Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry

In: Phronesis

Abstract

There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous.

  • AcerbiF. (2008). In what Proof would the Geometer use the Ποδιαία? The Classical Quarterly 58 pp. 120-126.

  • AcerbiF. (2013). Aristotle and Euclid’s Postulates. The Classical Quarterly 63 pp. 680-685.

  • AnnasJ. tr. (1976). Aristotle’s Metaphysics Books M and N. Oxford.

  • ApostleH. G. tr. (1966). Aristotle’s Metaphysics. Bloomington.

  • ArtmannB. (1994). A Proof for Theodorus’ Theorem by Drawing Diagrams. Journal of Geometry 49 pp. 3-35.

  • BäckA. (2014). Aristotle’s Theory of Abstraction. Heidelberg.

  • BarnesJ. (1976). Aristotle, Menaechmus and Circular Proof. The Classical Quarterly 26 pp. 278-292.

  • BarnesJ. ed. (1984). The Complete Works of Aristotle. Princeton.

  • BarnesJ. (1985). Aristotelian Arithmetic. Revue de Philosophie Ancienne 3 pp. 97-133.

  • BermanB. (2017). Why Can’t Geometers Cut Themselves on the Acutely Angled Objects of Their Proofs? Aristotle on Shape as an Impure Power. Méthexis 29 pp. 89-106.

    • Search Google Scholar
    • Export Citation
  • BurnyeatM. F. ed. (1979). Notes on Book Zeta of Aristotle’s ‘Metaphysics’. Study Aids (University of Oxford:. Sub-Faculty of Philosophy) 1. Oxford.

    • Search Google Scholar
    • Export Citation
  • BurnyeatM. F. (2005). Archytas and Optics. Science in Context 18 pp. 35-53.

  • CharltonW. tr. (1991). Philoponus: On Aristotle on the Intellect (De Anima 3.4-8). London.

  • ClearyJ. (1985). On the Terminology of ‘Abstraction’ in Aristotle. Phronesis 30 pp. 13-45.

  • Cleary J. (1989). Commentary on Halper’s ‘Some Problems in Aristotle’s Mathematical Ontology’. Proceedings of the Boston Area Colloquium in Ancient Philosophy 5 pp. 277-90.

  • ClearyJ. (1995). Aristotle and Mathematics: Aporetic Method in Cosmology and Metaphysics. Leiden.

  • CorkumP. (2012). Aristotle on Mathematical Truth. British Journal for the History of Philosophy 20 pp. 1057-1076.

  • Crubellier M. tr. (1994). Les livres Mu et Nu de la Métaphysique d’Aristotle. Diss. Université Charles De Gaulle Lille-III.

  • DistelzweigP. M. (2013). The Intersection of the Mathematical and Natural Sciences: The Subordinate Sciences in Aristotle. Apeiron 46 pp. 85-105.

    • Search Google Scholar
    • Export Citation
  • DolanW. W. (1972). Early Sundials and the Discovery of the Conic Sections. Mathematics Magazine 45 pp. 8-12.

  • FowlerD. H. (1987). The Mathematics of Plato’s Academy: A New Reconstruction. Oxford.

  • FranklinJ. (2014). An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure. London.

  • GaukrogerS. (1980). Aristotle on Intelligible Matter. Phronesis 25 pp. 187-197.

  • Halper E. (1989). Some Problems in Aristotle’s Mathematical Ontology. Proceedings of the Boston Area Colloquium in Ancient Philosophy 5 pp. 247-76.

  • HarteV. (1996). Aristotle Metaphysics H6: A Dialectic with Platonism. Phronesis 41 pp. 276-304.

  • HasperP. S. (2006). Sources of Delusion in Analytica Posteriora 1.5. Phronesis 51 pp. 252-284.

  • HeathT. (1921). A History of Greek Mathematics (2 vols). Oxford.

  • HeathT. (1949). Mathematics in Aristotle. New York.

  • HumphreysJ. (2017). Abstraction and Diagrammatic Reasoning in Aristotle’s Philosophy of Geometry. Apeiron 50 pp. 197-224.

