# Quantum superposition principle justified in a new non-Aristotelian finitary logic

- Publication Year:
- 2004

## Explore PlumX Metrics

What are PlumX Metrics? How can they help tell the story about this research? How can I use them?

Learn more- Repository URL:
- http://philsci-archive.pitt.edu/id/eprint/1923

- Author(s):

##### preprint description

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 consistency of T requires the existence of a non-classical model for T in which $P \& \neg P$ 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.