Fall 2024 Science and Human Understanding (UC Riverside)
Course Overview
This is a thematic introduction to the philosophy of science and mathematics. The theme is Revolution and Paradox. We will encounter key questions, concepts, and debates in the philosophy of science and mathematics by understanding and evaluating how philosophers in the early-to-mid 20th century formed their philosophical ideas in reaction to revolutions in science and paradoxical and surprising results in mathematics. To do so, we will learn some basic details of Albert Einstein’s theory of relativity in physics, Bertrand Russell’s paradox in set theory, and Kurt Gödel’s incompleteness theorems in metamathematics (what are set theory and metamathematics? I’ll tell you!) We will do so in a low-stakes way: no physics or mathematics background will be required for this class.
These revolutions and paradoxes help us see how we change our scientific and mathematical ideas. Here are some intuitive ideas about science and mathematics and how we change them. Scientific hypotheses and theories are justified by empirical evidence, collected by observations, experiments, and studies. Mathematical axioms are justified by reflection: thinking clearly about things like numbers, geometric figures, and functions and figuring out the correct axioms for them. If we are wrong about a hypothesis and need to change it, it is because we missed some empirical evidence or made a mistake in using the evidence we had. If we are wrong about axioms, it’s because we didn’t think clearly enough.
Due to the revolutions and paradoxes we will discuss, some of the philosophers we will study have thought these ideas are not completely right. According to them, we are not just appealing to experiences in science during a revolution, and we are not just appealing to reflection in mathematics to resolve a paradox. Some of them thought that radical changes in science and math involve conceptual changes: we are introducing new concepts or languages when we revise science and math. Other philosophers we will discuss objected to these ideas, forming their own ideas in response. This required philosophers to think more generally about the meaning of our words and concepts and how we gain knowledge using them. In part for this reason, the work we will discuss has been very influential in epistemology and the philosophy of language and mind. The philosophy of science and mathematics we will discuss therefore contributes to the philosophy of human understanding more generally.
This frames what will happen in the first eight weeks of class. In our last two weeks, we will look at some important ideas and debates that connect with ideas explored throughout the quarter that will aid your future exploration in the philosophy of science. We will debate whether scientists make value judgments and how this relates to confirming hypotheses and assigning them probabilities. Appropriate to the title of our course, we will also discuss whether understanding rather than truth is what science aims for.
Schedule with Readings
Below, ‘E4E’ is short for John Norton’s online textbook Einstein for Everyone. Use this link to find the chapters for E4E referred to below. After noting the chapter(s) assigned, I describe the general content of the chapter(s), but please note the titles of the chapter(s) are different.
Weeks 0-1 (R Sept 26, T Oct 1, R Oct 3): Special relativity and the meaning of scientific concepts.
R (Sept 26): Introduction. E4E, Chapter 2—Introducing Einstein’s special theory of relativity.
T (Oct 1): Percy Bridgman, The Logic of Modern Physics (here), pp. 1-12 (stop at the end of the paragraph ending with “connection between the two lengths”). E4E, Chapters 3-6—More on special relativity.
R (Oct 3): Bridgman, The Logic of Modern Physics, pp. 9-36 (re-read pp. 9-12; pp. 33-36 are in Chapter 2). Review/left-over material from E4E, Chapters 3-6. [Optional: E4E, Chapter 8]
Week 2: General relativity and the philosophy of geometry
T: E4E, Chapters 18-22—On Euclidean and non-Euclidean geometry. Document by me (Prof. Smith) on Kant’s analytic-synthetic and a priori-a posteriori distinctions.
R: Hans Reichenbach, “The Philosophical Significance of the Theory of Relativity,” skip section IV. E4E, Chapters 23-25—On general relativity.
Week 3: Critically evaluating Bridgman and Reichenbach
T: E4E, Chapter 15, sections 3 and 4—On verificationism and operationalism and Norton’s criticism of them. E4E, Chapter 35, except the “Gravity Geometrized” section—On philosophical ideas about geometry, space, and time inspired by general relativity such as Reichenbach’s, and Norton’s criticism of them.
R: Continue discussion of Tuesday’s material and prepare for the first assignment due next Saturday.
Week 4: Mathematical paradoxes and Rudolf Carnap’s response.
T: W.V. Quine, “The Ways of Paradox.” Document by me (Prof. Smith) on the paradoxes of set theory.
R: Rudolf Carnap, The Logical Syntax of Language, Foreword, Sections 1, 2, and 17. Carnap, “Intellectual Autobiography” (from The Philosophy of Rudolf Carnap), Sections 6 and 8. Document by me (Prof. Smith) on Gödel’s incompleteness theorems. First assignment due Saturday Oct 26th on Canvas.
Week 5: Rudolf Carnap versus W.V. Quine on meaning, mathematics, and experience.
T: Rudolf Carnap, The Philosophical Foundations of Physics, Chapter 1—focus on his informal exposition of the necessity of logic and mathematics on pp. 9-12. Carnap, Meaning and Necessity, Sections 1 and 2. Continued discussion of mathematical paradoxes/results if necessary.
R: W.V. Quine, “Two Dogmas of Empiricism.”
Week 6: Carnap versus Quine, continued.
T: Continue discussion of “Two Dogmas of Empiricism.” Quine, “Carnap and Logical Truth.” [Optional: Hilary Putnam, “The Analytic and the Synthetic.”]
R: Continue Quine discussion if necessary. Carnap, “Reply to W.V. Quine,” “Quine on Analyticity.”
Week 7: Thomas Kuhn’s revolutionary view of scientific revolution.
T: Peter Godfrey-Smith, Theory and Reality, Chapter 5 and Chapter 6, Sections 1 and 2. [Optional: Thomas Kuhn, The Structure of Scientific Revolutions, Chapters 1-4.]
R: Kuhn, The Structure of Scientific Revolutions, Chapters 9 and 10. Godfrey-Smith, Chapter 6, Sections 3, 4, and 5. Second assignment due Saturday Nov 16th on Canvas.
Week 8: Kuhn continued
T: Continue discussion of Kuhn R: No class: Thanksgiving
Week 9: Value judgments, probability, and underdetermination
T: Richard Rudner, “The Scientist Qua Scientist Makes Value Judgments.” Richard Jeffrey, “Valuation and Acceptance of Scientific Hypotheses”
R: Elizabeth Anderson, “The Use of Value Judgments in Science: A General Argument, with Lessons from a Case Study of Feminist Research on Divorce.”
Week 10: Truth and understanding
T: Catherine Elgin, “True Enough” (2004 paper)
R: Continue Elgin; review for exam.