This work aim to analyse relations between Arithmetic and Geometry indicated by Piero della Francesca in his treatise Libellus de quinque corporibus regularibus. Piero della Francesca was a painter and scholar of perspective, geometry and arithmetic, in his time. He carried out investigations on pictorial, geometric and architectural issues. Of the treatises he wrote, only three are preserved, on perspective, Geometry and Arithmetic. The central document selected for this research was the manuscript Libellus de quinque corporibus regularibus, (...) deposited in the Vatican Apostolic Library in digitized copy. Throughout this work we have tried to understand the Libellus de quinque corporibus regularibus as a result of the work of an artist and scholar who proposed ways of relating Arithmetic and Geometry using both his practical knowledge and the works of authors of antiquity. (shrink)

It is occasionally claimed that the important work of philosophers, physicists, and mathematicians in the nineteenth and in the early twentieth centuries made Kant’s critical philosophy of geometry look somewhat unattractive. Indeed, from the wider perspective of the discovery of non-Euclidean geometries, the replacement of Newtonian physics with Einstein’s theories of relativity, and the rise of quantificational logic, Kant’s philosophy seems “quaint at best and silly at worst”.1 While there is no doubt that Kant’s transcendental project involves his own (...) conceptions of Newtonian physics, Euclidean geometry and Aristotelian logic, the issue at stake is whether the replacement of these conceptions collapses Kant’s philosophy into an unfortunate embarrassment.2 Thus, in evaluating the debate over the contemporary relevance of Kant’s philosophical project one is faced with the following two questions: (1) Are there any contradictions between the scientific developments of our era and Kant’s philosophy? (2) What is left from the Kantian legacy in light of our modern conceptions of logic, geometry and physics? Within this broad context, this paper aims to evaluate the Kantian project vis à vis the discovery and application of non-Euclidean geometries. Many important philosophers have evaluated Kant’s philosophy of geometry throughout the last century,3 but opinions with regard to the impact of non-Euclidean geometries on it diverge. In the beginning of the century there was a consensus that the Euclidean character of space should be considered as a consequence of the Kantian project, i.e., of the metaphysical view of space and of the synthetic a priori character of geometry. The impact of non-Euclidean geometries was then thought as undermining the Kantian project since it implied, according to positivists such.. (shrink)

The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has (...) recently become a topic of intense interest due to the development of a general geometry of opposition (polygons and polyhedra) with many applications. A congress on the square with an interdisciplinary character has been organized on a regular basis (Montreux 2007, Corsica 2010, Beirut 2012, Vatican 2014, Rapa Nui 2016). The volume at hand is a sequel to two successful books: The Square of Opposition - A General Framework of Cognition, ed. by J.-Y. Béziau & G. Payette, as well as Around and beyond the Square of Opposition, ed. by J.-Y. Béziau & D. Jacquette, and, like those, a collection of selected peer-reviewed papers. The idea of this new volume is to maintain a good equilibrium between history, technical developments and applications. The volume is likely to attract a wide spectrum of readers, mathematicians, philosophers, linguists, psychologists and computer scientists, who may range from undergraduate students to advanced researchers. (shrink)

The use of digital tracking technologies is a widespread phenomenon. Millions of people around the world now track, document, and analyse their physical activities, vital functions, and daily habits through wearable devices, apps, and platforms. The aim is to assess and improve health, productivity, and wellbeing. The current Covid-19 pandemic has accelerated the uptake of tracking technologies. At the heart of this trend lies the quantification of the body, deemed as a key element in medical practice and personal self-care. (...) While often couched in positive promotional terms that highlight its value to users' mental, emotional, and physical health, it is also raising a host of issues and concerns that are at once ontological, ethical, political, social, legal, economic, and aesthetic. The Quantification of Bodies in Health aims to deepen understanding of this growing phenomenon and of the role of self-tracking practices in everyday life. It brings together established and emerging authors working at the intersection of philosophy, sociology, history, psychology, and digital culture, while bridging between philosophical and empirical approaches. A timely topic of extreme relevance and significance, The Quantification of Bodies in Health constitutes a useful and unique companion for anyone interested in the study of body quantification and self-tracking practices. (shrink)

Does geometry constitues a core set of intuitions present in all humans, regarless of their language or schooling ? We used two non verbal tests to probe the conceptual primitives of geometry in the Munduruku, an isolated Amazonian indigene group. Our results provide evidence for geometrical intuitions in the absence of schooling, experience with graphic symbols or maps, or a rich language of geometrical terms.

