Is Kant’s Transcendental Logic a Logic?

Abstract

This article investigates the computational foundations of Immanuel Kant’s transcendental logic and its relevance to artificial intelligence and machine consciousness. We demonstrate that while Kantian analytic judgments map to decidable computations on standard deterministic Turing machines, synthetic a priori judgments require extended models, specifically, Turing machines equipped with oracles, to capture their non-algorithmic, self-positing nature. Building on Johann Gottlieb Fichte’s formulation of consciousness as a self-negating loop (“I = not-I”), we formalize a consistent syllogistic system that accommodates non-trivial self-reference. By interpreting this system topologically via spanning simplicial complexes, we show that reflexive reasoning remains both logically consistent and polynomial-time decidable. Furthermore, we introduce quantitative evaluation frameworks, including a Turing Simulation Test and a Reflexion Loop Consciousness Test, to assess whether large language models exhibit minimal conscious-like behavior, such as escaping semantic stagnation and integrating contextual grounding. Thus, we argue that transcendental logic constitutes a viable, computationally tractable framework for modeling self-aware, synthetic reasoning in artificial agents.