Challenging the Double-Negation Principle: An Analysis of Strategic Theories of Sun Zi, Carnot, and Clausewitz through Intuitionist Logic

To study a subject similarly represented in Eastern and Western cultures, I examine some classical theories of war strategy according to a new analytical method. This method is based on the recognition that the most important strategic theories are organized as theories essentially not deduced from axioms according to classical logic. Such theories reason through doubly negated propositions (DNPs), whose meanings differ from those of their affirmative counterparts. This corresponds to the use of intuitionist logic instead of classical logic. An inspection of the works of the texts of Sun Zi, Lazare Carnot, and Clausewitz reveals many such propositions, and in each case the ordered sequence of DNPs suffices to reconstruct the core argument of the entire book. In particular, the analysis of Clausewitz suggests a new interpretation, markedly different from the standard one. A common logical style in strategic thinking of Eastern and Western cultures is thereby revealed. The results challenge the Western misconception of Eastern logic as primitive; rather, they suggest that Western culture should recognize intuitionist logic as equally legitimate not only in formal terms but also in the applications, particularly in the interpretation of Chinese thought.