This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...) is, I think, widespread agreement that recent insights here have lead to a genuine deepening of our understanding. (shrink)

A central doctrine of Kant's Critique of Pure Reason holds that the content of human experience is rooted in an affection of sensibility by unknowable things in themselves. This famous and puzzling affection doctrine raises two seemingly intractable old problems, which can be termed the Indispensability and the Consistency Problems. By what right does Kant present affection by supersensible entities as an indispensable requirement of experience? And how could any argument for such indispensability avoid violating the Critique's doctrine of noumenal (...) ignorance? This essay develops a new solution to both problems, setting out from the continuity between Kant's early and mature views on sensibility and mind-world relations. Kant's early writings subscribe to an interactionist cosmology opposed to both Leibniz's preestablished harmony and Malebranche's occasionalism. The modern debate on mind-world relations shaping Kant's early cosmology points us to a widely recognized motivation for interactionism, turning on a constraint on agency within certain noninteractionist cosmologies. In particular, Kant's early conversion to a libertarian theory of freedom, together with his rejection of occasionalism, provides the basis for a compelling argument for the indispensability of world-mind affection relations. Extended to the transcendental idealist framework, the same argument reveals noumenal affection as an indispensable presupposition of some knowledge claims consistently upheld by Kant. This leads in turn to a satisfying solution to the Consistency Problem, showing that the doctrine of noumenal affection is not merely consistent with, but is partly motivated by, Kant's commitment to noumenal ignorance. (shrink)

I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible.

In my dissertation, I present Hermann Cohen's foundation for the history and philosophy of science. My investigation begins with Cohen's formulation of a neo-Kantian epistemology. I analyze Cohen's early work, especially his contributions to 19th century debates about the theory of knowledge. I conclude by examining Cohen's mature theory of science in two works, The Principle of the Infinitesimal Method and its History of 1883, and Cohen's extensive 1914 Introduction to Friedrich Lange's History of Materialism. In the former, Cohen gives (...) an historical and philosophical analysis of the foundations of the infinitesimal method in mathematics. In the latter, Cohen presents a detailed account of Heinrich Hertz's Principles of Mechanics of 1894. Hertz considers a series of possible foundations for mechanics, in the interest of finding a secure conceptual basis for mechanical theories. Cohen argues that Hertz's analysis can be completed, and his goal achieved, by means of a philosophical examination of the role of mathematical principles and fundamental concepts in scientific theories. (shrink)

Leibniz’s mature philosophical understanding of the laws of nature emerges rather suddenly in the late 1670’s to early 1680’s and is signaled by his embrace of three central theses.1 The first, what I’ll call the thesis of Contingency, suggests that the laws of nature are not only contingent, but, in some sense, paradigmatically contingent; they are supposed to provide insight into the very nature of contingency as Leibniz comes to understand it. The second, what I’ll call the thesis of Providence, (...) suggests that the laws of nature provide a basis for a new argument from design by showing how reflection on God’s ends can be positively useful in the practice of natural philosophy. The third, what I’ll call thesis of .. (shrink)

This paper is a discussion of the treatment of Leibniz's conception of substance in Heidegger's The Metaphysical Foundations of Logic. I explain Heidegger's account, consider its relation to recent interpretations of Leibniz in the Anglophone secondary literature, and reflect on the ways in which Heidegger's methodology may illuminate what it is to read Leibniz and other figures in the history of philosophy.

(1) An introduction to the principles of conceptual modelling, combinatorial heuristics and epistemological history; (2) the examination of a number of perennial epistemological-methodological schemata: conceptual spaces and blending theory; ars inveniendi and ars demonstrandi; the two modes of analysis and synthesis and their relationship to ars inveniendi; taxonomies and typologies as two fundamental epistemic structures; extended cognition, cognitio symbolica and model-based reasoning; (3) Plato’s notions of conceptual spaces, conceptual blending and hypothetical-analogical models (paradeigmata); (4) Ramon Llull’s concept analysis and combinatoric (...) spaces; (5) Gottfried Leibniz’s development of compositional analysis and synthesis as a general modelling method and a paradigm for ars inveniendi; (6) Fritz Zwicky’s revival of the morphological method of analysis and construction, and its subsequent computerised applications. (shrink)

