamental property? Leibniz claimed the answer was no, and that the structureless intuition of extension concealed more fundamental properties and relations. This paper follows Leibniz's program through Herbart and Riemann to Grassmann and uses Grassmann's algebra of points to build up levels of extensions algebraically. Finally, the connection between extension and measurement is considered.

British Journal for the History of Philosophy, Volume 21, Issue 1, Page 207-209, January 2013.

In the early years of the eighteenth century Leibniz had several interactions with John Toland. These included, from 1702 to 1704, discussions of materialism. Those discussions culminated with the consideration of Toland's 1704 Letters to Serena, where Toland argued that matter is necessarily active. In this paper I argue for two main theses about this exchange and its consequences for our wider understanding. The first is that, despite many claims that Toland was at the time of Letters to Serena a (...) Spinozist, we can make better sense of him as a sort of Hobbesian materialist. The second main point concerns reasons for materialism, and in particular a story Locke tells in the Essay about materialists' motives. Toland defends his materialism by arguing that matter is active, and argues that matter is active by using a conceivability argument. But this is not the crude conceivability argument that Locke suggests motivates materialists. This (together with reflecting on some of Hobbes's arguments) suggests that we might well tell a Lockean story about reasons for early modern materialism, but not Locke's story. (shrink)

In the texts of the middle years (roughly, the 1680s and 90s), Leibniz appears to endorse two incompatible approaches to motion, one a realist approach, the other a phenomenalist approach. I argue that once we attend to certain nuances in his account we can see that in fact he has only one, coherent approach to motion during this period. I conclude by considering whether the view of motion I want to impute to Leibniz during his middle years ranks as a (...) kind of realism or rather as some kind of phenomenalism or idealism. (shrink)

This essay develops a interpretation of Leibniz’ theory of motion that strives to integrate his metaphysics of force with his doctrine of the equivalence of hypotheses, but which also supports a realist, as opposed to a fully idealist, interpretation of his natural philosophy. Overall, the modern approaches to Leibniz’ physics that rely on a fixed spacetime backdrop, classical mechanical constructions, or absolute speed, will be revealed as deficient, whereas a more adequate interpretation will be advanced that draws inspiration from an (...) invariantist conception of reality and recent non-classical theories of physics. (shrink)

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

This essay examines the metaphysical foundation of Leibniz’s theory of space against the backdrop of the subtantivalism/relationism debate and at the ontological level of material bodies and properties. As will be demonstrated, the details of Leibniz’ theory defy a straightforward categorization employing the standard relationism often attributed to his views. Rather, a more careful analysis of his metaphysical doctrines related to bodies and space will reveal the importance of a host of concepts, such as the foundational role of God, the (...) holism of both geometry and the material world’s interconnections, and the viability and adequacy of a property theory in characterizing his natural philosophy of space. (shrink)

The theses in this book are: 1) the tension between the Leibnizian theory of the tropes and their use is resolved in a "pragmatic of discourse" that gives the metaphor a richer dimension than the theorized one, that is, that of "a mechanism capable of combining elements coming from different conceptual spaces into a new metaphorical conceptual space, 'shapeless' to which the metaphor itself provides an adequate language to describe and structure it"; 2) the role of metaphors is placed for (...) Leibniz in the context of a 'multi-method' idea that combines the inventive and the formalizing moment and allows for a multiplicity of directions; 3) the Leibniz system is organized according to a 'logic' that is not deductive but analogical; 4) the valid relations in the system are not only connections of a logical nature; on the contrary, the organization is 'reticular', and the primacy of a relation depends from time to time on the prevalence assigned to a metaphor according to the problem being faced; 5) Leibniz's central metaphors are "emerging parts of a wider submerged translation", i.e. they are both expression and conceptualizing vehicle of a cognitive strategy that wants to govern the complexity of knowledge by organizing it around themes; this strategy is alternative to the Cartesian formulation of "Method" based on the disjunction of objects and notions and instead gives philosophical expression to the Baroque sense of the constant mutability that rules the world. (shrink)

Leibniz is well known for his formulation of the infinitesimal calculus. Nevertheless, the nature and logic of his discovery are seldom questioned: does it belong more to mathematics or metaphysics, and how is it connected to his physics? This book, composed of fourteen essays, investigates the nature and foundation of the calculus, its relationship to the physics of force and principle of continuity, and its overall method and metaphysics. The Leibnizian calculus is presented in its origin and context together with (...) its main contributors: Archimedes, Cavalieri, Wallis, Hobbes, Pascal, Huygens, Bernoulli, and Nieuwentijt. Many of us know and probably have used the Leibnizian formula: to .. (shrink)

A review of Futch's book on Leibniz' natural philosophy of time and space.

