PHIL 83279/ HPS 93814 – Kant and the Exact Sciences
Spring 2008
Course Description
This course examines Kant's philosophy in relation to the exact sciences, i.e., mathematics and physics. In the first part of the course, we will discuss Kant’s philosophy of geometry, arithmetic, and algebra, and Kant’s theory of matter, motion, and space. In the second part of the course, we will examine the challenges posed to the Kantian theory by new developments in the exact sciences, namely, the discovery of non-Euclidean geometries, Frege’s logicist program, and Einstein’s theories of relativity, as well as possible replies in a neo-Kantian spirit on behalf of Kant.
Readings
Immanuel Kant, “On the first ground of the distinction of regions in space;” Critique of Pure Reason, Metaphysical Foundations of Natural Science; Henri Poincare, Science and Hypothesis; Hermann von Helmholtz, “On the Origin and Significance of the geometric Axioms;” Gottlob Frege, Foundations of Arithmetic; Hans Reichenbach, The Theory of Relativity and A priori Knowledge; Ernst Cassirer, Einstein's Theory of Relativity, Considered from the Epistemological Standpoint; Michael Friedman, Dynamics of Reason; some additional photocopies of selected primary and secondary literature, available at least by Friday afternoon before the Thursday for which the reading in question is assigned, in our course carton box in the mailroom.
Requirements
Your grade will be based on a short presentation in class (about 10 minutes, 10%), and your term paper (90%). Your participation, or lack thereof, won’t harm you, but it can benefit you. Good participation will be rewarded with a grade increase of up to 1/3 of a letter grade. Excessive unexcused absences may result in failing the course.
Schedule
Week I ~ Jan.17
Logistics, General Intro, On the high road to transcendental idealism
Kant, “On the first ground of the distinction of regions in space”
Week II ~ Jan. 24
The nature of intuition
Relevant texts by Kant: CpR, Transcendental Aesthetic (B33-B45); (if you dare: CpR, The second half of the Transcendental Deduction, §§21-27 (B144-169), focus on §24 and §26); Logic, General Doctrine of Elements, Section I, Of Concepts, A. IX, 91ff., focus on §1, §7-16
Manley Thompson, “Singular Terms and Intuitions in Kant’s Epistemology”
Semi-optional: Lisa Shabel, “Kant’s ‘Argument from Geometry’” (we might not get to discuss all of this quite yet, but it might help with B40f.; anticipates some stuff we will talk about later)
Week III ~ Jan. 31
Mathematics versus philosophy, Geometry (1)
Relevant texts by Kant: CpR, Doctrine of Method, Discipline (B741-B766)
Jaakko Hintikka “Kant on the Mathematical Method”
Peter Strawson, The Bounds of Sense, part v: “Kant’s Theory of Geometry”
Week IV ~ Feb.7
Geometry (2)
Michael Friedman, Kant and the Exact Sciences, ch.1 “Geometry”
Emily Carson, “Kant on Intuition in Geometry”
Week V ~ Feb. 14
Arithmetic (1)
Relevant texts by Kant: CpR, The Schematism of the Pure Understanding (B176-187), The Axioms of Intuition (B201-B207)
Charles Parsons, “Arithmetic and the Categories”
Michael Young, “Construction, Schematism, and the Imagination”
Week VI ~ Feb. 21
Arithmetic (2) and Algebra
Michael Friedman, Kant and the Exact Sciences, ch. 2, “Concepts and Intuitions in the Mathematical Sciences”
Lisa Shabel, “Kant on the ‘Symbolic Construction’ of Mathematical Concepts”
Week VII ~ Feb. 28
Matter and motion
Kant, Metaphysical Foundations of Natural Science, parts I-III; (optional: CpR, The Analogies of Experience (B218-B265))
Optional: Gerd Buchdahl, “Kant’s ‘Special Metaphysics’ and the Metaphysical Foundations of Natural Science“
Week VIII
Break
Week IX ~ March 13
Newton and Kant on absolute motion and absolute space
Kant, Metaphysical Foundations of Natural Science, part IV
Newton, Principia, Definition VIII, Scholium
Optional: Michael Friedman, Kant and the exact Sciences, ch. 4
Week X ~ March 20
The challenge posed by non-Euclidean Geometry
Hermann v. Helmholtz, “On the Origin and Significance of the Geometrical Axioms”
Henri Poincaré, Science and Hypothesis, ch. iii+iv
Week XI ~ March 27
The challenge posed by ‘logicism’
Gottlob Frege, The Foundations of Arithmetic (selections); On the Foundations of Geometry and Formal Theories of Arithmetic (selections); maybe Grundgesetze (selections)
John McFarlane, “Frege, Kant and the Logic in Logicism”
Semi-optional: Michael Dummett, “Kant and Frege on Geometry”
Week XII ~ April 3
The challenge posed by the theory of relativity (1)
Hans Reichenbach, The Theory of Relativity and A Priori Knowledge
Week XIII ~ April 10
The challenge posed by the theory of relativity (2)
Ernst Cassirer, Einstein’s Theory of Relativity Considered from the Epistemological Standpoint
Moritz Schlick, “Critical or Empiricist Interpretation of Modern Physics?”
Week XIV ~ April 17
Michael Friedman, Dynamics of Reason, lectures I-II
Week XV ~ April 24
Michael Friedman, Dynamics of Reason, lecture III
General Wrap-up
Week XVI
Wed., May 7 ~ Final paper due at 12:00 p.m. in the box in front of my office