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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.
Readings by Session
Course readings.
| 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 |
|