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Reductionism and the Universal Calculus

Sarma, Gopal (2016) Reductionism and the Universal Calculus. [Preprint]

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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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Sarma, Gopalgopal.sarma@emory.edu0000-0002-9413-6202
Keywords: universal calculus, philosophical language, universal language, reductionism, scientific theories, Eugene Wigner, Gottfried Leibniz
Subjects: General Issues > Explanation
General Issues > History of Philosophy of Science
General Issues > Models and Idealization
General Issues > Reductionism/Holism
General Issues > Structure of Theories
General Issues > Thought Experiments
Depositing User: Dr. Gopal Sarma
Date Deposited: 14 Jul 2016 14:22
Last Modified: 14 Jul 2016 14:22
Item ID: 12280
Subjects: General Issues > Explanation
General Issues > History of Philosophy of Science
General Issues > Models and Idealization
General Issues > Reductionism/Holism
General Issues > Structure of Theories
General Issues > Thought Experiments
Date: July 2016
URI: http://philsci-archive.pitt.edu/id/eprint/12280

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