In this article, we publish the critical edition of Andalò di Negro’s De compositione astrolabii, with English translation and commentary. The mathematician and astronomer Andalò di Negro presumably redacted this treatise on the astrolabe in the 1330s, while residing at the court of King Robert of Naples. The present edition has three purposes: first, to make available a text missing from the previous compilations of works by Andalò di Negro; second, to revise a privately circulated edition of the text; and (...) third, to help disseminating one of the rare Latin texts presenting the principles of the stereographic projection which underlie the construction of the astrolabe. (shrink)

In view of the progress made in recent decades in the fields of stemmatology and the analysis of geometric diagrams, the present article explores the possibility of establishing the stemma codicum of a handwritten tradition from geometric diagrams alone. This exploratory method is tested on Ibn al-Haytham’s Epistle on the Shape of the Eclipse, because this work has not yet been issued in a critical edition. Separate stemmata were constructed on the basis of the diagrams and the text, and a (...) comparison showed no major differences. The greater reliability of a stemma codicum constructed on the basis of the diagrams rather than the text of a mathematical work is discussed and preliminary conclusions are drawn. (shrink)

The modern physiological optics introduces the notions related to the conditions of fusion of binocular images by the concept of correspondence, due to Christiaan Huygens, and by an experiment attributed to Christoph Scheiner. The conceptualization of this experiment dates, in fact, back to Ptolemy and Ibn al-Haytham. The present paper surveys Ibn al-Haytham's knowledge about the mechanisms of binocular vision. The article subsequently explains why Ibn al-Haytham, a mathematician, but here an experimenter, did not give the circular figure of the (...) theoretical horopter, construction due to Gerhard Vieth and Johannes Müller. But, on the other hand, it is clear that Ibn al-Haytham's experimental study puts in place the notion of corresponding points, the cases of homonymous and cross diplopia, and even prepares the discovery of Panum area. (shrink)

In Résolution des quatre principaux problèmes d’architecture (1673) then in Cours d’architecture (1683), the architect–mathematician Nicolas-François Blondel addresses one of the most famous architectural problems of all times, that of the reduction in columns (entasis). The interest of the text lies in the variety of subjects that are linked to this issue. (1) The text is a response to the challenge launched by Curabelle in 1664 under the name Étrenne à tous les architectes; (2) Blondel mathematicizes the problem in the (...) “style of the Ancients”; (3) The problem is reformulated and solved through the continuous drawing of the curve; (4) Blondel refutes the uniqueness of the curve by enumerating a variety of solutions (conchoid, spiral, parabola, ellipse, circle, hyperbola). This exuberance responds to an intention that does not coincide with the state of the art of mathematics at the end of the seventeenth century, nor with the taste for geometry of the Ancients, nor with any pedagogical project. This feature is explained by Blondel’s plan to found architecture on scientific bases. The reasons for his failure are analysed. (shrink)

A (critical) review of Hans Belting's essay.

A comparison of the manuscripts has shown that De li aspecti, the Italian version of Alhacen's De aspectibus, Vat. lat. 4595 (I), was copied from London, British Library, Royal 12 G vii (L). The discovery of long omissions in L, not reproduced in I, disproves this conclusion. The error has two reasons: a sampling too small, the confusion between phenetic and cladistic approaches.

This volume has 41 chapters written to honor the 100th birthday of Mario Bunge. It celebrates the work of this influential Argentine/Canadian physicist and philosopher. Contributions show the value of Bunge’s science-informed philosophy and his systematic approach to philosophical problems. The chapters explore the exceptionally wide spectrum of Bunge’s contributions to: metaphysics, methodology and philosophy of science, philosophy of mathematics, philosophy of physics, philosophy of psychology, philosophy of social science, philosophy of biology, philosophy of technology, moral philosophy, social and political (...) philosophy, medical philosophy, and education. The contributors include scholars from 16 countries. Bunge combines ontological realism with epistemological fallibilism. He believes that science provides the best and most warranted knowledge of the natural and social world, and that such knowledge is the only sound basis for moral decision making and social and political reform. Bunge argues for the unity of knowledge. In his eyes, science and philosophy constitute a fruitful and necessary partnership. Readers will discover the wisdom of this approach and will gain insight into the utility of cross-disciplinary scholarship. This anthology will appeal to researchers, students, and teachers in philosophy of science, social science, and liberal education programmes. 1. Introduction Section I. An Academic Vocation Section II. Philosophy Section III. Physics and Philosophy of Physics Section IV. Cognitive Science and Philosophy of Mind Section V. Sociology and Social Theory Section VI. Ethics and Political Philosophy Section VII. Biology and Philosophy of Biology Section VIII. Mathematics Section IX. Education Section X. Varia Section XI. Bibliography. (shrink)