Well prior to the invention of the term ‘biology’ in the early 1800s by Lamarck and Treviranus, and also prior to the appearance of terms such as ‘organism’ under the pen of Leibniz in the early 1700s, the question of ‘Life’, that is, the status of living organisms within the broader physico-mechanical universe, agitated different corners of the European intellectual scene. From modern Epicureanism to medical Newtonianism, from Stahlian animism to the discourse on the ‘animal economy’ in vitalist medicine, models (...) of living being were constructed in opposition to ‘merely anatomical’, structural, mechanical models. It is therefore curious to turn to the ‘passion play’ of the Scientific Revolution – whether in its early, canonical definitions or its more recent, hybridized, reconstructed and expanded versions: from Koyré to Biagioli, from Merton to Shapin – and find there a conspicuous absence of worry over what status to grant living beings in a newly physicalized universe. Neither Harvey, nor Boyle, nor Locke (to name some likely candidates, the latter having studied with Willis and collaborated with Sydenham) ever ask what makes organisms unique, or conversely, what does not. In this paper I seek to establish how ‘Life’ became a source of contention in early modern thought, and how the Scientific Revolution missed the controversy. (shrink)

Response to critical comments by Edward Slowik on my article 'Leibniz on Motion and the Equivalence of Hypotheses' in The Leibniz Review 18 (2008).

The famous philosopher Leibniz (1646-1716) was also active in the (cultural) politics of his time. His interest in forming scientific societies never waned and his efforts led to the founding of the Berlin Academy of Sciences. He also played a part in the founding of the Dresden Academy of Science and the St. Petersburg Academy of Science. Though Leibniz's models for the scientific society were the Royal Society and the Royal Science Academy of France, his pansophistic vision of scientific cooperation (...) sometimes took on utopian dimensions. In this paper, I will present Leibniz's ideas of scientific cooperation as a kind of religious activity and discuss his various schemes for the founding of such scientific societies. (shrink)

This essay comments on the complexity of the task of accommodating Leibniz’s account of relational motion with his dynamics, as evident in Anja Jauernig’s (2008) Leibniz Review article, and suggests some possible strategies for overcoming these obstacles.

This paper examines the young Kant’s claim that all motion is relative, and argues that it is the core of a metaphysical dynamics of impact inspired by Leibniz and Wolff. I start with some background to Kant’s early dynamics, and show that he rejects Newton’s absolute space as a foundation for it. Then I reconstruct the exact meaning of Kant’s relativity, and the model of impact he wants it to support. I detail (in Section II and III) his polemic engagement (...) with Wolffian predecessors, and how he grounds collisions in a priori dynamics. I conclude that, for the young Kant, the philosophical problematic of Newton’s science takes a back seat to an agenda set by the Leibniz-Wolff tradition of rationalist dynamics. This results matters, because Kant’s views on motion survive well into the 1780s. In addition, his doctrine attests to the richness of early modern views of the relativity of motion. (shrink)

This dynamical interpretation of the continuum is based on a threefold perspective. First, detailed differentiation of all standard realms of Leibnizian Weltanschauung – (R real), (P phenomenal), (I ideal). Second, analysis of the scope of the Law of Continuity famously formulated by Leibniz and mapping it onto this (RPI) structure. Third, finding the precise place of dynamics and force in this (RPI) continuum.

