Krause, D. (2011) The Problem of Identity and a Justification for Non-Reflexive Quantum Mechanics. [Preprint]
In this paper we try to justify our way of looking for an alternative approach to quantum mechanics,
which is based on a non-classical logic. We consider two specific questions related
to quantum theory, namely, entanglement and the indiscernibility of quanta. We characterize
individuals, and then explain in what sense entanglement is a concept which can be applied to
individuals in a restricted sense only. Then, we turn to indiscernibility and, after realizing that
this concept is of a fundamental importance, we mention the ‘traditional’ theory of identity
(TTI) of standard logic and mathematics, which underly the basic formalism of quantum theory.
Then we propose to call the Problem of Identity the question whether identity of objects
can be justified, and under what conditions. As in the Hume’s celebrated Problem of Induction,
we conclude that the attribution of transtemporal identity to an object (either a macroscopic
or a microscopic one) has no logic justification, and must be considered as a metaphysical hypothesis.
Numerical identity is also put aside for similar reasons. Then we guess that identity
is just an useful concept, but which in certain fields, mainly in the quantum realm, could be
substituted by a weaker concept of indiscernibility. This assumption motivates us to look for
an interpretation of quantum mechanics based on a non-classical logic, termed non-reflexive,
and the corresponding mechanics is called non-reflexive quantum mechanics.
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