  • HusseyE. (1991). Aristotle on Mathematical Objects. Apeiron 24 pp. 105-133.

  • JonesJ. (1983). Intelligible Matter and Geometry in Aristotle. Apeiron 17 pp. 94-102.

  • KnorrW. R. (1978). Archimedes’ Neusis-Construction in Spiral Lines. Centaurus 22 pp. 77-98.

  • KnorrW. R. (1986). The Ancient Tradition of Geometric Problems. Boston.

  • KnorrW. R. (1989). The Practical Element in Ancient Exact Sciences. Synthese 81 pp. 313-328.

  • LearJ. (1982). Aristotle’s Philosophy of Mathematics. The Philosophical Review 91 pp. 161-192.

  • LennoxJ. (1986). Aristotle, Galileo and the Mixed Sciences. In: W. A. Wallace (ed.) Reinterpreting Galileo (Washington, DC) pp. 29-51.

    • Search Google Scholar
    • Export Citation
  • MadiganA. tr. (1999). Aristotle: Metaphysics Book B and Book K 1-2. Oxford.

  • MakinS. tr. (2006). Aristotle: Metaphysics Theta. Oxford.

  • MansionS. (1978). Soul and Life in De anima. In: G. E. R. Lloyd and G. E. L. Owen (eds.) Aristotle on Mind and the Senses (Cambridge) pp. 1-20.

    • Search Google Scholar
    • Export Citation
  • MendellH. (2017). Aristotle and Mathematics. The Stanford Encyclopedia of Philosophy (Spring 2017 Edition) Edward N. Zalta (ed.) URL = https://plato.stanford.edu/archives/spr2017/entries/aristotle-mathematics.

    • Search Google Scholar
    • Export Citation
  • MignucciM. (1987). Aristotle’s Arithmetic. In: A. Graeser (ed.) Mathematics and Metaphysics in Aristotle (Bern) pp. 213-240.

  • ModrakD. K. W. (2001). Aristotle’s Theory of Language and Meaning. Cambridge.

  • MuellerI. (1970). Aristotle on Geometrical Objects. Archiv für Geschichte der Philosophie 52 pp. 156-171.

  • MuellerI. (1990). Aristotle’s Doctrine of Abstraction in the Commentators. In: R. Sorabji ed. Aristotle Transformed: The Ancient Commentators and Their Influence (London) pp. 463-480.

    • Search Google Scholar
    • Export Citation
  • NetzR. (1999). The Shaping of Deduction in Greek Mathematics: A Study of Cognitive History. Cambridge.

  • Neugebauer O. (1948). The Astronomical Origin of the theory of Conic Sections. Proceedings of the American Philosophical Society 92 pp. 136-8.

  • PettigrewR. (2009). Aristotle on the Subject Matter of Geometry. Phronesis 54 pp. 239-260.

  • PhilippeM.-D. (1948). Ἀφαίρεσις, πρόσθεσις, χωρίζειν dans la philosophie d’Aristote. Revue Thomiste 48 pp. 461-479.

    • Search Google Scholar
    • Export Citation
  • PolanskyR. (2007). Aristotle’s De Anima. Cambridge.

  • RossW. D. ed. (1953). Aristotle’s Metaphysics (2 vols.). Oxford.

  • RossW. D. ed. (1961). Aristotle’s De Anima. Oxford.

  • SidoliN. (2004). On the Use of the Term Diastēma in Ancient Greek Constructions. Historia Mathematica 31 pp. 2-10.

  • SidoliN. and SaitoK. (2009). The Role of Geometrical Construction in Theodosius’s Spherics. Archive for History of Exact Sciences 63 pp. 581-609.

    • Search Google Scholar
    • Export Citation
  • SorabjiR. (1972). Aristotle, Mathematics, and Colour. The Classical Quarterly 22 pp. 293-308.

  • Ver EeckeP. tr. (1933). Pappus d’Alexandrie: La Collection Mathématique. Paris.

  • WhiteM. J. (1993). The Metaphysical Location of Aristotle’s Μαθηματικά. Phronesis 38 pp. 166-182.

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