Philosophy 515/History 591

 Spring 2004

Galileo and Descartes

Professors Daniel E. Garber and Michael S. Mahoney

Thursdays, 9-12

Marx 201

Themes and Agenda

The course will deal with the thought of Galileo and Descartes about the physical world. The fundamental question is to understand the very different ways these two figures approached the study of nature. Can we know the nature of body and the ultimate causes of things, and do we need to know them in order to have genuine knowledge? What are laws of nature and how can we know them? How is it possible to apply mathematics to the world? Is it possible derive simple mathematical laws that govern the behavior of bodies in motion? What is the role of experience in coming to know about nature? More generally, what strategies did these two thinkers use to derive basic facts about the way the world is? These questions will be pursued both historically and philosophically. Historically, we will focus on understanding some of the main texts of these authors, read in the context of time, place, and circumstance. We will play particular attention to the shifting geography of knowledge, and the evolution of intellectual categories such as (natural) philosophy, (mixed) mathematics, and physico-mathematics. Philosophically, we will attempt to show the importance of approaching through real historical examples central questions in epistemology and the philosophy of science, questions about scientific knowledge, experience, and the mathematicization of nature.

The specific readings and topics covered will be determined by the participants in the seminar as we progress. A tentative sequence of topics is as follows:


Historical background (16thC Italian mechanics, practical and theoretical; Galileo's early projects and his experience as a university professor, etc.)
Motion and its laws: reason and experience
Two New Sciences, days 3 and 4, and related papers
Cosmology, or what does it mean to be at rest anyway?
Two Great World Systems
Letters on Sunspots
Comet Controversy (Assayer): how to win a battle and lose a war, and be wrong to boot.
Copernicanism and Theology
Letter to the Grand Duchess Christina and related papers: what exactly did Galileo do wrong?
Mathematics, mechanics, and matter theory
Two New Sciences, days 1 and 2
Question: What did Galileo mean when he called himself a philosopher?


Some historical background (Descartes' education and military apprenticeship; the introduction to mathematical science)
Descartes in the 1620s: methodological writings and the invention of analytic geometry (Rules for the Direction of the Mind and Geometry)
God and the physical world: space, motion, the laws of motion, and the system of the world (Le Monde and Principles of Philosophy)
Optics, nature and mathematics: the law of refraction and the explanation of color and the rainbow (Dioptrics and Meteors)

Descartes' critique of Galileo: mixed mathematics vs. natural philosophy, or, do you know anything at all if you don�t know everything all at once?
Two conceptions of the scientific enterprise: Descartes and Galileo (and their partisans) battle it out in mid-17thC Paris
Are either Galileo or Descartes mathematical physicists? Shifting boundaries in intellectual geography
How is it possible to establish ground-level facts about the way the world is?

Week 1 (2/5): 
Galileo Galilei, Discourses and Demonstrations Concerning Two New Sciences, Day 1, [49]-[54] and Day 3, [190]-[214] (bracketed page numbers refer to the National Edition and are included both the Crew-DeSalvio [ html] and Drake translations)
Week 2 (2/12): 
We'll continue our reading of Day III of the Discourses.

You can download a pdf copy of the original 1638 text here (high-speed connection only; it's a large file).

Some pertinent secondary sources include:
Maurice Clavelin, The Natural Philosophy of Galileo, Part III (Chapters 6 & 7); short version in his "Conceptual and technical aspects of the Galilean geometrization of the motion of heavy bodies", in Nature Mathematized, ed. William R. Shea, 23-50 [pdf]
P. Damerow et al., Exploring the Limits of Pre-Classical Mechanics, Chap. 3, sects. 3.6 & 3.7 [pdf]
Jerome R. Ravetz, "Galileo and the mathematization of speed", in La mathématisation des doctrines informes (Paris, 1972), 11-32; cf.discussion of paper, ibid. 33-42 [SM Q175.xM3] [pdf]
A.G. Molland, "The atomization of motion: A facet of the Scientific Revolution", Studies in the History and Philosophy of Science 13(1982):31-54 [pdf]

Week 3 (2/19):
Continuing with Day III

Week 4 (2/26):
Continuing with Day III

In the scholium following Prop. II, Galileo refers to "an old treatise on mechanics written at Padua for the use of his pupils." That is Le meccaniche (1600) and is available in Galileo Galilei, On motion and On mechanics, trans.I.E. Drabkin and Stillman Drake (Madison: University of Wisconsin Press, 1960). But for an even earlier treatment of forces and motions on inclined planes, closely related to the discussion in the scholium, see Chap. 14 of the treatise On motion.

For an analysis of these early works, read Chap. 3 of Clavelin's Natural Philosophy of Galileo

Week 5 (3/4): 

Week 6 (3/11):
Week 7 (3/25):
Descartes, Rules for the Direction of the Mind, Rules 1-6, 8, 12, 13-14. (Latin text) (Another Latin text)
Week 8 (4/1):
Continuing discussion of the Rules, Rules 13-16
Descartes, Dioptrics (or in Olscamp's trans. Optics), Discourses 1-4, 8, 10
Descartes, Meteors (or in Olscamp's trans. Meteorology), Discourse 8 (On the rainbow)

Daniel Garber, "Descartes and Experiment in the Discourse and Essays, in Essays on the Philosophy and Science of René Descartes, ed. Stephen Voss (Oxford U.P., 1993), Chap. 18 [pdf]
On Descartes' early work on the law of refraction, see John A. Schuster, "Descartes opticien: The Construction of the Law of Refraction and the Manufacture of its Physical Rationales, 1618-1629", in Descartes's Natural Philosophy, ed. Stephen Gaukroger, John Schuster, and John Sutton (2000), 258-312 [available online for PU users]

Week 9 (4/8): Descartes, Geometry (either the Olscamp or the Smith-Latham trans.)

Michael S. Mahoney, The Beginnings of Algebraic Thought in the Seventeenth Century", in S. Gaukroger (ed.), Descartes: Philosophy, Mathematics and Physics (Sussex: The Harvester Press/Totowa, NJ: Barnes and Noble Books, 1980), Chap.5

H.J.M. Bos, "On the representation of Curves in Descartes' Géométrie", Archive for History of Exact Science 24(1981), 295-338.

Week 10 (4/15):
Descartes, Principles of Philosophy, Part II ( Pars. 1-25 [Veitch trans.] Pars. 24-54; Part III, Paragraphs 56-59; and Letter to Clerselier [Mahoney trans.])
Descartes, The World, Chaps. 1-7
Week 11 (4/22):
Continuing with Principles and World, Part II, plus Part IV, Pars. 20-27 and World Chap. 11 on gravity.
Week12 (4/29):