Kinneret Academic College
Is it possible to encompass the full extent of the universe within a theory based on a finite set of first principles and inference rules ? The belief that it is possible to arrive at such a complete theory ("Theory of Everything" – TOE) has been, for many-many years and for most researches, a fundamental tenet of the scientific research. However, Gödel's incompleteness theorem implies that any formal structure, based on a finite number of first principles and inference rules, which is rich enough, cannot be at the same time both consistent and complete. Completeness, in terms of physics theories, implies determinism. Gödel's theorem (whenever it applies) points to incompleteness in the sense that there will always be claims that may be formulated within this formal system but are undecidable. A close inspection of Gödel's theorem demonstrates that this impossibility arises when the claims are self-referential, or, more precisely, when the system asks to define itself in its own terms. Self-referencing occurs in physics whenever the observer is also part of the observed system. Observers are integral part of the universe, therefore observations should be included in the subject- matter of the complete all-encompassing whole-universal theory, especially in view of the fact that arbitrarily chosen modes of observations may essentially determine empirical results. Consequently, Gödel's theorem seems to apply to physics, and incompleteness, hence non-determinism, unavoidable. The talk discusses self-referencing in Gödel's theorem and physics, its relation with our involvement in the universe, and consequences thereof.