Ancient Greek Philosophy and Mathematics

Readings

Study Guide

Study Guide (PDF): Questions to think about while you read.

WEEK #	TOPICS	READINGS
1	Introduction	No readings for this session.
I. Knowing
2	A. Logos as Definition: What is “What is?” B. Knowledge as Power / Knowledge as Virtue	Plato. The Meno by Plato (PDF). CreateSpace Independent Publishing Platform, 2012. ISBN: 9781470143671. Witt, April. “No Joke.” The Washington Post, October 24, 2004.
3	C. Definition and the Essence of Things D. The Idea of a Proof	Euclid. Euclid’s Elements. Green Lion Press, 2002. ISBN: 9781888009194. Book I (Definitions) Book II (propositions 1 and 4) Instructor’s guide to Elements (PDF). Aristotle. Book IV in Topics. NuVision Publications, 2005. ISBN: 9781595479723. Pappus. Commenary on Euclid (PDF), Book I. Descartes, Rene. The Geometry of René Descartes: With a Facsimile of the First Edition. Dover Publications, Incorporation, 1954. ISBN: 9780486600680. Analysis and Synthesis (PDF)
II. Logos and Arithmos
4	Quality, Quantity, Relation, Multitude, Magnitude, Logos as Ratio The Greek Conception of Number (What’s Not a Number?)	Euclid. Euclid’s Elements. Green Lion Press, 2002. ISBN: 9781888009194. Book V and VII. (study definitions and browse proofs) Aristotle. Chapters 6–8 in Categories. CreateSpace Independent Publishing Platform, 2013. ISBN: 9781494853068. Summary of Categories (PDF) Definitions of Arithmos and Unit (PDF) Nichomachus of Gerasa. Introduction to Arithmetic (PDF - 11.8MB).
III. Measuring the Unmeasurable
5	A. Putting the Irrational in Ratio	Aristotle. Prior Analytics. CreateSpace Independent Publishing Platform, 2016. ISBN: 9781530979042. (41a, 50a. Topics 158b: “Those magnitudes are in the same ratio whose anthuphairesis is the same.”) Euclid. Euclid’s Elements. Green Lion Press, 2002. ISBN: 9781888009194. Book V [Definitions 5] Book VII [Propsitions 1, 2] Book X [All definitions, Propsitions 1–3, 5, 6]
6	B. Fitting Ideas to the World	Plato. Laches. CreateSpace Independent Publishing Platform, 2016. ISBN: 9781536847628.
7	C. The Pursuit of Truth and the Idea of an Idea	Plato. The Republic. CreateSpace Independent Publishing Platform, 2014. ISBN: 9781503379985. Books VI–VII, 504d–535a.
8 & 9	D. The Truth as a Surd	Plato. Theaetetus. CreateSpace Independent Publishing Platform, 2014. ISBN: 9781505227550.
10	E. Potentiality as a Way of Being	Aristotle. Physics. Oxford University Press, 2008. ISBN: 9780199540280. (Selections)
IV. The Limits of Mathematics?
11	Aristotle’s Nicomachean Ethics	Aristotle. The Nichomachean Ethics. Penguin Classics, 2004. ISBN: 9780140449495. Book I-All chapters except 6, 9, and 10. (Anyone caught reading 6, 9, or 10 will be banished. Pay special attention to chapter 3.) Book II-Entire Book III-Read only chapters 6, 7, and 11 (if you’re inspired to read more, that would be both and dandy.)
12	Aristotle’s Nicomachean Ethics (cont.)	Aristotle. The Nichomachean Ethics. Penguin Classics, 2004. ISBN: 9780140449495. Book IV-Chapters 6 and 7. (If you want to see how the idea of virtue as a mean works in other virtues, then read more chapters. I recommend the Constitution Society website. Or MIT’s website. You can find the same translation in only downloadable form. (The nice thing about this site is that if you click on the table of contents, you find the translator’s chapter by chapter one-page summaries, which are accurate and I think helpful.
V. The Modern Conception of Number and the Detachment from Reality
13	Isaac Newton’s Arithmetica Universalis Richard Dedekind “Descartes, Algebra, and Alienation.”	Newton, Isaac. Arithmetica Universalis: Sive de Compositione Et Resolutione Arithmetica. Vol. 1. Andesite Press, 2015. ISBN: 9781298734976. Dedekind, Richard. Essays on the Theory of Numbers: I. Continuity and Irrational Numbers. II. The Nature and Meaning of Numbers (PDF). CreateSpace Independent Publishing Platform, 2016. ISBN: 9781534900974. Shiffman, Mark. “Descartes, Algebra, and Alienation.” Front Porch Republic, June 19, 2009.
14	“The World of Physics and the ‘Natural World” “The Sources of Modern Symbolic Mathematics”	Klein, Jacob. “The World of Physics and the ‘Natural’ World.” The St. John’s Review 33, no. 1 (1981): 22–34. Hopkins, Burt C. “The Basic Problem and Method of Klein’s Mathematical Investigations.” In The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein. Indiana University Press, 2011. ISBN: 9780253356710. [Preview with Google Books]