Reflections on the principle of continuity on the basis of Ibn al-haytham's commentary on proposition I.7 of euclid's elements
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Arabic Sciences and Philosophy 13 (1):101-136 (2003)
After his refutation of the doubts concerning Proposition I.7 (in the Book of solving doubts), Ibn al-Haytham mentions three possible ways in which circles may intersect, submitting them to the following “intuitive” argument: one part of one of the two circles is situated inside of the other circle, and its other part is situated outside of it. One is therefore tempted to believe that the commentator accepts the principle of continuity in the case of circles, since his argument has the following meaning: if a circle is divisible into two parts (or, again, passes through two points), one of which (or one of the two points) is situated inside the other circle, and the other outside of it, then the two circles cut one another. The author of this article proposes to establish the limits of this belief, on the basis of the following reflections: 1). It will be noted first of all that what could be called the ‘principle of the intersection of circles’ does not constitute ipso facto a principle in the mind of Ibn al-Haytham: no allusion is made to it in the commentary on Proposition I.1, among others. 2) It will be established later on that if one accepts (according to the explanation of Ibn al-Haytham in his Commentary on the premisses) that a line is the result of the movement of a point, the principle of continuity should be considered by him as something which is obvious by itself, without being stated. This conclusion will be based on an analysis of the notion of continuity in its classical meaning, and on Ibn al-Haytham’s commentary on Proposition X.1. 3) On the other hand, we should note the presence of a ‘sketch’ of topological language, which Ibn al-Haytham develops for the notion of a circle (particularly in the Commentary): one could say in this context that his reflection constitutes an important, if not principal, stage in the process which was to lead to the explicit formulation of the principle of continuity. Footnotes1 Je voudrais remercier chaleureusement Monsieur R. Rashed d'avoir bien voulu lire la première version de cet article, m'envoyer certaines de ses publications et me communiquer ses suggestions dont j'ai essayé de tirer le plus grand profit dans la révision que voici. Toutes les insuffisances qui s'y trouvent ne peuvent que m'être imputées.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Gérard Simon (1992). L'optique d'Ibn Al-Haytham Et la Tradition Ptoléméenne. Arabic Sciences and Philosophy 2 (02):203-.
Roshdi Rashed (2007). The Celestial Kinematics of Ibn Al-Haytham. Arabic Sciences and Philosophy 17 (1):7-55.
Nader El-bizri (2007). In Defence of the Sovereignty of Philosophy: Al-Baghdadi's Critique of Ibn Al-Haytham's Geometrisation of Place. Arabic Sciences and Philosophy 17 (1):57-80.
Alain Michel (2003). Géométrie Et Philosophie: De Thabit Ibn Qurra À Ibn Al-Haytham. Arabic Sciences and Philosophy 13 (2):311-315.
Eberhard Knobloch (2002). The Knowledge of Arabic Mathematics by Clavius. Arabic Sciences and Philosophy 12 (2):257-284.
Dominique Raynaud (2009). La perspective aérienne de Léonard de Vinci et ses origines dans l'optique d'ibn al-haytham ( de aspectibus , III, 7). Arabic Sciences and Philosophy 19 (2):225-246.
A. I. Sabra (1966). Ibn Al-Haytham's Criticisms of Ptolemy's. Journal of the History of Philosophy 4 (2).
Christian Houzel (2009). The New Astronomy of Ibn Al-Haytham. Arabic Sciences and Philosophy 19 (1):1-41.
Muhammad Saud (1990). The Scientific Method of Ibn Al-Haytham. Islamic Research Institute, International Islamic University.
Dominique Raynaud (2003). Ibn Al-Haytham on Binocular Vision: A Precursor of Physiological Optics. Arabic Sciences and Philosophy 13 (1):79-99.
Added to index2009-01-28
Total downloads18 ( #107,040 of 1,679,435 )
Recent downloads (6 months)2 ( #111,626 of 1,679,435 )
How can I increase my downloads?