Unlike the physical sciences, sociology is frequently described as an interpretative non-experimental science. Comparative epistemology sheds new light on this claim. 1. Experimentation is not a constant character of the physical sciences; 2. Experimental hypothetical-deductive reasoning, including the test of predictions, is also practicable in sociology. The argument is developed by a detailed step-wise comparison of the prediction of light ray deviation within the Sun’s gravitational field made in 1919 (physics) and the prediction of 8% cosmopolitanism of Cambridge University between (...) 1250 and 1350 (sociology). Extensive analysis of regent masters’ prosopographic notes yields the result of 9.5 percent cosmopolitanism, which is close to the theoretical prediction. Au contraire des sciences physiques, la sociologie est souvent décrite comme une science interprétative et non-expérimentale. L’épistémologie apporte un éclairage nouveau sur cette position : 1) L’expérimentation n’est pas un trait constant des sciences physiques ; 2) Le raisonnement expérimental est également applicable en sociologie. L’argument est développé en comparant en détail le test de la prédiction d’une déviation des rayons lumineux dans un champ de gravitation effectué en 1919 et le test de la prédiction d’un taux de cosmopolitisme de 8 % de l’université de Cambridge dans la période 1250-1350. Le dépouillement des notices prosopographiques des maîtres régents donne un résultat de 9,5 % proche de la prédiction théorique initiale. (shrink)

The concept of aerial perspective has been used for the first time by Leonardo da Vinci (1452-1519). This article studies its dependence on Ptolemy’s Optica and overall on the optical tradition inaugurated by Ibn al-Haytham’s Kitāb al-Manāẓir (d. after 1040). This treatise, that was accessible through several Latin and Italian manuscripts, and was the source of many Medieval commentaries, offers a general theory of visual perception emancipated from the case of the moon illusion, in which physical and psychological factors are (...) closely combined. Atmospheric extinction (not refraction, which it is sometimes confused with) affects the conjectured size of remote objects. This phenomenon is also the core source for a pictorial rendering of depth, that is based onto a principle different from the diminution of size. (shrink)

Contemporary sociology of scientific knowledge (SSK) is defined by its relativist trend. Its programme often calls for the support of philosophers, such as Duhem, Quine, and Wittgenstein. A critical re-reading of key texts shows that the main principles of relativism are only derivable with difficulty. The thesis of the underdetermination of theory doesn't forbid that Duhem, in many places, validates a correspondence-consistency theory of truth. He never said that social beliefs and interests fill the lack of underdetermination. Quine's idea of (...) a selective revision of hypotheses, as well as the neat incompatibility between holism and conventionalism, openly challenges the principles of relativism. Wittgenstein's work, which is not presented in book-form but rather as a tree, forces us to avoid aphoristic choices that credit any text-excising. This remark allows us to tackle the passages that sociological relativism is based on.Mathematical conventions are not anthropological objects. When Wittgenstein examines the "language-games," he only speaks of the functioning of natural language, not to be confused with scientific formal languages. We then should render the formula "language-game" by "well-defined, explicit and compulsory rules of communication", which is a much less attractive formula for relativism. Consequently, there does not exist a real continuity between the epistemologies of Duhem, Quine and Wittgenstein, and the recent works of the SSK. (shrink)

The modern physiological optics introduces the notions related to the conditions of fusion of bi- nocular images by the concept of correspondence, due to Christiaan Huygens (1704), and by an experiment attri- buted to Christoph Scheiner (1619). The conceptualization of this experiment dates, in fact, back to Ptolemy (90- 168) and Ibn al-Haytham (d. af. 1040). The present paper surveys Ibn al-Haytham's knowledge about the mecha- nisms of binocular vision. The article subsequently explains why Ibn al-Haytham, a mathematician, but here (...) an experimenter, did not give the circular figure of the theoretical horopter, construction due to Gerhard Vieth (1818) and Johannes Müller (1826). But, on the other hand, it is clear that Ibn al-Haytham's experimental study puts in place the notion of corresponding points, the cases of homonymous and cross diplopia, and even prepares the discovery of Panum area. L'optique physiologique moderne introduit les notions relatives aux conditions de fusion des images binoculaires par le concept de correspondance, prêté à Christiaan Huygens (1704), et par une expérience attribuée à Christoph Scheiner (1619). L'article montre que la conceptualisation de l'expérience remonte en fait à Ptolémée (90-168) et à Ibn al-Haytham (m. ap. 1040), et précise les connaissances que ce dernier avait des mécanismes de la vision binoculaire. Il est ensuite expliqué pourquoi Ibn al-Haytham, mathématicien mais ici expérimentateur, ne donne pas la forme circulaire de l'horoptère théorique, dont la construction revient à Gerhard Vieth (1818) et Johannes Müller (1826). En revanche, l'étude expérimentale d'Ibn al-Haytham met en place la notion de points correspondants, les cas de diplopie homonyme et croisée et prépare même la découverte de l'aire fusionnelle de Panum. (shrink)

