Paper
Can Axiomatic Physics Be Possible via Zermelo-Fraenkel Set Theory with the Axiom of Choice?
- Authors:
- Tadao Nakamura; Koji Nagata
- Abstract
- We review that a singleton set, i.e., {1} does not meet Zermelo-Fraenkel set theory with the axiom of choice. Our discussion relies on the validity of Addition and Multiplication. Our result shows the current axiomatic set theory has a contradiction even if we restrict ourselves to Zermelo-Fraenkel set theory, without the axiom of choice [K. Nagata and T. Nakamura, Adv. Studies Theor. Phys. 5, 57 (2011)]. On the other hand, Physics does not have any contradiction because we consider it as a set of experimental data. Axiomatizing all of physics (experimental data) is impossible when we accept Zermelo-Fraenkel set theory with the axiom of choice. Our discussion results in the fact that the answer of Hilbert’s 6th problem is pessimistic. All analyses are performed in a finite set of natural numbers.
- Keywords
- Quantum Measurement Theory; Quantum Computer; Set Theory; Formalism
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