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)

This paper compares Kant’s and Leibniz’s views on the relation between knowing subjects and known objects. Kant discusses Leibniz’s philosophy in the ‘Amphiboly’ section of the first Critique. According to Kant, Leibniz’s main error is mistaking objects in space and time for mind-independent things in themselves, that is, for monads. The paper argues that, pace Kant, Leibniz regards objects in space and time as mind-dependent. A deeper divergence between the two philosophers concerns knowing subjects. For Leibniz, they are substances. For (...) Kant, we cannot know whether they are substances. Kant conceives of knowing subjects as complex systems of cognitive capacities. (shrink)

In several of his writings from the 1680s, Leibniz presents an argument for the claim that there are no determinate or precise shapes in things, and states that shape contains something imaginary a...

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

Volume 28, Issue 2, March 2020, Page 408-411.

In The Philosophy of Change, the distinguished scholar of Chinese philosophy Chung-ying Cheng advances our understanding of the Yijing by analyzing its philosophy in comparison to Western philosophical traditions. Cheng focuses on critically comparing philosophies of science, religion, and metaphysics in Leibniz, Whitehead, Neville, and Cobb alongside classical Chinese views on reality, divinity, knowledge, and morality. The book begins and ends with questions related to the character of Chinese metaphysical traditions, which contrast with the mainline metaphysical traditions found in Western (...) Europe and North America. Cheng argues throughout the book that the philosophical underpinnings of basic concepts in Chinese culture are ultimately rooted in key claims found within the Yijing 易經 and one of its standard commentaries, the Yizhuan 易傳. The book serves as a complementary volume to the author's previous book, The Primary Way: Philosophy of the Yijing, which lays out a comprehensive and systematic philosophy based on the symbolism and text of the classical document and its traditional commentaries. (shrink)

In Part 3, I will discuss the problems of inertia and gravity in Leibniz, and present three conjectures: If Leibniz were really ready to insist on relativity, he would have to assert the relativity of inertial motion. In Leibniz’s theories of dynamics and geometry, there was a struggle between his predilection for straight line and his adherence to an optimality principle. Gravity, as well as inertia, can be considered as a universal feature of the world, so that the foundation of (...) both may have a common root. Further, drawing on the results in Part 1 and Part 2, I will argue for the need of a unified interpretation of Leibniz’s metaphysics and dynamics. My three conjectures as regards Leibniz’s possible treatment of inertia and gravity are proposed along a unified interpretation, in terms of my informational reconstruction of Leibniz’s philosophy. Finally, the most important features of the informational interpretation are summarized. The synopsis of the whole paper is added. (shrink)

This anthology is about the signal change in Leibniz’s metaphysics with his explicit adoption of substantial forms in 1678-79. This change can either be seen as a moment of discontinuity with his metaphysics of maturity or as a moment of continuity, such as a passage to the metaphysics from his last years. Between the end of his sejour at Paris and the first part of the Hanover period, Leibniz reformed his dynamics and began to use the theory of corporeal substance. (...) This book explores a very important part of the philosophical work of the young Leibniz. Expertise from around the globe is collated here, including Daniel Garber’s work based on the recent publication of Leibniz's correspondence from the late 1690s, examining how the theory of monads developed during these crucial years. Richard Arthur argues that the introduction of substantial forms, reinterpreted as enduring primitive forces of action in each corporeal substance, allows Leibniz to found the reality of the phenomena of motion in force and thus avoid reducing motion to a mere appearance. Amongst other themes covered in this book, Pauline Phemister’s paper investigates Leibniz’s views on animals and plants, highlighting changes, modifications and elaborations over time of Leibniz’s views and supporting arguments and paying particular attention to his claim that the future is already contained in the seeds of living things. The editor, Adrian Nita, contributes a paper on the continuity or discontinuity of Leibniz’s work on the question of the unity and identity of substance from the perspective of the relation with soul and mind. (shrink)

