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Avicenna on the Nature of Mathematical Objects

Published online by Cambridge University Press:  13 September 2016

MOHAMMAD SALEH ZAREPOUR
MOHAMMAD SALEH ZAREPOUR*
Affiliation:
University of Cambridge
*
*<[email protected]>
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Abstract

Some authors have proposed that Avicenna considers mathematical objects, i.e., geometric shapes and numbers, to be mental existents completely separated from matter. In this paper, I will show that this description, though not completely wrong, is misleading. Avicenna endorses, I will argue, some sort of literalism, potentialism, and finitism.

Certains auteurs ont proposé qu’Avicenne considérait les objets mathématiques, à savoir les formes géométriques et les nombres, comme étant mentaux et complètement séparés de la matière. Dans cet article, je vais montrer que cette description, qui n’est pas complètement fausse, est cependant trompeuse. Avicenne approuve, je soutiendrai, une sorte de littéralisme, de potentialisme et de finitisme.

Keywords

Avicennamathematical objectsestimationimmaterialityseparabilitydependency on materiality
Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 55 , Issue 3 , September 2016 , pp. 511 - 536
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Copyright © Canadian Philosophical Association 2016 

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References

Al-Daffa, Ali A., and Stroyls, John J. 1984 “Ibn Sīnā as a Mathematician,” in their Studies in the Exact Sciences in Medieval Islam. New York: John Wiley and Sons, 60–118.Google Scholar
Apostle, Hippocrates G. 1952 Aristotle’s Philosophy of Mathematics. Chicago: University of Chicago Press.Google Scholar
Ardeshir, Mohammad 2008 “Ibn Sīnā’s Philosophy of Mathematics,” in Rahman, S., Street, T., and Tahiri, H. (Eds.) The Unity of Science in the Arabic Tradition. New York: Springer, 43–61.Google Scholar
Avicenna 1952 The Healing [al-Shifā], Logic [al-mantiq], Isagoge [al-madkhal]. Edited by al-Ahwānī, A.F., Anawati, G.C., and al-Khuḍayri, M.M.. Cairo: Al-Maṭba’a al-Amīrīyyah.Google Scholar
Avicenna 1956 The Healing [al-Shifā], Logic [al-mantiq], Demonstration [al-burhān]. Edited by Afifi, A.E., revised by I.B. Madkour. Cairo: Government Press.Google Scholar
Avicenna 1957 Pointers and Reminders [al-ishārāt wa al-tanbihāt], Physics [al-Ṭabī’īīāt]. With Tūsī’s commentary at the bottom of page, edited by Dunyā, S.. Cairo: Dar al-Marif.Google Scholar
Avicenna 2004 The Metaphysics of ‘Alā’ī Encyclopedia [Ilāhīyyāt, Dānishnāmah ‘Alā’ī]. Edited, introduced, and annotated by Mo’īn, M.. Hamadan: Bū-Ali Sina University Press.Google Scholar
Avicenna 2005 The Metaphysics of The Healing [al-Shifā, al-Ilāhīyyāt]. Translated, introduced, and annotated by Marmura, M.E.. Provo: Brigham Young University Press.Google Scholar
Avicenna 2009a The Physics of The Healing [al-Shifā, al-Samā’ al-Ṭabī’ī]. Books I and II. Translated, introduced, and annotated by McGinnis, J.. Provo: Brigham Young University Press.Google Scholar
Avicenna 2009b The Physics of The Healing [al-Shifā, al-Samā’ al-Ṭabī’ī]. Books III and IV. Translated, introduced, and annotated by McGinnis, J., Provo: Brigham Young University Press.Google Scholar
Banchetti-Robino, Marina P. 2004 “Ibn Sīnā and Husserl on Intention and Intentionality,” Philosophy East and West 54 (1), 71–82.Google Scholar
Bäck, Allan 2013 “Avicenna’s Theory of Supposition,” Vivarium 51 (1–4), 81–115.CrossRefGoogle Scholar
Bäck, Allan 2014 Aristotles’s Theory of Abstraction. New York: Springer.CrossRefGoogle Scholar
Bertolacci, Amos 2012 “The Distinction of Essence and Existence in Avicenna’s Metaphysics: The Text and Its Context,” in Opwis, F. and Reisman, D. (Eds.) Islamic Philosophy, Science, Culture, and Religion: Studies in Honor of Dimitri Gutas. Leiden: Brill, 257–288.Google Scholar
Black, Deborah L. 1993 “Estimation (Wahm) in Avicenna: The Logical and Psychological Dimensions,” Dialogue 32 (2), 219–258.CrossRefGoogle Scholar
Black, Deborah L. 1999 “Mental Existence in Thomas Aquinas and Avicenna,” Mediaeval Studies 61, 45–79.CrossRefGoogle Scholar
Black, Deborah L. 2000 “Imagination and Estimation: Arabic Paradigms and Western Transformations,” Topoi 19 (1), 59–75.CrossRefGoogle Scholar
Black, Deborah L. 2010 “Intentionality in Medieval Arabic Philosophy,” Quaestio 10, 65–81.CrossRefGoogle Scholar
