This book reconstructs, both from the historical and theoretical points of view, Leibniz's geometrical studies, focusing in particular on the research Leibniz ...

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.

The “common notions” prefacing the Elements of Euclid are a very peculiar set of axioms, and their authenticity, as well as their actual role in the demonstrations, have been object of debate. In the first part of this essay, I offer a survey of the evidence for the authenticity of the common notions, and conclude that only three of them are likely to have been in place at the times of Euclid, whereas others were added in Late Antiquity. In the (...) second part of the essay, I consider the meaning and uses of the common notions in Greek mathematics, and argue that they were originally conceived in order to axiomatize a theory of equivalence in geometry. I also claim that two interpolated common notions responded to different epistemic needs and regulated diagrammatic inferences. (shrink)

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.

This book brings together papers of the conference on 'Space, Geometry and the Imagination from Antiquity to the Modern Age' held in Berlin, Germany, 27-29 August 2012. Focusing on the interconnections between the history of geometry and the philosophy of space in the pre-Modern and Early Modern Age, the essays in this volume are particularly directed toward elucidating the complex epistemological revolution that transformed the classical geometry of figures into the modern geometry of space. Contributors: Graciela De Pierris Franco Farinelli (...) Michael Friedman Daniel Garber Jeremy Gray Gary Hatfield Andrew Janiak Douglas Jesseph Alexander Jones Henry Mendell David Rabouin. (shrink)

In this paper, I attempt a reconstruction of the theory of intersections in the geometry of Euclid. It has been well known, at least since the time of Pasch onward, that in the Elements there are no explicit principles governing the existence of the points of intersections between lines, so that in several propositions of Euclid the simple crossing of two lines (two circles, for instance) is regarded as the actual meeting of such lines, it being simply assumed that the (...) point of their intersection exists. Such assumptions are labelled, today, as implicit claims about the continuity of the lines, or about the continuity of the underlying space. Euclid’s proofs, therefore, would seem to have some demonstrative gaps that need to be filled by a set of continuity axioms (as we do, in fact, find in modern axiomatizations).I show that Euclid’s theory of intersections was not in fact based on any notion of continuity at all. This is not only because Greek concepts of continuity (such as the Aristotelian ones) were largely insufficient to ground a geometrical theory of intersections, but also, at a deeper level, because continuity was simply not regarded as a notion that had any role to play in the latter theory. Had Euclid been asked to explain why the points of intersections of lines and circles should exist, it would have never occurred to him to mention continuity in this connection. Ancient geometry was very different from ours, and it is only our modern views on continuity that tend to give rise to the expectation that this latter must be included in the foundations of elementary mathematics.We may hope to reconstruct Euclid’s views on intersections if we undertake a critical examination both of the extension and of the limits of ancient diagrammatic practices. This is tantamount to attempting to understand to what extent the existence of an intersection point may be inferred just from the inspection of a diagram, and in which cases we need rather to supplement such inference by propositional rules. This leads us to discuss Euclid’s definition of a point, and to work out the details of the complex interaction between diagrams and text in ancient geometry. We will see, then, that Euclid may have possessed a theory of intersections that was sufficiently rigorous to dispel the main objections that could be advanced in antiquity. (shrink)

This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the 17th-century studies on (...) the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the 18th century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz’s essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz’s manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments. (shrink)

The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in (...) these fields with 19th- and 20th-Century conceptions of them. All of them have special care in framing Leibniz’s work in historical context, and sometimes offer wider historical perspectives that go much beyond Leibniz’s researches. A special emphasis is given to effective mathematical practice rather than purely epistemological thought. The book is addressed to all scholars of the exact sciences who have an interest in historical research and Leibniz in particular, and may be useful to historians of mathematics, physics, and epistemology, mathematicians with historical interests, and philosophers of science at large. (shrink)

Leibniz pursued the study of his new geometry, the analysis situs, throughout his lifetime. The following essays, the Ars Representatoria and the text Uniformis locus…, both go back to the early nineties of the seventeenth century. Although most of the analysis situs texts are still unpublished—which makes it very hard to see how this discipline might have evolved during the years—there seems to be no doubt that the beginning of 1690s marked a breakthrough in Leibniz’s studies.

ArgumentThe Fourth Postulate of Euclid’s Elements states that all right angles are equal. This principle has always been considered problematic in the deductive economy of the treatise, and even the ancient interpreters were confused about its mathematical role and its epistemological status. The present essay reconsiders the ancient testimonies on the Fourth Postulate, showing that there is no certain evidence for its authenticity, nor for its spuriousness. The paper also considers modern mathematical interpretations of this postulate, pointing out various anachronisms. (...) It further discusses the validity of the ancient proof by superposition of the Fourth Postulate. Finally, the article proposes an interpretation of the history of the concept of angle in Greek geometry between Euclid and Apollonius, and puts forward a conjecture on the interpolation of the Fourth Postulate in the Hellenistic age. The essay contributes to a general reassessment of the axiomatic foundations of ancient mathematics. (shrink)

(No abstract is available for this citation).

