Partitions and Objective Indefiniteness

Download Edit this record How to cite View on PhilPapers
Abstract
Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of reality. The problem of interpreting quantum mechanics (QM) is essentially the problem of making sense out of an objectively indefinite reality. These two types of reality can be respectively associated with the two mathematical concepts of subsets and quotient sets (or partitions) which are category-theoretically dual to one another and which are developed in two mathematical logics, the usual Boolean logic of subsets and the more recent logic of partitions. Our sense-making strategy is "follow the math" by showing how the logic and mathematics of set partitions can be transported in a natural way to Hilbert spaces where it yields the mathematical machinery of QM--which shows that the mathematical framework of QM is a type of logical system over ℂ. And then we show how the machinery of QM can be transported the other way down to the set-like vector spaces over ℤ₂ showing how the classical logical finite probability calculus (in a "non-commutative" version) is a type of "quantum mechanics" over ℤ₂, i.e., over sets. In this way, we try to make sense out of objective indefiniteness and thus to interpret quantum mechanics.
PhilPapers/Archive ID
ELLPAO
Revision history
Archival date: 2014-10-16
View upload history
References found in this work BETA
Mathematical Foundations of Quantum Mechanics.von Neumann, John & Beyer, R. T.
Group Structural Realism.Roberts, Bryan W.

View all 25 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2014-10-16

Total views
150 ( #23,593 of 45,642 )

Recent downloads (6 months)
22 ( #31,632 of 45,642 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.