| SES # | TOPICS | READINGS |
|---|---|---|
| 1 | Introduction | |
| Ancient and Modern Knowing | ||
| 2 | Knowledge as Power/Knowledge as Virtue | Bacon, Francis. Novum Organon. (excerpts) Descartes, Rene. Rules for Direction of the Mind. (excerpts) Plato. Meno. |
| 3 | The Idea of a Proof | Descartes, Rene. Geometry. (excerpts) Euclid. Elements. Book I and II. (selected proofs) Pappus. Commentary on Euclid. Book I. (excerpt) |
| Logos and Arithmos | ||
| 4 | Logos as Definition- What is "What is?" | Euclid. Elements. Book V. (selected definitions and proofs) |
| 5 | Logos as Ratio, Magnitude and Multitude, Quality and Quantity | Euclid. Elements. Book VII. (selected definitions and proofs) Aristotle. Categories. Chapters 6-8. |
| 6 | The Greek Conception of Number | Nicomachus of Gerasa. Introduction to Arithmetic. |
| 7 | The Idea of Number: Ancient vs. Modern | Newton, Isaac. Arithmetica Universalis. (excerpt) Dedekind, Richard. The Nature and Meaning of Numbers. |
| Measuring the Unmeasurable | ||
| 8 | Putting the Irrational in Ratio | Aristotle. Prior Analytics. 41a, 50a. Euclid. Elements. Books V, VII, and X. Def. 5. (selected proofs) |
| 9 | Fitting Ideas to the World | Plato. The Republic. |
| 10 | Fitting Ideas to the World (cont.) | Plato. The Republic. |
| 11 | The Truth as a Surd | Euclid. Elements. Book XII. (selected proofs) Theon of Smyrna. Mathematics Useful for Understanding. |
| 12 | The Truth as a Surd (cont.) | Euclid. Elements. Book XII. (selected proofs) Theon of Smyrna. Mathematics Useful for Understanding. |
| The Limits of Mathematics | ||
| 13 | A. Plato, Protagoras | Plato. Protagoras. |
| 14 | B. Aristotle, Nicomachean Ethics | Aristotle. Nicomachean Ethics. |
| 15 | Review | |
Table of Contents
Study Materials
Readings
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Readings are also listed by session.
Textbooks
Bacon, Francis. Novum Organon. Indianapolis, IN: Bobbs-Merrill, 1960. ISBN: 9780672602894.
Descartes, Rene. Rules for Direction of the Mind. Translated by Laurence J. Lafleur. Indianapolis, IN: Bobbs-Merrill, 1964.
———. Geometry. Translated by Paul J. Olscamp. Indianapolis, IN: Hackett Pub., 2001. ISBN: 9780872205673.
Newton, Isaac. Arithmetica Universalis.
Dedekind, Richard. Essays on the Theory of Numbers. Vol 2, The Nature and Meaning of Numbers. New York, NY: Dover Publications, 1963.
Theon of Smyrna. Mathematics Useful for Understanding Plato. Translated by R. D. Lawlor. Mecosta, MI: Wizard's Bookshelf, 1978. ISBN: 9780913510247.
Plato. Meno. 2nd ed. Indianapolis, IN: Hackett Pub. Co., 1976. ISBN: 9780915144242.
———. Protagoras. Translated by Stanley Lombardo and Karen Bell. Indianapolis, IN: Hackett Pub. Co., 1992. ISBN: 9780872200944.
———. Theatetus. Translated by Robin H. Waterfield. New York, NY: Penguin Classics, 1987. ISBN: 9780140444506.
———. Republic. Translated by R. E. Allen. New Haven, CT: Yale University Press, 2006. ISBN: 9780300114515.
Aristotle. Nicomachean Ethics. Translated by Christopher Rowe. New York, NY: Oxford University Press, 2002. ISBN: 9780198752714.
Euclid. Elements. Translated by Thomas L. Heath. Santa Fe, NM: Green Lion Press, 2002. ISBN: 9781888009194.
Nicomachus. Introduction to Arithmetic. Translated by Martin Luther D'Ooge. New York, NY: The Macmillan Co., 1926.