Protologic: Unveiling the foundations of logic through the ontology of formal systems

Over the past century, the discovery and proliferation of new logical systems have shifted the focus of logic studies toward the development and expansion of these systems. Despite this horizontal growth, foundational questions such as "Is there a foundational logical system?" or "Can logic itself be grounded?" have been largely overlooked. This study addresses these questions by investigating a foundational logical structure, or protologic, which is posited to underlie formal logic. Employing a transcendental approach, this research examines the necessary conditions for the construction of formal systems and finds that these systems fundamentally rely on the concepts of place, order, sameness, otherness, and togetherness. Among these, sameness, otherness, and togetherness are identified as essential concepts, forming the basis for protologic. Building on this foundation, it is proposed that protologic comprises specific logical connectives and principles: negation, grounded in the concepts of sameness and otherness, and universal affirmation, rooted in togetherness. Similarly, the principles of non-contradiction and identity are identified as foundational due to their reliance on these essential concepts, whereas other connectives and principles are determined to require non-fundamental concepts for their coherence. Thus, this study argues that protologic represents the necessary, shared foundation for all formal systems. The implications of this protologic are then evaluated within the context of contemporary debates on logical pluralism and anti-exceptionalism. While the study does not reject logical pluralism, it suggests that pluralism should be understood at the level of logical systems rather than as a challenge to an underlying logical foundation. In opposition to anti-exceptionalism, this research provides a counterexample by demonstrating that logic may indeed rest on an a priori foundation, grounded in the essential concepts identified as constitutive of protologic.