Ellerman, David (2024) A Fundamental Duality in the Exact Sciences: The Application to Quantum Mechanics. Foundations (MDPI), 4 (2). pp. 175-204.

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Abstract

There is a fundamental subsets–partitions duality that runs through the exact sciences. In more concrete terms, it is the duality between elements of a subset and the distinctions of a partition. In more abstract terms, it is the reverse-the-arrows of category theory that provides a major architectonic of mathematics. The paper first develops the duality between the Boolean logic of subsets and the logic of partitions. Then, probability theory and information theory (as based on logical entropy) are shown to start with the quantitative versions of subsets and partitions. Some basic universal mapping properties in the category of Sets are developed that precede the abstract duality of category theory. But by far the main application is to the clarification and interpretation of quantum mechanics. Since classical mechanics illustrates the Boolean worldview of full distinctness, it is natural that quantum mechanics would be based on the indefiniteness of its characteristic superposition states, which is modeled at the set level by partitions (or equivalence relations). This approach to interpreting quantum mechanics is not a jury-rigged or ad hoc attempt at the interpretation of quantum mechanics but is a natural application of the fundamental duality running throughout the exact sciences.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Ellerman, David david@ellerman.org 0000-0002-5718-618X
Keywords:	Subset-partition duality; logics of subsets and partitions; category-theory duality; logical entropy; quantum mechanics; objective indefiniteness
Subjects:	General Issues > Scientific Metaphysics General Issues > Philosophers of Science General Issues > Structure of Theories General Issues > Theory/Observation
Depositing User:	David Ellerman
Date Deposited:	15 Sep 2024 12:05
Last Modified:	15 Sep 2024 12:05
Item ID:	23486
Journal or Publication Title:	Foundations (MDPI)
Publisher:	MDPI
Official URL:	https://www.mdpi.com/2673-9321/4/2/13
DOI or Unique Handle:	10.3390/foundations4020013
Subjects:	General Issues > Scientific Metaphysics General Issues > Philosophers of Science General Issues > Structure of Theories General Issues > Theory/Observation
Date:	11 May 2024
Page Range:	pp. 175-204
Volume:	4
Number:	2
URI:	https://philsci-archive.pitt.edu/id/eprint/23486

Available Versions of this Item

• A Fundamental Duality in the Exact Sciences: The Application to Quantum Mechanics. (deposited 18 May 2024 07:55)
  • A Fundamental Duality in the Exact Sciences: The Application to Quantum Mechanics. (deposited 28 May 2024 15:17)
    • A Fundamental Duality in the Exact Sciences: The Application to Quantum Mechanics. (deposited 15 Sep 2024 12:05) [Currently Displayed]

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