  In the seminal essay, "On the unreasonable effectiveness of mathematics in
the physical sciences," physicist Eugene Wigner poses a fundamental
philosophical question concerning the relationship between a physical system
and our capacity to model its behavior with the symbolic language of
mathematics. In this essay, I examine an ambitious 16th and 17th-century
intellectual agenda from the perspective of Wigner's question, namely, what
historian Paolo Rossi calls "the quest to create a universal language." While
many elite thinkers pursued related ideas, the most inspiring and forceful was
Gottfried Leibniz's effort to create a "universal calculus," a pictorial
language which would transparently represent the entirety of human knowledge,
as well as an associated symbolic calculus with which to model the behavior of
physical systems and derive new truths. I suggest that a deeper understanding
of why the efforts of Leibniz and others failed could shed light on Wigner's
original question. I argue that the notion of reductionism is crucial to
characterizing the failure of Leibniz's agenda, but that a decisive argument
for the why the promises of this effort did not materialize is still lacking.