Summary We move words and words move us. To describe and explain how and why this happens, the present article focuses on Prague traditions, both on the philosophical and linguistic elements. The semantic and syntactic approach is summarized, as developed by Anton Marty, belonging to the Brentano school, and by Vilém Mathesius, founder of the Prague Linguistic Circle, as well as by Jan Firbas, who developed the functional sentence perspective (FSP) into the theory of communicative dynamism (CD). The four Principles (...) of FSP and the four factors of CD are highlighted, together with the related criticism that stems from a systematic work of corpus annotation, a true test procedure for any theory concerned with word order, the interplay between lexicon and morphology, rhythm, intonation and their effects on the addressee’s psychic and emotive processes and life. (shrink)

Brisant l’image idéale de la science consensuelle, les controverses scientifiques sont aujourd’hui devenues un sujet privilégié de la sociologie et de l’histoire des sciences. Elles sont par ailleurs impliquées au cœur des débats sur les méthodes des sciences sociales. Si l’analyse des controverses scientifiques doit beaucoup aux approches inaugurées par les courants relativistes et constructivistes des années 1970-1980, ce livre montre que les études contemporaines ont tout à gagner à réintroduire ce qui a été le principal tabou des trente dernières (...) années: la vérité. Cette conclusion n’est pas le résultat d’une méditation abstraite sur le destin de la sociologie et de l’histoire des sciences. C’est le résultat d’études de cas, portant sur des disciplines telles que la biologie (la thèse des générations spontanées, débattue entre Pasteur et Pouchet), de la médecine (le vitalisme opposé à la médecine expérimentale naissante), de la stéréotomie (les « Guerres perspectives » qui ont agité le Paris des années 1640), de la perspective (la mathématisation de la perspective dans l’Italie du 16e siècle) ou de l’optique (la question de l’intromission, discutée à Oxford). De querelles médiévales à des disputes plus récentes, ces études suivent un même fil conducteur : interroger les rôles de la rationalité, des conventions et des croyances collectives dans la construction des théories scientifiques. L’auteur défend une théorie incrémentaliste du progrès scientifique: pour autant qu’il suive des règles, le débat est un moyen pratique de tester la robustesse d’une théorie et de départager les théories rivales. Le fait que les débats soient souvent marqués par la passion et les émotions est sans intérêt ; l’important est que ces échanges réglés puissent, par la production d’arguments publics, s’approcher de la vérité. C’est une façon de répondre à la question : Pourquoi l’activité scientifique est-elle conflictuelle? (shrink)

Contrairement à une idée couramment admise aujourd’hui, la politique moderne ne se fonde pas seulement sur la défense et la promotion des droits de l’homme, mais aussi sur un effort pour recréer des pouvoirs légitimes dans un monde où l’autorité ne peut se fonder ni sur la nature, ni sur la tradition, ni sur la transcendance ; cet effort s’est traduit pas l’émergence, entre le XVIIIe et le XXe siècle d’un ensemble cohérent de compromis entre la logique libérale et les (...) exigences propres de la puissance, dont la politique contemporaine est aujourd’hui assez éloignée. On peut donc considérer que nous sommes sortis de l’« âge classique de la modernité », ce qui conduit à poser la question des conditions d’une synthèse nouvelle entre la liberté et la puissance. (shrink)

To students and practitioners of anamorphic art, the name of Jean-François Niceron is more than preeminent; it has become iconic. La Perspective Curieuse was first published in 1638. An augmented version was then translated into Latin by Mersenne in 1646. A newly amended and augmented version was retranslated into French by Roberval in 1652. This book is an English translation of the 1652 text, with reference to the 1638 and 1646 versions. Considering the continued high reputation of the book, the (...) mathematics have been checked for correctness and consistency, and the authors have provided a full commentary, pointing out the most difficult turns of the 17th-century French, the respective contributions of Niceron, Mersenne and Roberval, and explaining Niceron's greatest insights and weaknesses. (shrink)

Chicago, The University of Chicago Press, London, University of London Press, 2023, xiv + 343 pp., 49 halftones, $120.00 (hardback); £90.00, ISBN 978-1-908590-58-9 (Warburg Institute Studies and Texts 8). The late Abdelhamid I. Sabra (1924–2013) devoted a significant part of his work to the critical edition and English translation of the optics of Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham….

