The paper lists several editions of Euclid’s Elements in the Early Modern Age, giving for each of them the axioms and postulates employed to ground elementary mathematics.

In this paper I argue that Kant's distinction in the Inaugural Dissertation between the sensible and the intelligible arises in part out of certain open questions left open by his comparison between mathematics and metaphysics in the Prize Essay. This distinction provides a philosophical justification for his distinction between the respective methods of mathematics and metaphysics and his claim that mathematics admits of a greater degree of certainty. More generally, this illustrates the importance of Kant's reflections on mathematics for the (...) development of his Critical philosophy. (shrink)

Jill North offers answers to questions at the heart of the project of interpreting physics. How do we figure out the nature of the world from a mathematically formulated theory? What do we infer about the world when a physical theory can be mathematically formulated in different ways? The notion of structure is crucial to North's answers.

Im Mittelpunkt der vorliegenden Studie steht die Frage nach der Tragweite und Anwendungsrelevanz der Methodenlehre Émilie du Châtelets für die Physik im 18. Jahrhundert, mit der sich die Französin an der Diskussion um Energie- und Impulserhaltung und um das Prinzip der kleinsten Wirkung beteiligte. Andrea Reichenberger zeigt, dass Prinzipien und Hypothesen für Émilie du Châtelet als Fundament und Gerüst wissenschaftlicher Erkenntnis gelten. Im Zusammenspiel beider Komponenten erweisen sich das Prinzip des Widerspruchs und das Prinzip des zureichenden Grundes als regulative Leitlinien (...) und Handlungsmaxime für die auf Hypothesen gestützte Theoriebildung und -begründung. Die sich daraus ergebenden Konsequenzen für den Status und Inhalt der Newtonschen Axiome werden exemplarisch aufgezeigt. (shrink)

Science relies on models and idealizations that are known not to be true. Even so, science is epistemically reputable. To accommodate science, epistemology should focus on understanding rather than knowledge and should recognize that the understanding of a topic need not be factive. This requires reconfiguring the norms of epistemic acceptability. If epistemology has the resources to accommodate science, it will also have the resources to show that art too advances understanding.

It is often noted that institutional objects and artifacts depend on human beliefs and intentions and so fail to meet the realist paradigm of mind-independent objects. In this paper I draw out exactly in what ways the thesis of mind-independence fails, and show that it has some surprising consequences. For the specific forms of mind-dependence involved entail that we have certain forms of epistemic privilege with regard to our own institutional and artifactual kinds, protecting us from certain possibilities of ignorance (...) and error; they also demonstrate that not all cases of reference to these kinds can proceed along a causal model. As a result, realist views in ontology, epistemology, and semantics that were developed with natural scientific kinds in mind cannot fully apply to the everyday world. In closing I consider some wider consequences of these results for social science and philosophy. (shrink)

Equality, similarity and congruence are essential elements of Kant’s theory of geometrical cognition; nevertheless, Kant’s account of them is not well understood. This paper provides historical context for treatments of these geometrical relations, presents Kant’s views on their mathematical definitions, and explains Kant’s theory of their cognition. It also places Kant’s theory within the larger context of his understanding of the quality-quantity distinction. Most importantly, it argues that the relation of equality, in conjunction with the categories of quantity, plays a (...) pivotal and wide-ranging role in Kant’s account of mathematical cognition. (shrink)

Much early modern metaphysics grew with an eye to the new science of its time, but few figures took it as seriously as Emilie du Châtelet. Happily, her oeuvre is now attracting close, renewed attention, and so the time is ripe for looking into her metaphysical foundation for empirical theory. Accordingly, I move here to do just that. I establish two conclusions. First, du Châtelet's basic metaphysics is a robust realism. Idealist strands, while they exist, are confined to non-basic regimes. (...) Second, her substance realism seems internally coherent, so her foundational project appears successful.I have two aims in this paper. Historically, I show that du Châtelet's main source of inspiration was Christian... (shrink)