I aim to offer an innovative interpretation of Leibniz’s philosophy, first by examining how the various views that make up his ontology of individual substance involve a persistent rejection of atomism in natural philosophy and secondly, by exploring the significance of this rejection in the larger context of Seventeenth-century physics. My thesis is structured as a developmental story, each chapter analyzing the discontinuities or changes Leibniz makes to his views on individuation and atomism from his early to late years. The (...) goal is to illuminate underrepresented views on individuals and atoms throughout Leibniz’s works and thus bring a clearer understanding of his philosophy. I, therefore, argue that the New System of Nature, published towards the end of Leibniz’s middle period (1695), marks an important landmark in his philosophical evolution, a radical terminological and ontological shift in his metaphysics of substance. Once Leibniz elaborates the concept of “simple substance,” the future synonym of “monad,” the problem of individuation of his early and middle years (1663-1686) becomes secondary. The focus changes from what makes substances “individual” to what makes them “simple” and truly “one,” i.e., “metaphysical” atoms. I prove that this shift was marked by a two-tiered critical confrontation: a first, direct confrontation, 1) with Descartes’ physics, through the critique of the notion of extended matter and of Descartes’ principle of individuation through shared motion and, a second confrontation, 2) with different strands of Seventeenth-century atomism, including Cartesian Gérauld de Cordemoy’s quasi-“metaphysical” atomism and its attempt at improving Descartes’ individuating principle. I claim that this double confrontation ultimately led Leibniz to formulate a more fundamental ontology, in terms of the “metaphysical atomism” of his Monadology (1714). My analysis complicates a persistent scholarly assumption in recent Leibniz studies, claiming that, throughout his entire career, Leibniz continued to hold the same fundamental positions on substance, individuation and, implicitly, atoms. Against this type of general continuity thesis, I show that: 1) far from being a constant concern, Leibniz’s interest in what makes substances individual fades towards the end of his life (New Essays 1703, correspondence with Samuel Clarke, 1714); 2) I trace the changing fate of some of Leibniz’s early and middle period views on substance and the individual (the principle of the identity of indiscernibles, space-time as individuating properties) in his late works; and 3) I prove the claim that Leibniz really embraced atomism, either for a short time or all throughout his philosophy is problematic. While he does refer to some sort of atoms during his Paris period (1672-1676), this is insufficient proof of a commitment to atomism. Instead, the episode has to be understood in the broader framework of a bundle of interrelated issues, such as the problem of the cohesion of bodies and the problem of minds or mind-like principles individuating those bodies. Thus, as I show through an analysis of Leibniz’s arguments against atomism in the correspondences with his scientific contemporaries (Christiaan Huyghens 1692-1695, Nicholas Hartsoeker 1706-1714), rejecting physical atomism remains a fundamental and surprisingly constant point of his philosophy. (shrink)

Environmental philosophers have argued that Kant’s philosophy offers little for environmental issues. Furthermore, Kant scholars typically focus on humanity, ignoring the question of duties to the environment. In my dissertation, I turn to a number of underexploited texts in Kant’s work to show how both sides are misguided in neglecting the ecological potential of Kant, making the case for the green Kant at the intersection of Kant scholarship and environmental ethics. I build upon previous literature to argue that the green (...) Kant matters for both sides. Rather than a liability, Kant is indeed a conceptual resource. Though many conceive of Kant’s philosophy as environmentally problematic, I argue that underappreciated evolutionary, aesthetic, and holistic sides of Kant’s philosophy can provide conceptual resources for issues in climate change and environmental ethics. Some aspects, such as the pre-critical view of nature, are quite green and merely require an application, while others, such as Kant’s philosophy of history, require a green appropriation to be relevant. The theoretical foundations I develop in these texts will allow Kantians to articulate duties regarding nature and duties for sustainability. This re-thinking of Kant redresses the complaints environmental thinkers hold against Kant. By means of a philosophical interpretation, defense, and application of particular texts from Kant’s works such as Universal Natural History, Critique of Judgment, and Idea for a Universal History, I show how the greening of Kant is not only helpful for contemporary issues, but also defensible. This will make the green Kant agreeable to Kant scholars yet all the while relevant for today with regard to environmental ethics and, more importantly, climate change. (shrink)