On the inherent incompleteness of scientific theories

Abstract

We examine the question of whether scientific theories can be complete. For two closely related reasons, we argue that they cannot. The first reason is the inability to determine what are "valid observations", a result that is based on a self-reference Gödel/Tarski-like argument. The second reason is the existence of "meta-empirical" evidence of the inherent incompleteness of observations. These reasons, along with theoretical incompleteness, are intimately connected to the notion of belief and to theses within the philosophy of science: the Quine-Duhem (and underdetermination) theses and the observational/theoretical distinction failure. Some puzzling aspects of the philosophical theses become clearer in light of these connections. It also follows that there is no absolute measure of the information content of empirical data nor of the entropy of physical systems, and that no complete computer simulation of the natural world is possible. The connections with the mathematical theorems of Gödel and Tarski reveal the existence of other possible connections between scientific and mathematical incompleteness: computational irreducibility, complexity, infinity, arbitrariness, and self-reference. Finally, suggestions are offered of where a more rigorous (or formal) "proof" of scientific incompleteness may be found.