da Costa and Krause (Abs) Schrödinger Logics, “Abstract”, summary

 

by Corry Shores

 

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Summary of

 

Newton C.A. da Costa

and

Décio Krause

 

“Schrödinger Logics”

 

Abstract

 

 

 

Brief summary:

Da Costa and Krause will discuss logical systems called “Schrödinger logics.” In these systems, the principle of identity does not always hold. It is designed for application to elementary particles. In this context, the concept of identity as indistinguishability does not make much sense, given the physical nature of these particles. The authors will present a higher-order logical system that will separate the concepts of identity and indistinguishability. They will also provide a classical semantics for it. In this system, we cannot derive Leibniz’ Principle of the Identity of Indiscernibles, which reflects the fact that this principle may not actually hold at this scale.

 

 

 

 

Summary

 

Abstract

 

[I will quote the abstract as it is already a summary:]

Schrödinger logics are logical systems in which the principle of identity is not true in general. The intuitive motivation for these logics is both Erwin Schrödinger’s thesis (which has been advanced by other authors) that identity lacks sense for elementary particles of modern physics, and the way which physicists deal with this concept; normally, they understand identity as meaning indistinguishability (agreemment [sic] with respect to attributes). Observing that these concepts are equivalent in classical logic and mathematics, which underly [sic] the usual physical theories, we present a higher-order logical system in which these concepts are systematically separated. A ‘classical’ semantics for the system is presented and some philosophical related questions are mentioned. One of the main characteristics of our system is that Leibniz’ Principle of the Identity of Indiscernibles cannot be derived. This fact is in accordance with some authors who maintain that quantum mechanics violates this principle. Furthermore, our system may be viewed as a way of making sense some of Schrödinger logical intuitions about the nature of elementary particles.

(533)

 

 

 

 

 

 

 

da Costa, Newton C.A., and Krause, Décio. 1994. “Schrödinger Logics.” Studia Logica 53: 533-550.

 

 

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