Reductionism and the Universal Calculus

TL;DR

This paper explores the historical pursuit of a universal language and calculus, analyzing Leibniz's efforts and their failure through the lens of reductionism to understand the limits of mathematical modeling in physical sciences.

Contribution

It offers a philosophical analysis of Leibniz's universal calculus and discusses how reductionism explains its failure, providing insights into Wigner's question about mathematics' effectiveness.

Findings

Reductionism helps explain the failure of Leibniz's universal calculus.

Leibniz's efforts aimed to create a comprehensive symbolic language.

Understanding these historical efforts sheds light on the limits of mathematical modeling.

Abstract

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.