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El artículo examina tres propuestas de explicación del fenómeno de refracción de la luz formuladas por los pensadores medievales Roger Bacon, John Pecham y Erazmus Ciolek Witelo. Se muestra, en el caso de Bacon, que la explicación estaba soportada en una metafísica de la propagación de los poderes causales y anidaba un conflicto insalvable. En el caso de Pecham se muestra un mayor compromiso con la necesidad de una ley cuantitativa que, desafortunadamente, conduce a una explicación frustrada. Finalmente, se (...) valora el deseo de Witelo por introducir elementos cosmológicos en su explicación. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:LIGHT AND METAPHOR IN PLOTINUS AND ST. THOMAS AQUINAS KEVIN CORRIGAN St. Thomas More College University of Saskatchewan Saskatoon, Saskatchewan I HAVE TWO CONCERNS in this paper. The first is a broad concern, related to the nature of metaphor, which stems from the destructionist or deconstructionist tendencies in some contemporary phenomenology or phenomenological existentialism. According to these views, the logocentric emphasis of the Western tradition must be shown for (...) what it really is : an attempt to erect a cover upon a fundamental absence. In Nietzsche's well known view, "truths are illusions of which one has forgotten that they are illusions; worn-out metaphors which have become powerless to affect the senses, coins which have their obverse effaced and now are no longer of account as coins but merely as metal." 1 For Jacques Derrida all metaphoricity is caught up in an endless circle, which precludes any privileged vantage-point from which one might determine order, hierarchy and center-point. In particular, the unique heliotropic metaphor which, in Derrida's polemic, determines the whole course of Western philosophy " from the Platonic eidos to the Hegelian idea" 2 rests only upon the infinite absence of circularity, for the movement of transference " which turns the sun into metaphor " also inevitably "turns philosophical metaphor towards the sun." 3 1 Nietzsche, "On Truth and Falsity in their Ultramoral Sense (1873)," Works 2 (New York: Russell and Russell, 1964), p. 180. 2 J. Derrida, "White Mythology", trans. F. C. T. Moore, New Literary History 6 (1974), 1: 5-74 ["La mythologie blanche" in Rhetorique et philosophie, Poetique 5 (Paris: Editions du Seliu, 1971)], p. 55. a Ibid., p. 51. 187 188 KEVIN CORRIGAN In this paper I shall examine the thought of Plotinus and Aquinas, broadly described as idealist and realist respectively, with a view to determining whether or not this transference from the physical to the metaphysical is only an illicit, covert erasure of the material sense and a forgetting that all metaphor is self-implicating, that there is no non-metaphorical standpoint from which to grasp the order and structure of the metaphorical. My second concern is much more specific. It is, first, to compare Plotinus and Aquinas on light and metaphor-two thinkers who might be considered to be poles apart on these questions: on the one hand, Plotinus, the father of Neoplatonic emanationism with its insistence upon the primacy of divine light and the father, surely too, of the tradition of light-metaphysics in the later, mediaeval period; on the other hand, St. Thomas, staunchly realist in the Aristotelian tradition. Second, I will seek to show that this first impression of the gulf between the two thinkers is not borne out by a close textual analysis, and that their respective theories, despite the admitted significant difference in viewpoint, are in some respects very close indeed. Let us look briefly at the light-metaphysics tradition first. For Robert Grosseteste light is the source of all activity and its diffusion is not a material change or a change in place, but rather an instantaneous and substantial multiplication of itself in three dimensions.4 Thus, for the author of the De Intelligentiis light is the fundamental principle of motion and life: " Est autem prima lucis operatio in sensibilibus quad motum et vitam operatur in viventibus." 5 Since light is the noblest of corporeal things, it therefore has an intermediate place between pure form and matter, and for Grosseteste and also Bonaventure it is consequently named the forma corporeitatis, the fundamental form of body as 4 De philosophischen W erke des Robert Grosseteste, ed. Ludwig Baur, in Clemens Baeumker, Beitriige zur Geschichte der Philosophic des Mittelalters, vol. IX (Munster, 1912), De Luce, p. 51. 5 Clemens Baeumker, Witelo: Ein Philosoph und Naturforscher des XIII Jahrhunderts, Band III, Heft 2 of Beitriige zur Geschichte der Philosophie des Mittelalters (Munster, 1908), Liber de intelligentiis IX, p. 11. PLOTINUS AND ST. THOMAS AQUINAS 189 such, since light introduces dimension into matter. Light then is the substantial form of the physical universe.6 But how is physical light related to spiritual light? For the light-metaphysics tradition, spiritual light (whether the Uncreated Light which is God himself or the... (shrink)

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated , (...) was to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational methods in these (...) papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school. (shrink)

