History and Philosophy Of Science | Proof and Experiment: Why Science Matters to Philosophy
X100 | 7440 | Jeongmin Lee (Jude)

You are sitting in math or science class.  The professor writes a
bunch of equations and draws graphs or 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 have just said, just as
children do: why is that equation true, why should we believe the
earth rotates around the sun, and not vice versa, could there be an
absolute vacuum in the universe, etc.  We may expect the following
sort of dialogue 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.  The truth of
these last items is ‘self-evident’ or they are ‘true by
definition.’’’  Then a more fundamental question on the student’s
behalf is: why do derivations or proofs provide knowledge in
mathematics, and how should we understand the self-evident or
definitional character of mathematical axioms?  The professor might
be frustrated at this point, or simply dismiss these questions as
silly or “philosophical.”  Similar questions in science class will
presumably lead to the following answer from the instructor: “all
scientific theories are established by appealing to direct
observations and experiments.  In that sense, physics, chemistry,
and biology are all empirical or experimental sciences.”  Then how
do scientists us experience to gain knowledge or to justify their

Maybe these questions have never occurred to you, but there are
people who debated these topics for ages: philosophers.  Throughout
the entire history philosophy, the exact sciences (mathematics and
physics) have played a vital role in raising philosophical issues
and answering them, which in turn contributed to shaping distinctive
intellectual trends in the West.  Thus proof and experiment became
the essential tools for producing scientific knowledge as well as
the paradigmatic methodologies in philosophy.

With the two-part division of our scientific knowledge 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 and its
connection to philosophy with the examples of Euclid and Aristotle.
The quest for the idea of proof continues its adventure with the
invention of calculus by Newton and Leibniz in the early-modern
twentieth centuries.  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 one of the fundamental questions in philosophy: what is the
world made of, or what is the (material) constitution of the world,
and how can we know about it?  For this purpose, we will first
examine the emergence of experiments in early-modern natural
philosophy.  The debate between Hobbes and Boyle about the nature of
the air-pump experiment will provide us with a good transition point
from proof to experiment.  Newton’s bucket experiment will also be
an excellent introduction of the absolute vs. relative conception of
space.  In Newton’s prism experiment, we touch on the nature of
light, which has always been decisive in backing up the theory of
matter to date.  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 who are interest 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.