Derrida's introduction to his French translation of Husserl's essay "The Origin of Geometry," arguing that although Husserl privileges speech over writing in an account of meaning and the development of scientific knowledge, this privilege is in fact unstable.

A review of Roberto Torretti's book, "Philosophy of Geometry from Riemann to Poincare.".

The aim of this paper is to introduce Wittgenstein’s concept of the form of a language into geometry and to show how it can be used to achieve a better understanding of the development of geometry, from Desargues, Lobachevsky and Beltrami to Cayley, Klein and Poincaré. Thus this essay can be seen as an attempt to rehabilitate the Picture Theory of Meaning, from the Tractatus. Its basic idea is to use Picture Theory to understand the pictures of (...) class='Hi'>geometry. I will try to show, that the historical evolution of geometry can be interpreted as the development of the form of its language. This confrontation of the Picture Theory with history of geometry sheds new light also on the ideas of Wittgenstein. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

This edited volume explores the intersection of medicine and philosophy throughout history, calling attention to the role of quantification in understanding the medical body. Retracing current trends and debates to examine the quantification of the body throughout the early modern, modern and early contemporary age, the authors contextualise important issues of both medical and philosophical significance, with chapters focusing on the quantification of temperaments and fluids, complexions, functions of the living body, embryology, and the impact of quantified (...) reasoning on the concepts of health and illness. With insights spanning from the sixteenth century to the nineteenth century, this book provides a wide-ranging overview of attempts to ‘quantify’ the human body at various points. Arguing that medicine and philosophy have been constantly in dialogue with each other, the authors discuss how this provided a strategic opportunity both for medical thought and philosophy to refine and further develop. Given today’s fascination with the quantification of the body, represented by the growing profusion of self-tracking devices logging one’s sleep, diet or mood, this collection offers an important and timely contribution to an emerging and interdisciplinary field of study. -/- . (shrink)

As emphasized by Milne, an observer ultimately depends on the transmission and reception of light signals for the measurement of natural lengths and periods remote from his world point. The laws of geometry which are obeyed when these lengths and periods are plotted on a space-time depend, inevitably, on assumptions concerning the dependence of light velocity on the spatial and temporal coordinates. A convention regarding light velocity fixes the geometry, and conversely. However, the convention of flat space-time implies (...) nonintegrable “radar distances” unless the concept of coordinate-dependent units of measure is employed. Einstein's space-time has the advantage of admitting a special reference system $\hat R$ with respect to which the aether fluid is at rest and the total gravitational field vanishes. A holonomic transformation from $\hat R$ to another reference systemR belonging to the same space-time introduces a nonpermanent gravitational field and holonomic aether motion. A nonholonomic transformation from $\hat R$ to a reference systemR* which belongs to a different space-time introduces a permanent gravitational field and nonholonomic aether motion. The arbitrariness of geometry is expressed by extending covariance to include the latter transformation. By means of a nonholonomic (or units) transformation it is possible, with the aid of the principle of equivalence, to obtain the Schwarzschild and de Sitter metrics from the Newtonian fields that would arise in a flat space-time description. Some light is thrown on the interpretation of cosmological models. (shrink)

Craniology – the practice of inferring intelligence differences from the measurement of human skulls – survived the dismissal of phrenology and remained a widely popular research program until the end of the nineteenth century. From the 1970s, historians and sociologists of science extensively focused on the explicit and implicit socio-cultural biases invalidating the evidence and claims that craniology produced. Building on this literature, I reassess the history of craniological practice from a different but complementary perspective that relies on recent developments (...) in the epistemology of measurement. More precisely, I identify two aspects of the measurement culture of nineteenth-century craniologists that are crucial to understand the lack of validity of craniological inference: their neglect of the problem of coordination for their presupposed quantification of intelligence and their narrow view of calibration. Based on my analysis, I claim that these methodological shortcomings amplified the impact of the socio-cultural biases of craniologists, which had a pervasive role in their evidential use of measurement. Finally, my argument shows how the epistemology of measurement perspective can offer useful tools in debates concerning the use of biological evidence to foster social discourse and for analyzing the relationship between theory, evidence, and measurement. (shrink)

