X126 | 22906 | Jeongmin Lee

Jude Lee X126: Proof and experiment: why science matters to philosophy You are sitting in your math or science class. The professor writes a bunch of equations or draws diagrams on the board to demonstrate, for example, how y changes as a variable of x, how the earth is attracted to the sun, how the blood flows through the heart, etc. Now suppose that you decided to play devil’s advocate and ask “why” about everything the professor has just said (as children do): why is that equation true, why should we believe that the earth rotates around the sun, and not vice versa, etc. The following dialogue is exchanged between the math professor and the student: “well, we have just ‘derived’ that equation from previous ones.”/ “Then why are the previous ones true?”/ “Because those equations are further derivable from other theorems in the theory.”/ “Why are then mathematical theorems true?”/ “Because they can be proved from axioms, definitions, and postulates of the theory, and the truth of these last items is ‘self-evident’ or they are ‘true by definition.’” Then on the student’s behalf, why do derivations or proofs provide knowledge in mathematics, and how should we understand the self- evident or definitional character of mathematical axioms? Likewise in empirical sciences, if all scientific theories are established by appealing to direct observations and experiments, then how do scientists use experience to gain knowledge or to justify their theories? Maybe these questions have never occurred to you, but there are people who debated these topics for ages: philosophers. Throughout the entire history of philosophy, the exact sciences (mathematics and physics) have played a vital role in raising philosophical issues and supplying methods of proof and experiment, which in turn contributed to shaping distinctive intellectual trends in the West. With the two-part division of our scientific methods into proof and experiment in mind, for the first half of the semester, we will discuss the idea of rigorous proof beginning with the birth of mathematics among the ancient Greeks. We will first illustrate the idea of proof in Euclid’s geometry and Aristotle’s logic. The quest for the idea of proof continues its adventure with the invention of non-Euclidean geometries, Boole’s algebra of thought, and Frege’s modern logic in the nineteenth century. We will look at some samples of how the method of proof was reshaped in these new phases of development. For the second half of the semester, we turn our eyes to experimental knowledge in physics. In particular, we are interested in the implications some historic experiments in physics have had for our concept of matter. For this purpose, we will first examine the debate between Hobbes and Boyle about the nature of the air-pump experiment and the emergence of experiments in early-modern natural philosophy. Newton’s bucket experiment will also be an excellent introduction to any discussion of the absolute vs. relative conception of space. In Newton’s prism experiment, we touch on the nature of light, and two-slit and EPR experiments will explore the nature of light and matter further into quantum theory. This course might be of interest to philosophically-minded science students or philosophy students interested in the origins of scientific philosophy, but there is no prerequisite for this course. There will be simplified, in-class demonstrations of some of the experiments. Students will be asked to complete a number of short homework assignments and papers, and exams for their grades. For more information contact the instructor at jeolee@indiana.edu.