Philosophical Logic: A Phenomenological Approach by Schumann, Andrew;

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This book is an accessible introduction to philosophical logic's phenomenological approach, elucidating its principles and demonstrating its utility in uncovering the origins and development of logic. The analytical approach to philosophical logic which dominated early discourse posited that logic serves as a universal tool capable of articulating any consistent thought, representative of an era where formalism and rigor were prized as the ultimate pathways to clarity and precision. In recent times, however, the landscape of foundational mathematics has shifted with the emergence of univalent foundations. They, unlike symbolic logic and set theory, embrace the uncountable, infinite diversity of mathematical objects, something that was inconceivable within the confines of logical positivism.The phenomenological approach dispenses with the need for comprehensive logical calculi, focusing instead on smaller, modular units of logic referred to as logemes. The implications of this approach extend beyond historical analysis, holding significant potential for applications in artificial intelligence, machine learning, and more. By offering an expansive arsenal of homotopic tools, the phenomenological approach equips researchers and practitioners with innovative techniques for tackling complex problems in all fields.