The work of David R. Lachterman, The Ethics of Geometry, subtitled A Genealogy of Modernity, concerns essentially the status of geometry in Euclid’s Elements and in Descartes’s Geometry. It is a remarkable work, at once by the declared breadth of its ambitions and by the very great precision of its analyses, which are always supported by a prodigious philosophical culture. David Lachterman’s concern is to grasp, by way of an in-depth commentary of certain, particularly crucial passages of (...) these two foundational works, the change in geometry’s status from the one to the other, and this, as a sort of symptom of what the Moderns, since Descartes, will always experience as a necessary, inaugural rupture with regard to tradition. This change is underlaid, according to the author, by a profound change in the philosophical ethos, and in particular, in the geometer’s ethos. One must understand ethos, Lachterman explains, in the manner of Aristotle: those characteristic means that human beings have by which to act in the world or to behave in relation to one another, or to themselves. There is thus an “ethics” of geometry, namely, in the manner and the style of doing geometry, of behaving as a mathematician both toward apprentices and toward the veritable nature of the “entities” which are to be taught or learnt, and which give their discipline its name. That there is a difference of ethos between Euclid and Descartes implies, according to Lachterman, that there is also a difference in the source of intelligibility of the “mathematical,” understood in the most general sense. This in turn implies a deeper difference in the mode of being in general: it suffices to note that, in the ancient case, the source of intelligibility of the geometric figure lies in the nature of the figure itself, and that in the modern case, the same source is found in the “strategies” and “tactics” suited to bringing the figure to its visibility or to its embodiment, 315 in order to notice that this change in the mode of access to intelligibility must have had profound repercussions upon philosophical thought. It is in this sense that the author’s design is also, at the same time, not genetic, but genealogical. The break between ancient and modern mathematics pleas in favor of a consideration of the rupture of modern thought relative to ancient thought; thus, implicitly—and it is one of the great merits of this book that it shows this—against all homogenizing levelling, in Heidegger’s fashion, of the history of thought down to the history of “the” discipline of metaphysics. If there is something Heideggerian, in the best sense of the term, in Lachterman’s way of considering ethos as coextensive with modes of being, there is, on the other hand, and we ought to be very glad of it, something anti-Heideggerian in his original manner of bringing out the effective novelty of modern thought. For, according to him, modern thought is no longer to be defined, explicitly or exclusively, by the so-called “metaphysics of subjectivity.” Instead, it is defined by a self-regulated, operative, and constructive productivity of thought—and this as much with regard to itself as to its objects. To put it briefly, whereas ancient thought is rather polarized by the logico-eidetic, modern thought is polarized by a sort of methodical constructivism, the status of which is, in reality, very complex. If Descartes speaks of “the construction of a problem,” while Leibniz speaks of the “construction of an equation,” and Kant of the “construction of a concept,” everything depends—as we might guess—upon the multiple meanings that the term ‘construction’ may take on. Is it to be taken in the sense of an absolute creation, a quasi ex nihilo creation, which would render mathematics divine? Is it the creation of artefacts, or again, is it the methodical exploration of problems posed to thought by the existence of objects or corresponding ideas, themselves supposed to be somewhere in the divine understanding? We already discern the breadth and the depth of the debate, and we sense that the essential will be played out in Lachterman’s commentaries on the famous Cartesian solution of the problem of Pappus—the birth certificate, as we know, of analytic geometry. (shrink)

The personalistic theory of probability prescribes that a person should use personal probability assessments in decision-making and that these assessments should correspond with his judgments. Since the judgments exist solely in the assessor's mind, there is no way to prove whether or not this requirement is satisfied. De Finetti has proposed the development of methods which should oblige the assessor to make his assessments correspond with his judgments. An ideal Assessor is hypothesized and his behavior is investigated under a number (...) of such methods. The implications of these methods for the theory of personal probability are discussed. Finally, although the present interest is primarily normative, the practicability of the methods is also discussed. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

The Foundations of Geometry was first published in 1897, and is based on Russell's Cambridge dissertation as well as lectures given during a journey through the USA. This is the first reprint, complete with a new introduction by John Slater. It provides both an insight into the foundations of Russell's philosophical thinking and an introduction to the philosophy of mathematics and logic. As such it will be an invaluable resource not only for students of philosophy, but also for those (...) interested in Russell's philosophical development. Foundations of Geometry consists of four chapters which explore the various concepts of geometry and their philosophical implications, including a historical overview of the development of geometrical theory. (shrink)

For $n < \omega$ , expand the structure (n, S, I, F) (with S the successor relation, I, F as the initial and final element) by forming graphs with edge probability n-α for irrational α, with $0 < \alpha < 1$ . The sentences in the expanded language, which have limit probability 1, form a complete and stable theory.

