Linked bibliography for the SEP article "Aristotle and Mathematics" by Henry Mendell
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Collections of essays and journals referred to below with
abbreviations
Barnes (1975-9): |
Barnes, Jonathan, Schofield, Malcolm, and Sorabji,
Richard, eds., 1975-9, Articles on Aristotle. Vol. 1: Science.
Vol. 2: Ethics and Politics. Vol. 3: Metaphysics. Vol. 4: Psychology
and Aesthetics. London: Duckworth. |
Berti (1981): |
Berti, Enrico, ed.. 1981, Aristotle on Science the
«Posterior Analytics.» Proceedings of the eigth
Symposium Aristotelicum, 1978. Padova: Editrice Antenore. |
Graeser (1987): |
Graeser, A. ed., 1987, Mathematics and Metaphysics in
Aristotle. Akten des X. Symposium Aristotelicum. Bern: Haupt. |
QS: |
Quellen und Studien zur Geschichte der Mathematik Astronomie
und Physik Abt. B: Studien |
Collections of mathematical passages in Aristotle with extensive
discussions
- Blancanus, Josephus (Guiseppi Biancani). 1615. Aristotelis loca
mathematica ex universis ipsius operibus collecta et explicata.
Bologna: Sumptibus Hieronymi Tamburini. (Scholar)
- Heath, Thomas L. 1949. Mathematics in Aristotle. Oxford: Oxford University Press, (reprint. New York: Garland Press, 1980). (Scholar)
- Heiberg, I.L. 1904. "Mathematisches zu Aristoteles," in
Abhandlungen zur Geschichte der Mathematischen Wissenschaften.
Vol. 18: 1-49. Leipzig: Teubner. (Scholar)
Works on philosophical issues in Aristotle on mathematics or use of
mathematics in discussing philosophical discussions
- Annas, Julia, 1976, Aristotle's Metaphysics Books M and N (English translation and commentary). Oxford Clarendon Aristotle, ed. J.L. Ackrill. Oxford: Oxford University Press. 2nd ed., 1988. (Scholar)
- Annas, Julia, 1975, "Aristotle, Number and Time." Philosophical Quarterly 25: 97-113. (Scholar)
- Annas, Julia, 1987, "Die Gegenstände der Mathematik bei
Aristotles." In Graeser (1987), pp. 131-47. (Scholar)
- Apostle, Hippocrates George, 1952, Aristotle's Philosophy of Mathematics. Chicago: Chicago University Press. (Scholar)
- Barnes, Jonathan, 1975, Aristotle's Posterior Analytics. Oxford: Oxford University Press. 2nd ed., 1993. (Scholar)
- Barnes, Jonathan, 1985, "Aristotle's Arithmetic." Revue de
Philosophie Ancienne 3: 97-133. (Scholar)
- Barnes, Jonathan, 1969, "Aristotle's Theory of Demonstration." Phronesis 14: 123-52. Revised in Articles. Vol. 1, ed. Barnes et al., 65-87. (Scholar)
- Barnes, Jonathan, 1981, "Proof and the Syllogism." In Berti (1981),
17-59. (Scholar)
- Cleary, John, 1985, "On the Terminology of
‘Abstraction’ in Aristotle." Phronesis 300:
13-45. (Scholar)
- Cleary, John, 1989, "Commentary on Halper's ‘Some Problems in Aristotle's Mathematical Ontology.’" Proceedings of the Boston Area Colloquium in Ancient Philosophy 5: 277-290. (Scholar)
- Cleary, John J. 1995, Aristotle & Mathematics: Aporetic Method in Cosmology & Metaphysics. Philosophia Antiqua 67. Leiden: Brill. (Scholar)
- Gaukroger, Stephen, 1980, "Aristotle on Intelligible Matter." Phronesis 25: 187-197. (Scholar)
- Gomez-Lobo, A, 1977, "Aristotle's Hypotheses and Euclid's
Elements." Review of Metaphysics 30: 430-439. (Scholar)
- Görland, Albert, 1899, Aristoteles und die Mathematik. Marburg: N.G. Elwert'sche Verlagsbuchhandlung (reprint: Frankfurt/Main: Minerva, 1985). (Scholar)
- Halper, Edward, 1989, "Some Problems in Aristotle's Mathematical
Ontology." Proceedings of the Boston Area Colloquium in Ancient
Philosophy 5: 247-276. (Scholar)
- Hintikka, Jaakko, 1972, "On the Ingredients of an Aristotelian Science." Nous 6: 55-69 (Scholar)
- Hintikka, Jaakko, 1980, "Aristotelian Induction." Revue Internationale de Philosophie 34: 422-440. (Scholar)
- Hintikka, Jaakko, 1973, Time and Necessity: Studies in Aristotle's Theory of Modality. Oxford: Oxford University Press. (Scholar)
- Hussey, Edward, 1983, Aristotle's Physics III & IV.
