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Prolongments of "Ensaio": Schrödinger Logics and Quasi-Set Theory

Krause, Décio (2022) Prolongments of "Ensaio": Schrödinger Logics and Quasi-Set Theory. [Preprint]


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In his "Ensaio sobre os Fundamentos da Lógica", Newton da Costa advanced at least two interesting ideas to relate logic with quantum theory in a different direction than that of standard ‘quantum logics’, contributing to initiating the systematic investigations in the field of non-reflexive logics with the introduction of a system of logic where the standard notion of identity is not appliable to all objects, as some like Schrödinger believed with regards quantum elementary particles. In this chapter, we revise his system, relate the subject with philosophical and logical discussions about identity and individuation of quantum objects, and also show how they were extended in the directions of a group of higher-order logics and of a theory of quasi-sets. So, we show how the two challenges proposed by da Costa were solved, first with the development of a the- ory of quasi-sets and then by founding in such a theory a semantics for a special case of an intensional Schrödinger logic which encompasses da Costa’s system and which copes with Dalla Chiara and Toraldo di Francia’s claim that “microphysics is a world of intensions". Some further applications of these systems are also referred to, so as some philosophical ideas are further advanced. The References at the end provide material for more detailed analyses.

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Item Type: Preprint
Krause, Décio
Keywords: Identity, indiscernibility, individuality, non-individuality, Schrödinger logics, non-reflexive logics, nonreflexive logics, quasi-set theory, quantum logics, Newton da Costa, non-standard semantics, quantum theories, Manin Problem.
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Depositing User: Décio Krause
Date Deposited: 24 Jul 2022 16:34
Last Modified: 24 Jul 2022 16:34
Item ID: 20958
Subjects: Specific Sciences > Mathematics > Foundations
Specific Sciences > Mathematics > Logic
Date: 22 July 2022

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