Bostock, David 2012 “Aristotle’s Philosophy of Mathematics,” in Shields, C. (Ed.) The Oxford Handbook of Aristotle. Oxford: Oxford University Press, 465–491.CrossRefGoogle Scholar
Corkum, Phil 2012 “Aristotle on Mathematical Truth,” British Journal for the History of Philosophy 20 (6), 1057–1076.CrossRefGoogle Scholar
Crane, Tim 2001 Elements of Mind. Oxford: Oxford University Press.Google Scholar
Crane, Tim 2013 The Objects of Thought. Oxford: Oxford University Press.Google Scholar
Franklin, James 2014 An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure. New York: Palgrave McMillan.CrossRefGoogle Scholar
Gutas, Dimitri 2003 “Medical Theory and Scientific Method in the Age of Avicenna,” in Reisman, D.C. (Ed.) Before and After Avicenna: Proceedings of the First Conference of the Avicenna Study Group. Boston: Brill, 145–162.CrossRefGoogle Scholar
Hasse, Dag N. 2001 “Avicenna on Abstraction,” in Wisnovsky, R. (Ed.) Aspects of Avicenna. Princeton: Markus Wiener Publishers, 39–72.Google Scholar
Hasse, Dag N. 2013 “Avicenna’s Epistemological Optimism,” in Adamson, P. (Ed.) Interpreting Avicenna. Cambridge: Cambridge University Press, 109–119.CrossRefGoogle Scholar
Hussey, Edward 1991 “Aristotle on mathematical objects,” Apeiron 24 (4), 105–134.Google Scholar
Lear, Jonathan 1982 “Aristotle’s Philosophy of Mathematics,” The Philosophical Review 91 (2), 161–192.Google Scholar
Marmura, Michael 1979 “Avicenna’s Chapter on Universals in the Isagoge of His Shifā,” in Welch, A.T. and Cacia, P. (Eds.) Islam: Past Influence and Present Challenge. Edinburgh: Edinburgh University Press, 34–56.Google Scholar
Marmura, Michael 1980 “Avicenna on the Division of Sciences in the Isagoge of His Shifā,” Journal for the History of Arabic Science 4 (2), 239–251.Google Scholar
Marmura, Michael 1992 “Quiddity and Universality in Avicenna,” in Morewedge, P. (Ed.) Neoplatonism and Islamic Thought. New York: State University of New York Press, 77–87.Google Scholar
Marmura, Michael 2005 “Translator’s Introduction,” in his translation of The Metaphysics of The Healing. Provo: Brigham Young University Press, xix-xxv.Google Scholar
Marmura, Michael 2006 “Avicenna’s Critique of Platonists in Book VII, Chapter 2 of the Metaphysics of his Healing,” in Montgomery, (Ed.), Arabic Theology, Arabic Philosophy: From the Many to the One: Essays in Celebration of Richard M. Frank. Louvain: Peeters Oublishers, 355–369.Google Scholar
McGinnis, John 2006a “A Penetrating Question in the History of Ideas: Space, Dimensionality and Interpenetration in the Thought of Avicenna,” Arabic Sciences and Philosophy 16 (1), 47–69.CrossRefGoogle Scholar
McGinnis, John 2006b “Making Abstraction Less Abstract,” Proceedings of the American Catholic Philosophical Association 80, 169–183.CrossRefGoogle Scholar
McGinnis, John 2007 “Logic and Science: The role of Genus and Difference in Avicenna’s Logic, Science and Natural Philosophy,” Documenti e Studi sulla Filosofia Medievale 18, 165–186.Google Scholar
McGinnis, John 2010 Avicenna. Oxford: Oxford University Press.Google Scholar
Mueller, Ian 1970 “Aristotle on Geometrical Objects,” Archiv für Geschichte der Philosophie 52 (2), 156–171.CrossRefGoogle Scholar
Mueller, Ian 1990 “Aristotle’s Doctrine of Abstraction in the Commentators,” in Sorabji, R. (Ed.) Aristotle Transformed: The Ancient Commentators and Their Influence. Cornell University Press, 463–480.Google Scholar
Porro, Pasquale 2011 “Immateriality and Separation in Avicenna and Thomas Aquinas,” in Hasse, D.N. and Bertolacci, A. (Eds.) The Arabic, Hebrew and Latin reception of Avicenna’s Metaphysics. Berlin: De Gruyter, 275–307.CrossRefGoogle Scholar
Rashed, Roshdi 1984 “Mathématiques et philosophie chez Avicenne,” dans Jolivet, J. et Rashed, R. (dir) Etudes sur Avicenne. Collection sciences et philosophie arabes. Paris: Les Belles Lettres, 29–39.Google Scholar
Rashed, Roshdi 2008 “The Philosophy of Mathematics,” in Rahman, S., Street, T., and Tahiri, H. (Eds.) The Unity of Science in the Arabic Tradition. New York: Springer, 153–182.Google Scholar
Tahiri, Hassan 2016 Mathematics and the Mind: An Introduction into Ibn Sīnā’s Theory of Knowledge. New York: Springer.CrossRefGoogle Scholar
White, Michael J. 1993 “The Metaphysical Location of Aristotle’s Μαθηματιϰά,” Phronesis 38 (2), 166–182.CrossRefGoogle Scholar
Wisnovsky, Robert 2000 “Notes on Avicenna’s Concept of Thingness (šay’iyya),” Arabic Sciences and Philosophy 10 (2), 181–221.CrossRefGoogle Scholar