The Ethics of Geometry is a study of the relationship between philosophy and mathematics. Essential differences in the ethos of mathematics, for example, the customary ways of undertaking and understanding mathematical procedures and their objects, provide insight into the fundamental issues in the quarrel of moderns with ancients. Two signal features of the modern ethos are the priority of problem-solving over theorem-proving, and the claim that constructability by human minds or instruments establishes the existence of relevant entities. These figures (...) are combined in the emblematic statement of Salomon Maimon, "In mathematical construction we are, as it were, gods." Construction is the mark of modernity. The disciplines of classical philology, literary interpretation and the history of philosophy and of mathematics are woven together in this volume. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

The genetic communication system includes the following components: the parent, which represents the information source and which emits messages; the gametes, which are the messenger carriers; and the offspring, which results from the decoding of two of these messages and can, in turn, become an information source.In a diploid species, a pair of heterozygous homologous loci may emit two equally probable messages, the quantity of genetic information (Q) produced being equivalent to: Q=log2 2=1 bit. For n independent pairs of heterozygous (...) homologous loci, Q=n.log2 2=n bits. The evolution of Q is examined whenever the parent is used in inbreeding or crossbreeding. In the case of inbreeding, the initial Q is depleted as the loci become homozygous; for hybridization the evolution of Q is unpredictable. (shrink)

Increasing societal concerns regarding the potential deleterious effects of future climate change have galvanized efforts to manage the problem both through reduction of greenhouse gases and through development of plans to reduce the impacts of climate change that cannot be avoided. These critical activities require making decisions under conditions of considerable uncertainty regarding future conditions in physical and human systems. As the focus on providing information about future climate for taking actions to cope with climate change, the science of uncertainty (...) of climate change will develop more and more with the needs of decision makers in mind. (shrink)

Online medical reference websites are utilized by health care providers to enhance their education and decision making. However, these resources may not adequately reveal pharmaceutical-author interactions and their potential conflicts of interest. This investigation: evaluates the correspondence of two well-utilized CoI databases: the Centers for Medicare and Medicaid Services Open Payments and ProPublica’s Dollars for Docs and quantifies CoIs among authors of a publicly available point of care clinical support website which is used to inform evidence-based medicine decisions. Two data (...) sources were used: the hundred most common drugs and the top fifty causes of death. These topics were entered into a freely available database. The authors were then input into CMSOP and PDD and compensation and number of payments were determined for 2013–2015. The subset of highly compensated authors that also reported “Nothing to disclose” were further examined. There was a high degree of similarity between CMSOP and PDD for compensation and payment number. The amount received was 1.4% higher in CMSOP than in PDD. The articles where the authors had received the greatest compensation were in neurology, oncology, and endocrinology. Two authors reporting “Nothing to disclose” received appreciable and potentially relevant compensation. CMSOP and PDD produced almost identical results. CoIs were common among authors but self-reporting may be an inadequate reporting mechanism. Recommendations are offered for improving the CoI transparency of pharmaceutical-author interactions in point-of-care electronic resources. (shrink)

Online medical reference websites are utilized by health care providers to enhance their education and decision making. However, these resources may not adequately reveal pharmaceutical-author interactions and their potential conflicts of interest. This investigation: evaluates the correspondence of two well-utilized CoI databases: the Centers for Medicare and Medicaid Services Open Payments and ProPublica’s Dollars for Docs and quantifies CoIs among authors of a publicly available point of care clinical support website which is used to inform evidence-based medicine decisions. Two data (...) sources were used: the hundred most common drugs and the top fifty causes of death. These topics were entered into a freely available database. The authors were then input into CMSOP and PDD and compensation and number of payments were determined for 2013–2015. The subset of highly compensated authors that also reported “Nothing to disclose” were further examined. There was a high degree of similarity between CMSOP and PDD for compensation and payment number. The amount received was 1.4% higher in CMSOP than in PDD. The articles where the authors had received the greatest compensation were in neurology, oncology, and endocrinology. Two authors reporting “Nothing to disclose” received appreciable and potentially relevant compensation. CMSOP and PDD produced almost identical results. CoIs were common among authors but self-reporting may be an inadequate reporting mechanism. Recommendations are offered for improving the CoI transparency of pharmaceutical-author interactions in point-of-care electronic resources. (shrink)

