Die Absicht des vorliegenden Buches ist es, das Geflecht der unterschiedlichen Fragestellungen, die mit dem Stichwort „Fichte und seine Zeit“ verbunden sind, in Betracht zu ziehen und ihre internen Zusammenhänge und ihre Geschlossenheit deutlich zu machen. The intention of this book is to take the network of different issues that are associated with the main theme " Fichte and his time" into consideration and make their internal relationships and their closeness significantly.

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

In this paper, we argue that Williamson’s arguments against luminosity and the KK principle do not work, at least in a scientific context. Both of these arguments are based on the presence of a so-called “buffer zone” between situations in which one is in a position to know p and situations in which one is in a position to know ¬p. In those positions belonging to the buffer zone ¬p holds, but one is not in a position to know ¬p. (...) The presence of this buffer zone triggers two types of sorites arguments. We show that this kind of argument does not hold in a scientific context, where the buffer zone is controlled by a quantitative measurement of the experimental error. (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)

Efforts to improve patients’ understanding of their own medical treatments or research in which they are involved are progressing, especially with regard to informed consent procedures. We aimed to design a multisource informed consent procedure that is easily adaptable to both clinical and research applications, and to evaluate its effectiveness in terms of understanding and awareness, even in less educated patients.

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)

The Machiavellian intelligence hypothesis and the social brain hypothesis have revolutionized traditional views on how primate cognition can be studied. Beyond the study of individual problem-solving capacities of various primates, these hypotheses have demonstrated the close relationship between the complexity of primate social life and the emergence of more sophisticated cognitive skills. The social brain hypothesis demonstrated the existence of a close correlation between the volume of the neocortex and the number of individuals in primate social groups. The amount of (...) studies in this area have increased dramatically and have successfully enhanced our understanding of the evolutionary roots of complex social phenomena, including theory of mind, cultural transmission, social learning, and shared attention. The cognitive capacities present in primates also underlie the evolution of cognitive capacities in humans. This chapter introduces present avenues taken in research on primate social cognition, and it walks the reader through the chapters of this volume. (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 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)

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.

Name der Zeitschrift: Klio Jahrgang: 96 Heft: 1 Seiten: 273-282.

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)

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)

A number of experiences have demonstrated how digital solutions are effective in improving quality of life (QoL) and health outcomes for older adults. Smart Health Age-Friendly Environments (SHAFE) is a new concept introduced in Europe since 2017 that combines the concept of Age-Friendly Environments with Information Technologies, supported by health and community care to improve the health and disease management of older adults and during the life-course. This chapter aims to provide an initial overview of the experiences available not only (...) in Europe, based on the research work of the participants of the International Interdisciplinary Network on Health and Well-being in an Age-Friendly Digital World (NET4Age-Friendly), which could be of interest to preventive, health and social authorities. The chapter reports good practices, pain points, and bottlenecks that may require a collaborative, interdisciplinary research approach to facilitate the transformations towards smart, sustainable, health and age-friendly cities and communities. (shrink)

Despite that it is commonly accepted that migraine is a disorder of the nervous system with a prominent genetic basis, it is comorbid with a plethora of medical conditions. Several studies have found bidirectional comorbidity between migraine and different disorders including neurological, psychiatric, cardio- and cerebrovascular, gastrointestinal, metaboloendocrine, and immunological conditions. Each of these has its own genetic load and shares some common characteristics with migraine. The bidirectional mechanisms that are likely to underlie this extensive comorbidity between migraine and other (...) diseases are manifold. Comorbid pathologies can induce and promote thalamocortical network dysexcitability, multi-organ transient or persistent pro-inflammatory state, and disproportionate energetic needs in a variable combination, which in turn may be causative mechanisms of the activation of an ample defensive system with includes the trigeminovascular system in conjunction with the neuroendocrine hypothalamic system. This strategy is designed to maintain brain homeostasis by regulating homeostatic needs, such as normal subcortico-cortical excitability, energy balance, osmoregulation, and emotional response. In this light, the treatment of migraine should always involves a multidisciplinary approach, aimed at identifying and, if necessary, eliminating possible risk and comorbidity factors. (shrink)

Electronic text edition of Giambattista Vico, De nostri temporis studiorum ratione, in Latin. It includes the page numbers of the original edition of 1709, available among the online resources of the ISPF web portal www.giambattistavico.it.

The recent discovery of a mirror neuron system sets a challenge for a philosophy of experience such as phenomenology, because in humans and monkeys the mirror system seems to transform seen actions into an inner representation of these actions. This paper tries to outline the guidelines of a transcendental-phenomenological analysis of alterity, different from empirical research. The transcendental research must provide a criterion for interpreting the results of empirical science. On this basis the paper compares the phenomenological analysis of alterity (...) with some results of neuroscientific research. It is argued that Edmund Husserl presents an analysis that enables us to avoid misinterpretations of the role and function of the mirror neuron system. (shrink)

Researchers agree on ascribing the De incarnatione Christi contra Apollinarium and the De salutari epiphania contra Apollinarium to two different authors, who probably shared the same theological education. The latter not only uses a mature theological style but shows a better knowledge of Apollinarius of Laodicea and his disciples’ writings. Even though the two authors try to demonstrate the presence of a perfect humanity in Christ, against Apollinarian thought, we can find some important differences in their works concerning the topic (...) of the impeccabilitas of Christ and the relationship between sin and freedom. They explain in a different way the theory of salvation according to Apollinarius: while according to the author of De incarnatione Christi contra Apollinarium the man can save himself through the imitation of Christ, for the other writer salvation has been accomplished only because Christ is devoid of any trace of sin. (shrink)

El presente trabajo presenta algunas reflexiones surgidas del trabajo que la Congregación para la Educación Católica está realizando en los últimos años para ayudar a las instituciones universitarias católicas a desempe- ñar su misión. Estas reflexiones se organizan en torno a cuatro polos: la urgencia de aceptar los desafíos más relevantes que la educación superior tiene hoy en día; las líneas primordiales de la Constitución Apostólica Ex corde Ecclesiae; la vida académica; y el rol de la teología y de la (...) pastoral en las universidades católicas. (shrink)

The tensorial relativistic quantum mechanics in (1+1) dimensions is considered. Its kinematical and dynamical features are reviewed as well as the problem of finding the Dirac spinor for given finite multivectors. For stationary states, the dynamical tensorial equations, equivalent to the Dirac equation, are solved for a free particle, for a particle inside a box, and for a particle in a step potential.