Philosophical Logic

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.

Contents:

• Introduction
• Argumentation and Logic
• Trade Networks and Logical Reasoning
• Divine Order and Logical Reasoning
• Stoic Logical Reasoning as Logemes
• Mozi's and Aristotle's Logical Reasoning as Logemes
• Logical Reasoning in Modern Times and Logical Positivism
• Non-Classical Logics and Semantic Analysis
• Transcendental Logic
• Conclusion

Readership: This book is suitable for scholars and students of philosophy — particularly those studying logic, phenomenology, and the history of logical reasoning; mathematics, particularly univalent foundations, homotopy theory, and advanced logical frameworks — and computer science — particularly in artificial intelligence, machine learning, and computational logic. It is also suitable for technology practitioners engaged in AI, machine learning, and data science, or general enthusiasts interested in the evolution of logic, its historical roots, and its contemporary applications in science and technology.