History and Philosophy Of Science | Proof & Experiment
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.