The year 2009 marks the 400th anniversary of the publication of one of the most revolutionary scientific texts ever written. In this book, appropriately entitled, Astronomia nova, Johannes Kepler developed an astronomical theory which departs fundamentally from the systems of Ptolemy and Copernicus. One of the great innovations of this theory is its dependence on the science of optics. The declared goal of Kepler in his earlier publication, Paralipomena to Witelo whereby The Optical Part of Astronomy is Treated, was (...) to solve difficulties and expose illusions astronomers face when conducting astronomical observations with optical instruments. To avoid observational errors that had plagued the antiquated measuring techniques for calculating the apparent diameter and angular position of the luminaries, Kepler designed a novel device: the ecliptic instrument. In this paper we seek to shed light on the role optical instruments play in Kepler's scheme: they impose constraints on theory, but at the same time render astronomical knowledge secure. To get a comprehensive grasp of Kepler's astonishing achievements it is required to widen the approach to his writings and study Kepler not only as a mathematico-physical astronomer, but also as a designer of instruments and a practicing observer. (shrink)

References to mirrors were frequent in medieval texts both theological and literary, and their meanings have been abundantly studied, especially recently. Medieval writers were primarily inspired by St. Paul's famous metaphor in his First Letter to the Corinthians 13.12–13: “Now we see only puzzling reflections in a mirror, but then we shall see face to face. My knowledge now is partial; then it will be whole, like God's knowledge of me. In a word, there are three things that last forever: (...) faith, hope, and love; but the greatest of them all is love.” Mirrors were also likened to art in many texts; and so they have functioned mightily in investigations of visuality. To cite just one medieval text among many, on Mallorca in 1276, Inghetto Contardo defended pictures against a Jew's alleged attack by asserting that “the holy mother Church sets images out as a kind of mirror, so that seeing them with corporal eyes they see them with the eyes of the mind.” The claim here was that physical images, made possible by Christ's incarnation, were available to human senses and could be formed into a complete picture when they were assimilated with a memory of God's true nature. Hildegard of Bingen had already summed up the idea succinctly: “That [faith] Adam had when he saw with bodily eyes the invisible light of God … but after his disobedience, neither Adam nor any other man could have this vision; for that reason, the faithful can gaze at God only with the interior vision of the soul, in the mirror of faith, and trust to be able to be saved with him who can do all things.” Inghetto was also assimilating the ancient trope to new theories of vision being promulgated at the time by Roger Bacon, Robert Grosseteste, and Witelo and in such popular works as Peter of Limoges's Tractatus moralis de oculo, a preacher's manual composed exactly at the time of the Mallorca debate and very widely circulated afterward. In these, the site of seeing was literally a mirror, namely, the “crystalline humor” where God's light, located in the anterior part of the brain, is unified with rays from the eyes into a double vision. (shrink)

This article seeks the origin, in the theories of Ibn al-Haytham (Alhazen), Descartes, and Berkeley, of two-stage theories of spatial perception, which hold that visual perception involves both an immediate representation of the proximal stimulus in a two-dimensional ‘‘sensory core’’ and also a subsequent perception of the three dimensional world. The works of Ibn al-Haytham, Descartes, and Berkeley already frame the major theoretical options that guided visual theory into the twentieth century. The field of visual perception was the first area (...) of what we now call psychology to apply mathematics, through geometrical models as used by Euclid, Ptolemy, Ibn al-Haytham, and Descartes (among others). The article shows that Kepler’s discovery of the retinal image, which revolutionized visual anatomy and entailed fundamental changes in visual physiology, did not alter the basic structure of theories of spatial vision. These changes in visual physiology are advanced especially in Descartes' Dioptrics and his L'Homme. Berkeley develops a radically empirist theory vision, according to which visual perception of depth is learned through associative processes that rely on the sense of touch. But Descartes and Berkeley share the assertion that there is a two-dimensional sensory core that is in principle available to consciousness. They also share the observation that we don't usually perceived this core, but find depth and distance to be phenomenally immediate, a point they struggle to accommodate theoretically. If our interpretation is correct, it was not a change in the theory of the psychology of vision that engendered the idea of a sensory core, but rather the introduction of the theory into a new metaphysical context. (shrink)

_ Source: _Volume 29, Issue 1, pp 86 - 102 The aim of this paper is to give an overview of the place that Hobbes assigns to optics in the context of his classification of sciences and disciplinary boundaries. To do this, I will begin with an account of Hobbes’s conception of philosophy or science, and particularly his distinction between true and hypothetical knowledge. I will also show that in his demarcation between mathematics or geometry and natural philosophy Hobbes was (...) influenced by Galileo’s _Dialogue_. I then analyse the consequences of this distinction for optics, and conclude by clarifying its status among the scientific disciplines. (shrink)