Does intelligence imply contradiction?

Contradiction is often seen as a defect of intelligent systems and a dangerous limitation on efficiency. In this paper we raise the question of whether, on the contrary, it could be considered a key tool in increasing intelligence in biological structures. A possible way of answering this question in a mathematical context is shown, formulating a proposition that suggests a link between intelligence and contradiction. A concrete approach is presented in the well-defined setting of cellular automata. Here we define the models of “observer”, “entity”, “environment”, “intelligence” and “contradiction”. These definitions, which roughly correspond to the common meaning of these words, allow us to deduce a simple but strong result about these concepts in an unbiased, mathematical manner. Evidence for a real-world counterpart to the demonstrated formal link between intelligence and contradiction is provided by three computational experiments. The structure of this paper (1) Introduction (2) Background: contradiction in science, mathematics, philosophy (3) Some notes about our epistemological approach (4) A way of formalizing the problem • 4.1. A cellular automaton as a “world” in which we can study entities • 4.2. An observer judges the presence of entities • 4.3. A definition of the intelligence of an entity • 4.4. A definition of the contradictory nature of an entity (5) The key result in our model (6) Computational experiments (7) Some controversial points: our answers Preprint submitted to Elsevier Science 30 July 2008