Since his Metaphysische Anfangsgründe der Naturwissenschaft was first published in 1786, controversy has surrounded Immanuel Kant’s conception of matter. In particular, the justification for both his dynamical theory of matter and the related dismissal of mechanical philosophy are obscure. In this paper, I address these longstanding issues and establish that Kant’s dynamism rests upon Leibnizian, metaphysical commitments held by Kant from his early pre-Critical texts on natural philosophy to his major critical works. I demonstrate that, throughout his corpus and inspired (...) by Leibniz, Kant endorses the a priori law of continuity of alteration as a truth of metaphysics, according to which all alterations in experience must occur gradually through all intervening degrees. The principle thus legislates against mechanical philosophy’s absolutely impenetrable atoms, as they would would involve instantaneous changes of velocity in impact. This reveals the metaphysical incoherencies in mechanical philosophy and leaves Kant’s own dynamical theory of matter, grounded on material forces, as the only viable approach to physical explanation. Subsequently, I demonstrate that Kant nevertheless made conceptual space in his system for the theoretical consideration of mechanical explanations, which makes manifest one of the positive roles that the faculty of reason can play with respect to natural science. (shrink)

In the Resolution of the Second Antinomy of the first Critique and the Dynamics chapter of the Metaphysical Foundations of Natural Sciences, Kant presents his critical views on mereology, the study of parts and wholes. He endorses an unusual position: Matter is said to be infinitely divisible without being infinitely divided. It would be mistaken to think that matter consists of infinitely many parts—rather, parts “exist only in the representation of them, hence in the dividing”. This view, according to which (...) parts are created through division somehow, was criticized as obscure early on, and has not received much attention since. Against this trend, I show how a coherent position, which I call Mereological Conceptualism, can be extracted from the sparse textual basis. (shrink)

Most commentators agree that Leibniz advocates some version of a doctrine of the ideality or reducibility of relations, but there is considerable disagreement about what exactly this doctrine means. I argue that Leibniz’s views on relations are more complex than has been previously appreciated, and that, despite some ‘reductionist’ strands in Leibniz’s position, it is seriously misleading to describe him as a reductionist about relations without adding some important qualifications. The complexity of Leibniz’s views on relations tends to be obscured (...) by the common assumption that they can be captured in one unified thesis, or a small number of closely related theses, and by the widespread neglect to take Leibniz’s division of reality into several ontological levels into consideration. I disentangle ten Leibnizian theses about relations, extrinsic denominations, and their relation to intrinsic denominations. Some of these theses express a kind of dependence of extrinsic denominations on intrinsic ones, and some of them can even be counted as articulations of a form of reductionism. But, overall, the general tenor of Leibniz’s position on extrinsic denominations remains non-reductionist. (shrink)

: Newton's critics argued that his treatment of gravity in the Principia saddles him with a substantial dilemma. If he insists that gravity is a real force, he must invoke action at a distance because of his explicit failure to characterize the mechanism underlying gravity. To avoid distant action, however, he must admit that gravity is not a real force, and that he has therefore failed to discover the actual cause of the phenomena associated with it. A reinterpretation of Newton's (...) distinction between the "mathematical" and the "physical" treatment of force indicates how he can reject each horn of this dilemma. (shrink)

Ausgangspunkt der Betrachtung von Aristoteles’ Ansichten zur Ontologie mathematischer Gegenstände ist die Sichtweise seines Lehrers Platon auf die Gegenstände der Mathematik. Dieser war der Ansicht, dass die eigentlichen Gegenstände der mathematischen Wissenschaften Geometrie und Arithmetik sowohl unveränderlich als nicht wahrnehmbar sind, und daher als getrennt von den physikalischen Gegenständen existierend angenommen werden müssen. Die Gründe, die Platon dafür hatte, sind von zweierlei Art.

The first edition of Newton’s Principia opens with a “Praefatio ad Lectorem.” The first lines of this Preface have received scant attention from historians, even though they contain the very first words addressed to the reader of one of the greatest classics of science. Instead, it is the second half of the Preface that historians have often referred to in connection with their treatments of Newton’s scientific methodology. Roughly in the middle of the Preface, Newton defines the purpose of philosophy (...) as a twofold task: to investigate the forces of the phenomena of nature and, once having established the forces, to demonstrate the remaining phenomena. Newton then introduces a distinction between the first two books, which deal with general propositions, and the third, where the propositions are applied to particular instances of celestial phenomena. From these phenomena, Newton claims, the force of gravity, thanks to which bodies tend toward the Sun, is derived. By assuming this force in mathematical propositions, other motions are deduced: the motions of the planets, the comets, the moon, and the sea. Newton then declares his hope that phenomena relative to small particles will also be explained, as per the celestial ones, thanks to the understanding of attractive forces hitherto unknown to philosophers. The Preface ends with a well-deserved laudatio of Edmond Halley and an apologetic passage concerning certain imperfections in the presentation of advanced subjects, such as the motions of the moon. It is these lines to which historians have given most attention in their various studies. (shrink)

ABSTRACTÉmilie du Châtelet’s recently-discovered Essai sur l’optique offers new insights into her early natural philosophy. Here I analyse the Essai in detail, focusing on Du Châtelet’s use of attr...

