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Acts of Geometrical Construction in the Spherics of Theodosios

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From Alexandria, Through Baghdad

Abstract

Two ways of talking about mathematics, the ideal agents of Philip Kitcher and Brian Rotman, and David Wells' s analogy to abstract games like chess and go, are brought together and put to the test on the Hellenistic mathematical text Spherics by Theodosios. The subject of agents or players, as in a game or play, is discussed.

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References

  • Berggren, J.L., 1991. The relation of Greek spherics to early Greek astronomy. In: Bowen, A. (ed.), Science and Philosophy in Classical Greece. Garland, New York, pp. 227–248.

    Google Scholar 

  • Berggren, J.L., Thomas R.S.D., 2006. Euclid’s Phasnomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy. Garland, New York. Reprinted: American Mathematical Society and London Mathematical Society, Providence, 2006.

    Google Scholar 

  • Chase, W.G., Simon, H.A., 1973. Perception in chess. Cognitive Psychology 4, 55–81.

    Article  Google Scholar 

  • Czinczenheim, C, 2000. Édition, traduction et commentaire des Sphériques de Théodose. Lille. (Thèse de docteur de l’Université Paris IV.)

    Google Scholar 

  • Engeler, ?., 1967. Algorithmic properties of structures. Mathematical Systems Theory 1, 183–195.

    Article  MathSciNet  MATH  Google Scholar 

  • Friederich, S., 2011. Motivating Wittgenstein’s perspective on mathematical sentences as norms. Philosophia Mathematica 19, 1–19.

    Article  MathSciNet  MATH  Google Scholar 

  • Harari, O., 2003. The concept of existence and the role of constructions in Euclid’s Elements. Archive for History of Exact Sciences 57, 1–23.

    Article  MathSciNet  MATH  Google Scholar 

  • Hellman, G., 1989. Mathematics Without Numbers: Towards a Modal-Structural Interpretation. Oxford University Press, Oxford.

    MATH  Google Scholar 

  • Heath, T.L., 1921. A History of Greek Mathematics, 2 vols. Clarendon Press, Oxford. Reprinted: Dover, New York, 1951.

    Google Scholar 

  • ——— 1926. The Thirteen Books of Euclid’s Elements, 3 vols., 2nd edition. Cambridge University

    MATH  Google Scholar 

  • Press, Cambridge. Reprinted: Dover, New York, 1956.

    Google Scholar 

  • Heiberg, J.L., 1927. Theodosius Tripolites [word deleted in corrigenda] Sphaerica. Abhandlungen der Gesellschaft der Wissenschaften zu Göttingen, Philologisch-historische Klasse (N.S.) 19, no. 3, i-xvi, 1–199.

    Google Scholar 

  • Kitcher, P, 1984. The Nature of Mathematical Knowledge. Oxford University Press, Oxford.

    Google Scholar 

  • Morrow, G.R., 1970. Proclus, A Commentary on the First Book of Euclid’s Elements. Princeton University Press, Princeton.

    Google Scholar 

  • Mueller, I., 1981. Philosophy of Mathematics and Deductive Structure in Euclid’s Elements. MIT Press, Cambridge, MA.

    Google Scholar 

  • Netz, R., 2009. Ludic Proof: Greek Mathematics and the Alexandrian Aesthetic. Cambridge University Press, Cambridge.

    Book  MATH  Google Scholar 

  • Pambuccian, V., 2008. Axiomatizing geometric constructions. Journal of Applied Logic 6, 24–46.

    Article  MathSciNet  MATH  Google Scholar 

  • Pollard, S., 2010. "As if" reasoning in Vaihinger and Pasch. Erkenntnis 73, 83–95.

    Article  MathSciNet  MATH  Google Scholar 

  • Robson, E., 2008. Mathematics in Ancient Iraq: A Social History. Oxford University Press, Oxford.

    MATH  Google Scholar 

  • Rotman, B., 1993. Ad Infinitum: The Ghost in Turing’s Machine. Stanford University Press, Palo Alto.

    MATH  Google Scholar 

  • Sidoli, N., Kusuba, T., 2008. Naṣīr al-Dīn al-ṬTūsī’s revision of Theodosius’s Spherics. Suhayl 8, 9—46.

    MathSciNet  MATH  Google Scholar 

  • Sidoli, N., Saito, K., 2009. The role of geometrical construction in Theodosius’s Spherics. Archive for History of Exact Sciences 63, 581–609.

    Article  MathSciNet  MATH  Google Scholar 

  • Sweller, J., Clark, R., Kirschner, P., 2010. Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics. Notices of the American Mathematical Society 57, 1303–1304.

    Google Scholar 

  • Tharp, L., 1989. Myth and mathematics: A conceptualistic philosophy of mathematics I. Synthese 81, 167–201.

    Article  MathSciNet  Google Scholar 

  • Thomas, R., 2009. Mathematics is not a game but... The Mathematical Intelligencer 31, no. 1, 4–8.

    Article  MathSciNet  MATH  Google Scholar 

  • al-Ṭūsī, Naṣīr al-Dīn, 1940. Kitāb al-Ukar li-Thā’ūdhūsiyus, Osmania Oriental Publications Bureau, Hyderabad. Reprinted: Sezgin, F. (ed.), 1998. A Collection of Mathematical and Astronomical Treatises as Revised by Naṣīraddīn aṭ-Ṭīsī, 2 vols. Institute for the History of Arabic-Islamic Science at the Johann Wolfgang Goethe University, Frankfurt am Main.

    Google Scholar 

  • Wells, D.G.., 2010. Philosophy and Abstract Games. Rain Press, London.

    Google Scholar 

  • Zeuthen, H.G., 1896. Die geometrischen Construction als "Existenzbeweis" in der antiken Geometric Mathematische Annalen 47, 222–228.

    MathSciNet  MATH  Google Scholar 

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Thomas, R. (2014). Acts of Geometrical Construction in the Spherics of Theodosios. In: Sidoli, N., Van Brummelen, G. (eds) From Alexandria, Through Baghdad. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36736-6_11

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