This volume gathers together for the first time are all the key texts in a crucial debate in modern philosophy, centered on Leibniz's famous 1695 essay, the "New System of the Nature of Substances and their Communication," in which he introduced his strikingly original theory of metaphysics. His "system" became increasingly famous and drew him into discussion and development of these ideas, both in public and in private, with a variety of thinkers, most notably the great French philosopher Pierre Bayle. (...) Woolhouse's and Francks's new English edition gives the only full representation of this debate, and will therefore be essential reading for anyone who wishes to gain a proper understanding of Leibniz's philosophy and its intelletual context. All the texts are newly translated and extensively annotated; many appear in English for the first time. (shrink)

This chapter offers a proceduralist argument against capital punishment. More specifically, it contends that the possibility of irrevocable mistakes precludes the just administration of the death penalty. At stake is a principle of political morality: legal institutions must strive to remedy their mistakes and to compensate those who suffer from wrongful sanctions. The incompatibility of remedy and execution is the crux of the irrevocability argument: because the wrongly executed cannot enjoy the morally required compensation, execution is impermissible. Along with defending (...) his key premises, Yost explains the complicated role that sentencing uncertainty plays in the argument. He concludes by noting some of the flaws in substantive consequentialist and retributivist justifications of capital punishment. (shrink)

Plato's dialogues frequently criticize traditional Greek myth, yet Plato also integrates myth with his writing. Daniel S. Werner confronts this paradox through an in-depth analysis of the Phaedrus, Plato's most mythical dialogue. Werner argues that the myths of the Phaedrus serve several complex functions: they bring nonphilosophers into the philosophical life; they offer a starting point for philosophical inquiry; they unify the dialogue as a literary and dramatic whole; they draw attention to the limits of language and the limits of (...) knowledge; and they allow Plato to co-opt cultural authority as a way of defining and legitimating the practice of philosophy. Platonic myth, as a species of traditional tale, is thus both distinct from philosophical dialectic and similar to it. Ultimately, the most powerful effect of Platonic myth is the way in which it leads readers to participate in Plato's dialogues and to engage in a process of self-examination. (shrink)

This book explores the interrelationships between optics, vision and perspective before the Classical Age, examining binocularity in particular. The author shows how binocular vision was one of the key juncture points between the three concepts and readers will see how important it is to understand the approach that scholars once took. In the Middle Ages and the Renaissance, the concept of Perspectiva – the Latin word for optics – encompassed many areas of enquiry that had been viewed since antiquity as (...) interconnected, but which a erwards were separated: optics was incorporated into the field of physics (i.e., physical and geometrical optics), vision came to be regarded as the sum of various psycho-physiological mechanisms involved in the way the eye operates (i.e., physiological optics and psychology of vision) and the word ‘perspective’ was reserved for the mathematical representation of the external world (i.e., linear perspective). The author shows how this division, which emerged as a result of the spread of the sciences in classical Europe, turns out to be an anachronism if we confront certain facts from the immediately preceding periods. It is essential to take into account the way medieval scholars posed the problem – which included all facets of the Latin word perspectiva – when exploring the events of this period. (shrink)

Many books explain what is known about the universe. This book investigates what cannot be known. Rather than exploring the amazing facts that science, mathematics, and reason have revealed to us, this work studies what science, mathematics, and reason tell us cannot be revealed. In The Outer Limits of Reason, Noson Yanofsky considers what cannot be predicted, described, or known, and what will never be understood. He discusses the limitations of computers, physics, logic, and our own thought processes. Yanofsky describes (...) simple tasks that would take computers trillions of centuries to complete and other problems that computers can never solve; perfectly formed English sentences that make no sense; different levels of infinity; the bizarre world of the quantum; the relevance of relativity theory; the causes of chaos theory; math problems that cannot be solved by normal means; and statements that are true but cannot be proven. He explains the limitations of our intuitions about the world -- our ideas about space, time, and motion, and the complex relationship between the knower and the known. Moving from the concrete to the abstract, from problems of everyday language to straightforward philosophical questions to the formalities of physics and mathematics, Yanofsky demonstrates a myriad of unsolvable problems and paradoxes. Exploring the various limitations of our knowledge, he shows that many of these limitations have a similar pattern and that by investigating these patterns, we can better understand the structure and limitations of reason itself. Yanofsky even attempts to look beyond the borders of reason to see what, if anything, is out there. (shrink)