This paper explores various metaphysical aspects of Leibniz’s concepts of space, motion, and matter, with the intention of demonstrating how the distinctive role of force in Leibnizian physics can be used to develop a theory of relational motion using privileged reference frames. Although numerous problems will remain for a consistent Leibnizian relationist account, the version developed within our investigation will advance the work of previous commentators by more accurately reflecting the specific details of Leibniz’s own natural philosophy, especially his handling (...) of the dynamical interactions of plenum bodies. (shrink)

Leeuwenhoekin kokeilut mikroskoopilla 1600-luvun lopulla olivat G. W. Leibnizille suuri innoituksen lähde. Monadologia-teoksessaan Leibniz hehkutti keksinnön merkitystä ja antoi ymmärtää, että sillä löydetyt pikkuruiset eliöt todistivat hänen metafyysisen pluralisminsa oikeaksi. Hänen mukaansa "huomataan, että pienimmässäkin osasessa ainetta on kokonainen elävien olioiden, eläinten, entelekhioiden ja sielujen maailma." Näin Leibnizin ajatus elämän jatkumosta sai uutta pontta. -/- Keksinnön vaikutus näkyy myös Leibnizin teoksessa Uusia esseitä inhimillisestä ymmärryksestä, jossa hän esittelee pienet perseptiot, joita voidaan pitää tietoteoreettisena vastineena pieneliöille. -/- Tarkastelen esitelmässäni Leibnizin reaktioita (...) mikroskooppiin ja sen antamaan uuteen kuvaan elämästä ja keskustelen joistakin Leibnizin filosofian piirteistä, joissa voidaan huomata uuden keksinnön vaikutusta. -/- An article on the continuum of life in Leibniz's philosophy. (shrink)

Mein Ziel in dieser Arbeit ist es zu bestimmen, in welchem Umfang Leibniz moderne Ansichten in drei Bereichen der Biologie vertreten hat, nämlich in der Frage zum Ursprung von Fossilien, zum Aussterben von Arten und zur Evolution von Arten. In neuerer Zeit haben Forscher behauptet, Leibniz hätte folgende Thesen akzeptiert: (1) Fossilien haben einen organischen Ursprung; (2) einige Arten sind ausgestorben; (3) einige Arten haben sich im Laufe der Zeit entwickelt. Anhand der Betrachtung einer Reihe von Leibniz' Schriften, eingeschlossen solche, (...) die vielfach übersehen wurden, zeige ich, dass diese Behauptungen falsch und dass Leibniz' tatsächliche Ansichten zu diesen Fragen wie folgt sind: (1) einige Fossilien haben einen organischen Ursprung; (2) während die Arten selbst nicht ausgestorben sind, sind es aber einige Unterarten; (3) während sich die Arten selbst nicht entwickelt haben, hat es Evolution innerhalb von Artengruppen gegeben. Diese Ansichten, so meine Argumentation, sind überhaupt nicht besonders „modern", und sie fielen mit Sicherheit nicht aus dem Rahmen des späten 17. und frühen 18. Jahrhunderts. (shrink)

According to Robert Sleigh Jr., “The opening remarks of DM.18 make it clear that Leibniz took the results of DM.17 as either establishing, or at least going a long way toward establishing, that force is not identifiable with any mode characterizable terms of size, shape, and motion.” Sleigh finds this puzzling and suggests that other commentators have generally been insufficiently perplexed by the bearing that the DM.17 has on the metaphysical issue. In this brief paper, I examine the solution that (...) Sleigh offers to his puzzle, and present an alternative way of understanding the relationship between these two sections of the Discourse. (shrink)

This item is a chapter from a book in progress, entitled "True Motion". Leibniz’s mechanics was, as we shall see, a theory of elastic collisions, not formulated like Huygens’ in terms of rules explicitly covering every possible combination of relative masses and velocities, but in terms of three conservation principles, including (effectively) the conservation of momentum and kinetic energy. That is, he proposed what we now call (ironically enough) ‘Newtonian’ (or ‘classical’) elastic collision theory. While such a theory is, for (...) instance, vital to the foundations of the kinetic theory of gases, it is not applicable to systems – like gravitational systems – in which fields of force are present. Thus, Leibniz’s mechanical principles never led to developments of the order of Newton’s in the Principia (additionally, he hamstrung their application by embedding them in a baroque philosophical system). (shrink)