Online medical reference websites are utilized by health care providers to enhance their education and decision making. However, these resources may not adequately reveal pharmaceutical-author interactions and their potential conflicts of interest. This investigation: evaluates the correspondence of two well-utilized CoI databases: the Centers for Medicare and Medicaid Services Open Payments and ProPublica’s Dollars for Docs and quantifies CoIs among authors of a publicly available point of care clinical support website which is used to inform evidence-based medicine decisions. Two data (...) sources were used: the hundred most common drugs and the top fifty causes of death. These topics were entered into a freely available database. The authors were then input into CMSOP and PDD and compensation and number of payments were determined for 2013–2015. The subset of highly compensated authors that also reported “Nothing to disclose” were further examined. There was a high degree of similarity between CMSOP and PDD for compensation and payment number. The amount received was 1.4% higher in CMSOP than in PDD. The articles where the authors had received the greatest compensation were in neurology, oncology, and endocrinology. Two authors reporting “Nothing to disclose” received appreciable and potentially relevant compensation. CMSOP and PDD produced almost identical results. CoIs were common among authors but self-reporting may be an inadequate reporting mechanism. Recommendations are offered for improving the CoI transparency of pharmaceutical-author interactions in point-of-care electronic resources. (shrink)

BackgroundThe rating of perceived exertion scales with respiratory and muscular illustrations are recognized as simple and practical methods to understand individual psychometric characteristics in breathing and muscle exertion during exercise. However, the implementation of respiratory and muscular RPE to quantify training load in futsal training camps has not been examined. This study investigates respiratory and muscular RPE relationships during domestic training camps and overseas training camps in an under 20 futsal national team.MethodsData collected from eleven field players were used for (...) comparison in this study. All players reported Borg CR10 RPE and 7-scales respiratory RPE and muscular RPE after training sessions and matches. Additionally, total distance covered and training impulse were used to quantify external and internal loads via the Polar Team Pro system. Paired-sample t-tests were used to compare the RPECR10, RPErespiration, RPEmuscle, TD, and TRIMP between DTC and OTC. Furthermore, linear regression was performed to determine the relationships among all RPE scales, TD, and TRIMP.ResultsThe RPECR10, TD, and TRIMP showed significant difference between DTC and OTC. Furthermore, linear regression analyses showed significant correlation between RPErespiration and RPEmuscle, RPECR10 and RPErespiration, and RPECR10 and RPEmuscle.ConclusionPictorial RPErespiration or RPEmuscle can be used as an alternative to quantify perceived measures of internal loads during DTC and OTC in futsal players. Interpretation of perceived measures of training load and cardiac-related responses in association with external training loads during short-term training camps would be useful in further understanding the demands of futsal players’ experience in these circumstances. (shrink)

본 연구는 기하학에 대한 구조-구성주의 인식론을 정당화하는 것이다. 즉 구조주의와 구성주의를 융합하는 필자의 고유한 인식론으로 기하학적 인식의 본성을 해명하는 것이다. 그러나 현재의 연구는 이러한 큰 주제에 접근하기 위한 예비적 연구로서 칸트의 기하학적 직관 개념에 대한 역사-비판적 분석을 제공하는 데 한정된다. 잘 알려져 있는 것처럼, 칸트는 수학적 인식, 특히 기하학적 인식을 위해서 직관이 핵심적으로 중요하다고 주장했다. 그런데 칸트가 말하는 기하학적 인식을 위한 직관의 역할이 무엇인지는 여전히 논쟁적이다. 이점과 관련해서 역사적으로 대립적인 두 가지 해석이 있다. 하나는 베스(E. Beth), 힌티카(J. Hintikka), 프리드만(M. Fridman) (...) 등으로 이어지는 논리적 해석이며, 다른 하나는 파슨스(Parsons)와 칼슨(E. Carson)에 의해 제공된 현상학적 해석이다. 이에 필자는 특히 프리드만과 칼슨의 논쟁을 중심으로 두 해석의 내용을 재구성하고, 다음에 두 해석의 종합 가능성을 해명하고자 한다. 이를 위해 헬름홀츠-피아제의 인식론, 즉 “군 이론”에 근거한 새로운 구성주의 인식론을 제안할 것이다. 그러나 본고에서는 1차적 근사의 차원에서 그 개략적 구조만을 소개하는 데 만족하고, 종합의 구체적 내용인, 헬름홀츠-피아제의 공간 인식론에 근거한 구조-구성주의 공간 이론은 다른 지면에서 전개될 것이다. (shrink)

This paper consists roughly of three parts. In the first part, an attempt has been made to find some tenable interpretation of Hamilton's logic. This results in accepting that Hamilton's logic can be "saved" if it is understood as being an everday language version of Euler's relations, i.e., extensional relations between terms. In the second part, the propositions of Euler and the propositions of Aristotle are compared and found to be interdefinable: every proposition of Aristotle can be defined by a (...) disjunction of Euler's propositions, and every proposition of Euler can be defined by a conjunction of Aristotle's propositions. In the third part, extensional interpretation is applied to the traditional logic. As a result the 19 traditional syllogisms are reduced to 11. (shrink)