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What Is the Shared Underlying Protocol of Different Logical Systems? —Proto-Logic and Object-Attribute Association Modality

Chen, Ting
PhilArchive · Papers
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philosophy
Logical pluralism faces the collapse problem, as formulated by Stei (2023): any position that simultaneously affirms a plurality of correct logics, competition among them at the level of application, and the normativity of logical consequence will inevitably collapse into monism or nihilism. Existing responses—whether appealing to derivative normativity (Tajer, 2024) or metalinguistic stipulation—leave a more fundamental question unanswered: in virtue of what can different logical systems coexist and be compared at all? This paper argues that the root of the dilemma lies in the fact that every logical system has always presupposed distinctions—true and false, premise and conclusion—yet has never asked about the conditions that make distinction possible. Through an argument from operational self-refutation and an analysis of asymmetric existential dependence, this paper establishes a minimal ontological structure: the possibility of distinction (the self-sufficient primal ground), distinction itself, and products of distinction. From this structure, three Primal Laws are derived by ontological reductio—the Primal Law of Non-Contradiction (the condition under which distinction is meaningful), the Primal Law of Excluded Middle (the binary exhaustion of distinction modalities), and the Primal Law of Identity (the non-self-sufficiency of distinction products)—together with a further derived Mutual Exclusion Principle. It is then shown that Leibniz’s principle of the Indiscernibility of Identicals secretly presupposes all three Primal Laws. On this basis, the paper argues that Primal Logic constitutes the shared ground protocol underlying all logical systems, and provides a preliminary demonstration of its positive inferential capacity, thereby grounding logical pluralism without recourse to monism. Keywords: Primal Logic; the possibility of distinction; logical pluralism; collapse problem; Indiscernibility of Identicals
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