We propose a formal framework for interpretable machine learning. Combining elements from statistical learning, causal interventionism, and decision theory, we design an idealised explanation game in which players collaborate to find the best explanation for a given algorithmic prediction. Through an iterative procedure of questions and answers, the players establish a three-dimensional Pareto frontier that describes the optimal trade-offs between explanatory accuracy, simplicity, and relevance. Multiple rounds are played at different levels of abstraction, allowing the players to explore overlapping causal (...) patterns of variable granularity and scope. We characterise the conditions under which such a game is almost surely guaranteed to converge on a optimal explanation surface in polynomial time, and highlight obstacles that will tend to prevent the players from advancing beyond certain explanatory thresholds. The game serves a descriptive and a normative function, establishing a conceptual space in which to analyse and compare existing proposals, as well as design new and improved solutions. (shrink)

Since language is the collective focus of this series, the present paper follows both historiographical and theoretical perspectives. The first deals with Prague as a Middle-European town, with a German and Czech University from 1882, where a philosopher, Anton Marty, from the Brentano school, focuses on language and semasiology in the framework of a psychology from an empirical standpoint. He cites Christian von Ehrenfels, and underscores the relational approach to psychic dynamism but, crucially, he emphasises the oscillations between linguistic “sketches” (...) and semantic comprehension. Sprache ist eine Skizze, listeners are lead through suggestions, Nebenvorstellungen, to grasp meanings, Bedeutungen which do not coincide with the mere addition of explicit, variable components. Simultaneously, Vilém Mathesius, forthcoming founder (1926) of the Prague Linguistic Circle, dealing with English language and literature, enquires into the spontaneous ability of listeners to grasp, infer, integrate ellipsis in a sentence, consisting of a missing word, in omissione vocabuli, quod non dictum tamen cogitatur. Language enquiries will then require psychology, will aim to explain inferences, to infer implicit from explicit. The effort to obtain the whole, via super- or even subsummativity processes, has been a special topic for Gestalt psychology. Context being the proper habitat for both language and mind, we follow the fil rouge which leads directly to Gestalt contributions and further developments, e.g., inferential semantics and pragmatics. In conversation, as in architecture, less is more. We strive to prove this. (shrink)

The perfect compass, used by al-Qūhī, al-Sijzī and his successors for the continuous drawing of conic sections, reappeared after a long eclipse in the works of Renaissance mathematicians like Francesco Barozzi in Venice. The resurgence of this instrument seems to have depended on its interest to solve new optico-perspective problems. Having reviewed the various instruments designed for the drawing of conic sections, the article is focused on the sole conic compass. Theoretical and empirical applications are detailed. Contrarily to the common (...) thesis of an independant discovery, various elements suggest a direct descent between the birkār al-tāmm of the Arabic mathematical tradition and the Italian conic compass. Then we present the most probable transmission hypothesis involving: 1° Ibn Yūnus and his disciples of Mosul, 2° Sultan Malik al-Kāmil in Damas, 3° Master Theodore and Frederick II at the court of Sicily, 4° Andalò di Negro and Robert of Anjou in Naples, 5° Lorenzo della Volpaia, Vinci, Sangallo and Michelangelo in Florence, 6° Ausonio, Contarini, Thiene and Francesco Barozzi in Venice. (shrink)

This article studies a fragment on the conic sections that appear in the Codex Atlanticus, fols. 611rb/915ra. Arguments are put forward to assemble these two folios. Their comparison with the Latin texts available before 1500 shows that they derive from the De speculis comburentibus of Alhacen and the De speculis comburentibus of Regiomontanus, joined together in his autograph manuscript. Having identified the sources, and discussed their mathematics, the issue of their transmission is targeted. It is shown that these notes were (...) written by Paolo dal Pozzo Toscanelli, through whom they reached the notebooks of Leonardo da Vinci. (shrink)

From the concrete experience of war, Michael S. Yandell constructs a phenomenology of “negative revelation” in which false or distorted claims of goodness and justice disintegrate and become meaningless, adding depth to the term moral injury.

The controversy between the medical schools of Paris and Montpellier extends roughly from the death of Barthez (1806) to the publication of the Introduction to the study of experimental medicine of Claude Bernard (1865), with a peak during which the controversy merges with the polemic between Louis Peisse and Jacques Lordat (1840-1843). This study aims to document as accurately as possible the arguments that were exchanged during this controversy, by seeking their reasons and explaining how the experimental medicine in Paris (...) ultimately took the lead over the vitalism championed by the school of medicine in Montpellier. (shrink)