Aristotle’s Philosophy of Mathematics and Mathematical Abstraction

Yıl 2017, Cilt: 7 Sayı: 2, 33 - 49, 30.12.2017

Murat Kelikli

https://doi.org/10.18491/beytulhikme.375777

Öz

Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this reason, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the concept of abstraction. In our work, I will try to explain the mathematical abstraction that Aristotle has developed to understand mathematical philosophy.

Anahtar Kelimeler

Aristotle, mathematics, philosophy of mathematics, abstraction, mathematical abstraction

Kaynakça

• Annas, J. (2003). Aristotle’s Metaphysics Book M and N. Oxford: Clarendon Press.
• Bäck, A. (2014). Aristotle's Theory of Abstraction. Heidelberg: Springer.
• Barnes, J. (2002). Aristoteles: Düşüncenin Ustaları (çev. B. Ö. Düzgören). İstanbul: Altın Kitaplar.
• Becker, O. (1936). Die Lehre vom Geraden und Ungeraden im Neunten Buch der Euklidischen Elemente. (Versuch einer Wiederherstellung in der ursprünglichen Gestalt). Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung B: Studien, 3, 533-553.
• Becker, O. (1959). Die Archai in der Griechischen Mathematik. Archiv für Begriffsgeschichte, 4, 210-226.
• Bonitz, H. (1849). Aristotelis Metaphysica, Pars Posterior. Bonn.
• Cajori, F. (2014). Matematik Tarihi (çev. D. İlalan). Ankara: ODTÜ Yayınları.
• Duralı, Ş. T. (2011). Felsefe - Bilimin Doğuşu: Aristoteles'te Canlılar ve Bilim Sorunu. İstanbul: Dergah Yayınları.
• Einarson, B. (1936). On Certain Mathematical Terms in Aristotle's Logic: Part I . The American Journal of Philology, 57 (2), 33-54.
• Einarson, B. (1936). On Certain Mathematical Terms in Aristotle's Logic: Part II . The American Journal of Philology, 57 (2), 151-172.
• Franklin, J. (2014). An Aristotelian Realist Philosophy of Mathematics. New York: Palgrave Macmillan.
• Hankel, H. (1869). Die Entwickelung der Mathematik in den Letzten Jahrhunderte. Tübingen: Fr. Fues’sche Sortimentsbuchhandlung.
• Hardy, G. H. (1993). Bir Matematikçinin Savunması (çev. N. Arık). Ankara: Tubitak Yayınları.
• Heath, T. (1921). A History of Greek Mathematics, vol. 2. Oxford: Clarendon Press.
• Knorr, R. W. (1938). Construction as Existence Proof in Ancient Geometry. Ancient Philosophy, 3, 125-148.
• Knorr, R. W. (1975). The Evolution of the Euclidean Elements. Dordrecht: D. Reidel Publishing Co.
• Laertios, D. (2003). Ünlü Filozofların Yaşamları ve Öğretileri (çev. C. Şentuna). İstanbul: Yapı Kredi Yayınları.
• Lear, J. (1982). Aristotle's Philosophy of Mathematics. The Philosophical Review, 91 (2), 161-192.
• Lee, H. D. P. (1935). Geometrical Method and Aristotle’s Account of First Principles. Classical Quarterly, 29, 113-124.
• Liddell, H. G. and Scott, R. (1996). A Greek-English Lexicon: With a Revised Supplement. Oxford: Clarendon Press.
• Locke, J. (1690). An Essay Concerning Human Understanding. Vol. II.
• Mueller, I. (1970). Aristotle on Geometrical Objects. Archiv für Geschichte der Philosophie, 52, (2), 156-171.
• Netz, R. (2003). The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Cambridge: Cambridge University Press.
• Ross, W. D. (1949). Aristotle's Prior and Posterior Analytics. Oxford: Clarendon Press.
• Ross, W. D. (2002). Aristoteles (çev. A. Aslan, Z. Kurtoğlu, İ. O. Anar, Ö. Y. Kavasoğlu). İstanbul: Kabalcı Yayınevi.
• Studtmann, P. (2002). The Body Problem in Aristotle. Apeiron, 35 (3), 211-234.
• Szabó, Á. (1969). Anfänge der griechischen Mathematik, München und Wien: R. Oldenbourg.
• Szabó, Á. (1978). The Beginnings of Greek Mathematics. Dordrect: Springer.
• Van der Waerden, B. L. (1978). Die Postulate und Konstruktionen der Frühgriechischen Geometrie. Archive for History of Exact Sciences, 18, 343-357.
• Von Aster, E. (1945). Bilgi Teorisi ve Mantık (çev. M. Gökberk). İstanbul: M. Sadık Kağıtçı Matbaası.
• Von Fritz, K. (1955). Die APXAI in der Griechischen Mathematik. Archiv für Begriffsgeschichte, 1, 13-103.
• Waschkies, H.-J. (2004). Introduction. Classiccs in the History of Greek Mathematics (ed. J. Christianidis). Dordrecht: Kluwer Academic Publishers.
• Yıldırım, C. (2016). Matematiksel Düşünme. İstanbul: Remzi Kitabevi.