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When Does a Formal Distinction Obtain? Specification, Instantiation, and the Metaphysics of Primitive Identity

Pelley, Mark
PhilArchive · Papers
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philosophy
A formal specification can fix identity conditions without, by that fact alone, settling what metaphysical item instantiates those conditions or where the relevant distinction obtains. The paper separates three questions that discussions of primitive symbols often run together: what a calculus specifies as distinct, what if anything bears or instantiates the specified distinction, and what determines why that distinction obtains. The first result is a Specification–Instantiation Constraint: if a theorist asks a metaphysical individuation question rather than merely how to operate a calculus, the answer must either identify an instantiation locus or explicitly decline the further metaphysical demand. A worked case shows that the same formal alphabet is compatible with deflationary formalism, ante rem structuralism, type realism, and token-based realizations, so the syntax alone underdetermines the ontological locus of primitive identity. A second result, the Determination–Instantiation Separation, follows: what is sufficient to fix or explain a profile is not thereby the bearer at which the profile obtains; a source-to-bearer inference requires an additional bridge. This separation is distinguished from the closely related ground/identity distinction already drawn in the metaphysical-grounding literature, and its own narrower and more general application is stated. The paper then distinguishes the whole result from the stronger claim that all individuation is metaphysically relational. Structuralist accounts by Resnik and Shapiro satisfy the constraint through relational positions; type realism supplies a different ontology; a theorist who takes system-relative specification as exhaustive remains a coherent deflationary rival. Agápēic Relational Metaphysics enters only at the end as one metaphysical realization of the stronger constitutive-contrast thesis. Nothing in the independent argument establishes act-form individuation, numerical identity between formal contrast and the ur-fact, libertarian sourcehood, or any uniquely ARM-specific conclusion.
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