Studia Logica

, Volume 53, Issue 4, pp 533–550 | Cite as

Schrödinger logics

  • Newton C. A. da Costa
  • Décio Krause


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 understandidentity as meaningindistinguishability (agreemment with respect to attributes). Observing that these concepts are equivalent in classical logic and mathematics, which underly 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's logical intuitions about the nature of elementary particles.


Elementary Particle Quantum Mechanic Mathematical Logic Physical Theory Computational Linguistic 
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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Newton C. A. da Costa
    • 1
  • Décio Krause
    • 2
  1. 1.Department of PhilosophyUniversity of São PauloBrazil
  2. 2.Department of MathematicsFederal University of ParanáBrazil

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