Trans. and commentary. Clarendon Aristotle Series. Oxford: Oxford
University Press. (Scholar)
- Hussey, Edward, 1991, "Aristotle on Mathematical Objects," in I. Mueller (ed.), Peri tôn Mathêmatôn. Apeiron 24 nr. 4 (Dec.): 105-134. (Scholar)
- Jones, Joe, 1983, "Intelligible Matter and Geometry in Aristotle." Apeiron 17: 94-102. (Scholar)
- Kouremenos, Theokritos, 1995. Aristotle on Mathematical Infinity. Stuttgart: Franz Steiner. (Scholar)
- Lear, Jonathan, 1982 "Aristotle's Philosophy of Mathematics." Philosophical Review 91: 161-92. (Scholar)
- Lear, Jonathan, 1979, "Aristotelian Infinity." Proceedings of
the Aristotelian Society 80: 187-210. (Scholar)
- Lear, Jonathan, 1988, Aristotle: The Desire to Understand, ch. 6 §2. Cambridge: Cambridge University Press. (Scholar)
- Lee, H.D.P., 1935, "Geometrical Method and Aristotle's Account of First Principles." Classical Quarterly 29: 113-123. (Scholar)
- Mendell, Henry, 1998, "Making Sense of Aristotelian Demonstration". Oxford Studies in Ancient Philosophy, 16, 160-225. (Scholar)
- Mendell, Henry, 1987, "Topoi on Topos: the Development of Aristotle's Theory of Place." Phronesis 32: 206-231. (Scholar)
- Milhaud, Gaston, 1903, "Aristote et les mathematiques." Archiv für Geschichte der Philosophie 16: 367-92. (Scholar)
- Modrak, Deborah, 1989, "Aristotle on the Difference between Mathematics and Physics and First Philosophy." Apeiron 22: 121-139. (Scholar)
- Mueller, Ian, 1978, Review of Julia Annas, Aristotle's Metaphysics Books M and N (1st. ed., Oxford: Oxford University Press, 1976). Philosophical Review 87: 479-485 (Scholar)
- Mueller, Ian, 1970, "Aristotle on Geometrical Objects." Archiv für die Gesch. der Philosophie 52: 156-171 (reprint. in Barnes, Articles, vol. 3) (Scholar)
- Mueller, Ian, 1990, "Aristotle's Doctrine of Abstraction in the
commentators." In Richard Sorabji (ed.), Aristotle Transformed: the
Ancient Commentators and their Influennce, Ithaca: Cornell
University Press, 463-479. (Scholar)
- McKirahan, R.D., 1992, Principles and Proofs: Aristotle's Theory of Demonstrative Science. Princeton: Princeton University Press. (Scholar)
- Mignucci, M, 1987, "Aristotle's Arithmetic." In Graeser,
175-211. (Scholar)
- Philippe, M.D., 1948, "Aphairesis, Prosthesis, khôrizein dans la philosophie d'Aristote." Revue Thomiste 48: 461-79. (Scholar)
- Sorabji, Richard, 1973, "Aristotle, Mathematics, and Color." Classical Quarterly 22: 293-308. (Scholar)
- Tiles, J.E., 1983, "Why the Triangle has 2 Right Angles Kath’
Hauto." Phronesis 28: 1-17. (Scholar)
- White, Michael J., 1992. The Continuous and the Discrete. Oxford: Oxford University Press. (Scholar)
Works focussing on mathematical issues either in Aristotle or
importantly related to Aristotle
- Becker, Oskar, 1933, "Eudoxos-Studien I. Eine voreudoxische
Proportionenlehre und ihre Spuren bei Aristoteles und Euklid."
