THE QUANTUM SUPERPOSITION PRINCIPLE JUSTIFIED IN A NEW NON-ARISTOTELIAN FINITARY LOGIC
Radhakrishnan Srinivasan · International Journal of Quantum Information · 2004
In the proposed non-Aristotelian finitary logic (NAFL), truths for formal propositions can exist only with respect to axiomatic theories, essentially as temporary axiomatic declarations in the human mind. An undecidable proposition P in a consistent NAFL theory T is true/false with respect to T if and only if it has been axiomatically declared as true/false by virtue of its provability/refutability in an interpretation T* of T. In the absence of any such axiomatic declarations, P is in a superposed state of 'neither true nor false' and the consistency of T requires the existence of a non-classical model for T in which P&¬P is the case. Here T* is an axiomatic NAFL theory that, like T, resides in the human mind and acts as the 'truth-maker' for (a model of) T. Quantum superposition is justified by identifying 'axiomatic declarations' for the truth/falsity of P (by virtue of its provability/refutability in T*) with 'measurement' in the real world. NAFL also explains and de-mystifies the phenomenon of entanglement. NAFL severely restricts classical infinitary reasoning, but possibly provides sufficient machinery for a consistent axiomatization of quantum mechanics.