A Class of Deductive Theories that cannot be Deterministic: Classical and Quantum Physics are not deterministic

Abstract

The problem of the determinism of Quantum Mechanics has been a main one during the 20th century. At the same time, in the context of Logic and Set Theory, the importance of ancient paradoxes as well as the appearance of many new ones, has shed light on and deeply influenced the foundations of Mathematics and somehow of Physics. But, strangely, concerning Physics, a paradox which we call the Memory Paradox has remained yet undiscovered, despite its simplicity and remarkable consequences, mostly in Physics and surprisingly in classical Physics that appear to be non deterministic, contrary to the general belief since Newton, Laplace, etc.. The non determinism of Quantum Physics follows without any supplementary hypothesis. This paper extends a previous one (arXiv: 1203.2945v1 [physics.gen-ph] 13 Mar 2012).