QS 2: 311-333. (Scholar)
- Becker, Oskar, 1933, "Eudoxos-Studien II. Warum haben die Griechen
die Existenz der vierten Proportionale angenommen?" QS 2:
369-387. (Scholar)
- Becker, Oskar, 1936, "Eudoxos-Studien III. Spuren eines
Stetigkeitsaxioms in der Art des Dedekind'schen zur Zeit des Eudoxos."
QS 3: 236-244. (Scholar)
- Becker, Oskar, 1936, "Eudoxos-Studien IV. Das Prinzip des
ausgeschlossenen Dritten in der griechischen Mathematik." QS
3: 370-388. (Scholar)
- Euclid, 1926, The Elements of Euclid. 3 vols. 2nd. ed.
Eng. trans. with comm. T.L. Heath. Cambridge: Cambridge U. P.,
(reprint: New York, Dover, 1956). (Scholar)
- Euclide, 1994, 1998, 1998 Les Éléments. 4
volumes (3 completed) French trans. with commentary by Bernard Vitrac,
Paris: Presses Universitaires de France. (Scholar)
- Einarson, Benedict, 1936, "On Certain Mathematical Terms in
Aristotle's Logic." American Journal of Philology 57: 33-44
(Part I), 151-172 (Part II). (Scholar)
- Fowler, D.H., 1987, The Mathematics of Plato's Academy.
Oxford: Oxford University Press, (2nd ed., 1999). (Scholar)
- Heath, T.L., 1921, A History of Greek Mathematics. Oxford: Oxford University Press, (reprint: New York, Dover, 1981) (Scholar)
- Knorr, Wilbur R., 1978, "Archimedes and the Pre-Euclidean
Proportion Theory." Archives Internationales d'Histoire des
Sciences 28: 183-244. (Scholar)
- Knorr, Wilbur R., 1983, "Construction as Existence Proof in Ancient Geometry", Ancient Philosophy 3, 125-49. (Scholar)
- Knorr, Wilbur R., 1975, The Evolution of the Euclidean Elements. Synthese Historical Library 15. Dordrecht: Reidel. (Scholar)
- Knorr, Wilbur R., 1986, The Ancient Tradition of Geometric
Problems. Boston: Birkhäuser, (reprint, New York:
Dover). (Scholar)
- Mendell, Henry R., 1984, "Two Geometrical Examples from Aristotle's Metaphysics." Classical Quarterly 34: 359-72. (Scholar)
- Mendell, Henry R., 2001, "The Trouble with Eudoxus". In Pat Suppes,
Julius Moravcsik, and Henry Mendell (eds.), Ancient and Medieval
Traditions in the Exact Sciences: Essays in Memory of Wilbur
Knorr, Stanford: CSLI (distr. University of Chicago Press),
59-138. (Scholar)
- Mueller, Ian, 1969, "Euclid's Elements and the Axiomatic Method." British Journal for the Philosophy of Science 20: 289-309. (Scholar)
- Mueller, Ian, 1974, "Greek Mathematics and Greek Logic." In John Corcoran (ed.), Ancient Logic and its Modern Interpretations (Dordrecht, Reidel), 35-70. (Scholar)
- Mueller, Ian, 1981, Philosophy of Mathematics and Deductive Structure in Euclid's Elements. Cambridge: MIT Press. (Scholar)
- Netz, Reviel, 1999, The Shaping of Deduction in Greek Mathematics: a Study in Cognitive History. Cambridge: Cambridge University Press. (Scholar)
- Proclus Diadochus, 1992, A Commentary on the First Book of
Euclid's Elements. Trans. with intro. and notes by Glenn R.
Morrow. Forward by Ian Mueller. Princeton: Princeton University
Press. (Scholar)