Does intelligence imply contradiction?

TL;DR

This paper explores whether contradiction can be a fundamental component of intelligence, proposing a mathematical framework and computational experiments to investigate the link between contradiction and intelligence.

Contribution

It introduces a formal mathematical model linking contradiction and intelligence within cellular automata, supported by computational experiments.

Findings

Contradiction can be a tool to increase intelligence in systems.

A formal link between contradiction and intelligence is established mathematically.

Experimental evidence supports the role of contradiction in intelligent behavior.

Abstract

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.