When, in 1735, Alexander Gottlieb Baumgarten added a new discipline to the philosophical system, he not only founded modern aesthetics but also contributed to shaping the modern concept of art or 'fine art'. In The Founding of Aesthetics in the German Enlightenment, Stefanie Buchenau offers a rich analysis and reconstruction of the origins of this new discipline in its wider context of German Enlightenment philosophy. Present-day scholars commonly regard Baumgarten's views as an imperfect prefiguration of Kantian and post-Kantian aesthetics, but (...) Buchenau argues that Baumgarten defended a consistent and original project which must be viewed in the context of the modern debate on the art of invention. Her book offers new perspectives on Kantian aesthetics and beauty in art and science. (shrink)

This challenging study places fiction squarely at the centre of the discussion of metaphysics. Philosophers have traditionally treated fiction as involving a set of narrow problems in logic or the philosophy of language. By contrast Amie Thomasson argues that fiction has far-reaching implications for central problems of metaphysics. The book develops an 'artifactual' theory of fiction, whereby fictional characters are abstract artifacts as ordinary as laws or symphonies or works of literature. By understanding fictional characters we come to understand how (...) other cultural and social objects are established on the basis of the independent physical world and the mental states of human beings. (shrink)

Antoine Arnauld and Pierre Nicole were philosophers and theologians associated with Port-Royal Abbey, a centre of the Catholic Jansenist movement in seventeenth-century France. Their enormously influential Logic or the Art of Thinking, which went through five editions in their lifetimes, treats topics in logic, language, theory of knowledge and metaphysics, and also articulates the response of 'heretical' Jansenist Catholicism to orthodox Catholic and Protestant views on grace, free will and the sacraments. In attempting to combine the categorical theory of the (...) proposition with a Cartesian account of knowledge, their Logic represents the classical view of judgment which inspired the modern transformation in logic and semantic theory by Frege, Russell, Wittgenstein and recent philosophers. This edition presents a new translation of the text, together with a historical introduction and suggestions for further reading. (shrink)

This book is a major contribution to the history of philosophy in the later medieval period (1250-1350). It focuses on cognitive theory, a subject of intense investigation during these years. In fact many of the issues that dominate philosophy of mind and epistemology today - intentionality, mental representation, scepticism, realism - were hotly debated in the later medieval period. The book offers a careful analysis of these debates, primarily through the work of Thomas Aquinas, John Olivi, and William Ockham. Each (...) of these figures attempts to reconceptualise cognition along direct realist lines, criticising in the process the standard Aristotelian account. Though of primary interest to medieval philosophers, the book presupposes no background knowledge of the medieval period, and will therefore interest a broader community of philosophers concerned with the origins of contemporary cognitive theory. (shrink)

What is the relation between time and change? Does time depend on the mind? Is the present always the same or is it always different? Aristotle tackles these questions in the Physics. In the first book in English exclusively devoted to this discussion, Ursula Coope argues that Aristotle sees time as a universal order within which all changes are related to each other. This interpretation enables her to explain two striking Aristotelian claims: that the now is like a moving thing, (...) and that time depends for its existence on the mind. (shrink)

The thirty chapters work through various fundamental metaphysical issues, sometimes focusing more on scholastic thought, sometimes on the seventeenth century.

This book presents a detailed analysis of three ancient models of spatial magnitude, time, and local motion. The Aristotelian model is presented as an application of the ancient, geometrically orthodox conception of extension to the physical world. The other two models, which represent departures from mathematical orthodoxy, are a "quantum" model of spatial magnitude, and a Stoic model, according to which limit entities such as points, edges, and surfaces do not exist in (physical) reality. The book is unique in its (...) discussion of these ancient models within the context of later philosophical, scientific, and mathematical developments. (shrink)