Abstract
This book offers a comprehensive exploration of axiological logic, delving into the philosophical foundations and implications of value theory. It begins by situating the concept of goodness within a broader ontological framework, examining the philosophical underpinnings of logic and arguing for an ontological interpretation that extends beyond mere methodological considerations. By exploring intentional, real, and ideal modes of existence, the book establishes a robust framework for evaluating propositions based on their value relations, introducing key concepts such as goodness, evil, and axiological neutrality. The core of the book introduces a novel semantics for axiological logic, focusing on a relational approach to evaluative properties. It presents the "Local Peak Property" and "Global Peak Property," which posit that goodness is determined by being the best among possible alternatives. A necessitation rule is also developed, asserting that all necessary truths are inherently good, thereby linking logical necessity with axiological value. The theory of values is explored in depth, with major results including the "Benatar-Plantinga Principle," which suggests that the value of a proposition is determined by its least valuable logical consequence. This chapter argues against axiological foundationalism, proposing that values are interdependent rather than grounded in a single foundational entity. The complexities and limitations of aggregating value judgments are also discussed, highlighting the nuanced nature of value summation. The book addresses the naturalistic fallacy by bridging the gap between descriptive and evaluative propositions, demonstrating that evaluative propositions can be logically implied by descriptive ones. An incompleteness theorem is presented, illustrating the limitations of formal systems in capturing the richness of axiological logic. The final chapter advocates for a platonic perspective in axiology, arguing that axiological truths serve as a universal standard for evaluating the world, independent of contingent facts. This perspective underscores the normative significance of goodness and the interconnected nature of values, offering a platonic framework for understanding axiological logic.