in Bayreuth (2011)
On Greek Mathematics and Philosophy of Mathematics
of Ancient Mathematics
Euclid in Nürnberg
||College of Arts & letters
Office: E&T 422
Phone: (323) 343-4178
<>FAX: (323) 343-4193
Email: email@example.com (please note that this address has changed as of April 2006)
I have taught mostly ancient philosophy, especially scientific issues in 5th and 4th cent. BCE philosophy. However, I used to teach annually
a course in the history of the philosophy of science, which focused on astronomy
and mathematics. This course used lots of graphics to illustrate Greek
mathematics and astronomy, much on my website, and spread sheets to illustrate Babylonian astronomy. I loved teaching introductory logic. However, ...
I am now EMERITUS!!!!
My principal areas of interest at present include ancient Greek philosophy
(especially Aristotle and Plato), ancient Greek mathematics, ancient astronomy
(especially Eudoxus). These focus on the relation between philosophical
issues in ancient treatments of scientific problems and how ancient philosophers
responded to those issues. Current projects involve Aristotle's Physics, Aristotelian
logic, decision theorems in Aristotle, conceptions of number in the 4th and 3rd century B.C.E, treatments of quantitative relations in Greek mathematics, infinitary
arguments in Greek mathematics, the relation between first principles
in Aristotle and in Greek mathematics, sources for Eudoxus, 4th cent.
B.C.E. conceptions of astronomy, and Plato's analogy of the Divided Line,
and his Phaedo.
I continue to develop interesting ways of presenting ancient mathematics and astronommy, for which visit Vignettes
of Ancient Mathematics.
As an early user of Macs and Word (since 1985), I would like to protest the policies of both corporations. Both Microsoft and Apple inhibit scholars or anyone from having access to a long history of their work. It is two decades since I was last able to read the original files for my doctoral dissertation with the original pagination, etc. Now, I can only with difficulty access the thousands of files composed in Word 4.0 and 5.1, and even then much of what I see is garbled. I dread each upgrading to the next Mac System when these files will become just unreadable. Of course, one can find old computers with conversion programs, but then one loses the creation dates, an important way of keeping track of one's work (as Steve Jobs bragged when the Apple was introduced--or so I recall). I mention this, as I am sure that others have had similar ugly experiences. Do these corporations think that people are only interested last week's work? As a user of Apple and Office for 38 years, I used to admire Apple and cherish Office. Microsoft and Apple have both become either callous and disgusting or just ignorant and arrogant!
Representative Professional Activities
“Betwixt and Between: Plato and the objects of mathematics.” Forthcoming in David Ebrey and Richard Kraut, The Cambridge Companion to Plato (Cambridge: Cambridge University Press, 2022).
“Why did the Greeks Develop Proportion Theory: a conjecture.” In Michalis Sialaros, Revolutions and Continuity in Greek Mathematics (Berlin: De Gruyter, 2018), 189-233.
“What’s Location Got to Do With It? Place, Space and the Infinite in Classical Greek mathematics.” In Vincenzo de Risi (ed.), Mathematizing Space: The Objects of Geometry from Antiquity to the Early Modern Age (Heidelberg: Birkhäuser, 2015), 15-63.
“Plato by the Numbers.” In Logos and Language: Essays in Honour of Julius Moravacsik. Ed. by Dagfinn Føllesdal and John Woods. London: College Publications, 2009, pp. 141-76. Access article
"Two Traces of Two-Step Eudoxan Proportion Theory in Aristotle: A Tale of Definitions in Aristotle, With a Moral," Archive for History of the Exact Sciences, 61 (2007): 3-37.
||"Putting Aristotle's Physics in its place: a discussion
of B. Morison, On Location," Oxford Studies in Ancient
Philosophy, 25 (Summer 2005), 327-66.
||Eloge for Wilbur Knorr. Isis 92 (2001): 339-343.
||with Pat Suppes and Julius Moravcsik (eds.). Ancient and Medieval
Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr
(Stanford: CSLI (distr. University of Chicago Press), 2001.
||"The Trouble with Eudoxus." In previous, 59-138.
||"Making Sense of Aristotelian Demonstration." Oxford Studies
in Ancient Philosophy, 16 (1998), 160-225. Access article
||"Reflections on Eudoxus, Callippus and their Curves: Hippopedes
and Callippopedes". Centauru, vol. 40, nr. 3-4 (1998), 177-275.
Some Recent and Future Talks and Activities
||“Some Unjustified Interpretations of Plato on Principles and Diagrams.” Philosophy and Mathematics—Plato Definition, Power(s), Division. École Normale, Paris|
||Presentation of Aristotle, Metaphysics Μ 6-9. Workshop on MN, Humbodt University, Berlin|
“Generating Sorts of Number in the Parmenides,” 29-30 May. “Plato and cosmology in the Parmenides.” Société d’Etudes Platoniciennes, École Normale, Paris
||“Betwixt and Between: Plato on Mathematics,” 29-30 March. Ta Metaxu—Knowing where to draw the line: Intermediates and Dianoia in Plato, Harriet L. Wilkes Honors College|
||“Number Play in the Mid-Fourth Cent. BCE,” 27 Oct., a workshop in honor of Ken Saito’s retirement, Stanford University|
||co-teacher with Alan Code and Reviel Netz, Seminar: Continuity and Infinity, Spring Term, Stanford University|
||“Pushing and Tugging in the Mechanical Tradition: Aristotle’s Physics VII.” Conference: On Mathemata: Commenting on Ancient Greek and Arabic Mathematical Texts. Humboldt University, Berlin. 17-18 Nov., 2016||2016
||“First Principles within a Science: Aristotle’s Theory and Practice.” 3rd Campinas Conference on Aristotle’s Theory of Demonstration.
||“Reasoning about what to Choose.” Aristotle Workshop, UCLA, 11-12 March; also Workshop Organizer.|
||“Introduction to the End of the Physics.” Opening Lecture. The Central European Reading Group in Ancient Philosophy: Aristotle's Physics VIII.5-10, 7-9 June 2015.|
||“The Only Good Philosopher.” Classics Dept., Tel Aviv University, 20 May 2015|
||“Putting Aristotle's Physics Together: Traces of Early Editorial Practice.” Research Training Group, Philosophy, Science, and the Sciences, Humboldt University. Opening Workshop of the Summer Semester, 16 April 2015|
“On levels of abstraction in science and an assumption of unique existence in Archimedes' Equilibrium of Planes.” Institute Jussieu, Paris, 15 April 2015
||Discussion of Apollonius, Conics II. Workshop: Aspects of Apollonius’ Conic Sections, Topoi Excellence Cluster, Humboldt University, Berlin
Ph.D. Phil. 1986
B.A. Phil. 1974
St. John's College
A.B. Classics & Phil. 1971
SCHEDULE 2022 (Spring): my last class at CSULA
||Day & Time
OFFICE HOURS: Winter 2022: E&T 422 (CSULA)