This paper introduces the Paraconsistent Strategies Theorem, which posits that in every minimally complex business—defined as those with two or more product or service lines—the strategy of the business as a whole will be at most paraconsistent, never entirely consistent. Drawing on principles of paraconsistent logic and the I³ framework (Irrationality × Innovation = Impact), we argue that embracing strategic contradictions can drive innovation and create lasting competitive advantage in complex business environments.

The study presents a proof of the theorem and explores its implications through examples of Alphabet Inc., Amazon, and 3M, demonstrating how these companies successfully leverage paraconsistent strategies across diverse business lines. We propose a methodology for assessing strategic paraconsistency and offer a comprehensive framework for implementing paraconsistent strategies.

The paper discusses the management implications of this approach, including cultivating a culture of constructive irrationality, adapting organizational structures, and developing new performance measurement systems. While acknowledging the limitations and potential risks of paraconsistent strategies, we argue that in increasingly complex and dynamic markets, the ability to manage strategic contradictions may become critical for organizational success.

This research contributes to the fields of strategic management and organizational theory by providing a novel perspective on how businesses can thrive amidst complexity and contradiction, opening new avenues for both theoretical exploration and practical application.