Research on the implementation of corporate social responsibility (CSR) has revealed the critical role of CSR departments vis-à-vis functional departments. While both CSR and functional departments influence CSR implementation, the question of how they work together remains underexamined. We address this question by mobilizing and merging two complementary yet separate perspectives on CSR implementation: “coordination” and “enactment.” Building on a comparative case study involving seven large Swiss financial institutions that have established CSR departments and implemented CSR to varying extents, we (...) inductively derive six courses of actions conducing to CSR implementation, involving both coordination and enactment. We distinguish between four courses of actions in the CSR departments ( centralizing, coalescing, orchestrating, and consulting) and two courses of actions in the functional departments ( decentralizing and tailoring). As our data suggest that coordination and enactment work in tandem, we capture these insights in a model of CSR implementation as coordinated enactment. Our research contributes to the literature by explaining how CSR departments and functional departments enact and simultaneously coordinate CSR at a particular implementation stage, thus illuminating how and why the variance in CSR implementation occurs. (shrink)

Business and society (B&S) scholarship that uses the theoretical perspective of institutionalism combines different research approaches to values. Within the B&S literature drawing on institutionalism, we identified and categorized the research on values according to a spectrum of normative and/or descriptive approaches (including both and neither approaches). Primarily, we focused on how the normative and descriptive approaches interrelate and integrate. We argue that drawing on John Dewey’s pragmatism and Philip Selznick’s institutionalism can help further an integrative approach, which holds great (...) potential for advancing theorization in the B&S field while increasing its practical relevance. (shrink)

Business sustainability aims to combine market logic with social welfare logic. In literature, it is commonly assumed that sustainability and the social welfare logic associated with it are characterized by a long-term orientation. However, this assumption is problematic because this principle may not apply in certain contexts. This qualitative study challenges this assumption and focuses on the mechanisms by which time affects the adoption of sustainability practices in the context of socially responsible investing (SRI) practices in Swiss banks and insurance (...) companies. The article provides insights into the mechanisms associated with different time horizons and investigates their effects on the adoption of SRI in financial intermediaries. It also shows how the dimension of time shapes interactions between the two institutional logics underlying SRI in business organizations through specific mechanisms. (shrink)

This paper outlines an account of conditionals, the evidential account, which rests on the idea that a conditional is true just in case its antecedent supports its consequent. As we will show, the evidential account exhibits some distinctive logical features that deserve careful consideration. On the one hand, it departs from the material reading of ‘if then’ exactly in the way we would like it to depart from that reading. On the other, it significantly differs from the non-material accounts which (...) hinge on the Ramsey Test, advocated by Adams, Stalnaker, Lewis, and others. (shrink)

Probability ratio and likelihood ratio measures of inductive support and related notions have appeared as theoretical tools for probabilistic approaches in the philosophy of science, the psychology of reasoning, and artificial intelligence. In an effort of conceptual clarification, several authors have pursued axiomatic foundations for these two families of measures. Such results have been criticized, however, as relying on unduly demanding or poorly motivated mathematical assumptions. We provide two novel theorems showing that probability ratio and likelihood ratio measures can be (...) axiomatized in a way that overcomes these difficulties. (shrink)

This paper develops a probabilistic analysis of conditionals which hinges on a quantitative measure of evidential support. In order to spell out the interpreta- tion of ‘if’ suggested, we will compare it with two more familiar interpretations, the suppositional interpretation and the strict interpretation, within a formal framework which rests on fairly uncontroversial assumptions. As it will emerge, each of the three interpretations considered exhibits specific logical features that deserve separate consideration.

Le polbusting est une pratique de recreation et récréation esthétique à travers laquelle les protagonistes de la culture électronique détournent et ridiculisent les messages et les corps de la politique contemporaine. Ces performances incarnent emblématiquement la vocation et la sensibilité transpolitiques de la culture postmoderne, indiquant la fête et le jeu comme les matrices sur lesquelles elle se fonde. Ainsi, il apparaît indispensable, pour comprendre la relation contemporaine entre imaginaire, médias et politique, de prendre sérieusement en considération ce qui se (...) produit dans les nouveaux paysages médiatiques, dans la mise en scène de la vie quotidienne, dans la culture de l’éphémère et dans tout ce qui a, jusqu'à présent, constitué la marge et l’ombre de la vie sociale. (shrink)

This paper investigates the logic of reasons. Its aim is to provide an analysis of the sentences of the form ‘p is a reason for q’ that yields a coherent account of their logical properties. The idea that we will develop is that ‘p is a reason for q’ is acceptable just in case a suitably defined relation of incompatibility obtains between p and ¬q. As we will suggest, a theory of reasons based on this idea can solve three challenging (...) puzzles that concern, respectively, contraposing reasons, conflicting reasons, and supererogatory reasons, and opens a new perspective on some classical issues concerning non-deductive inferences. (shrink)

Both in the bibliography and in the citation in the text, Michelle Gibbons’ article below has been mistakenly attributed to “Gibson.” The proper reference to the article should be: Gibbons, M.. Reassessing discovery: Rosalind Franklin, scientific visualization, and the structure of DNA. _Philosophy of Science, 79_, 63–80.

This paper develops a formal theory of non-monotonic consequence which differs from most extant theories in that it assumes Contraposition as a basic principle of defeasible reasoning. We define a minimal logic that combines Contraposition with three uncontroversial inference rules, and we prove some key results that characterize this logic and its possible extensions.