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It is not the case that Van Inwagen's relative identity logic permits formally consistent trinitarian claims that map onto Vohánka's demonstrably impossible non-theological analogues.
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Reasons For
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1.
If non-theological analogues are demonstrably impossible, the relative identity framework explaining both equally well suggests it obscures rather than solves the problem.
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2.
Formal consistency in a logic system doesn't establish that the system accurately models reality or resolves substantive metaphysical puzzles about composition.
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3.
The claim relies on unpacking 'relative identity' and 'divine nature' in ways that may equivocate, making the appearance of consistency an artifact of notation.
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Reasons Against
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Reason against
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1.
Relative identity allows 'x is identical to y relative to sortal F' without absolute identity, enabling three persons to be one God relative to divine nature.
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2.
Vohánka's non-theological analogues fail because they lack the metaphysical uniqueness of divine properties that ground theological relative identity claims.
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3.
Formal consistency differs from metaphysical possibility; Van Inwagen's logic shows Trinity avoids logical contradiction even if analogues remain impossible.
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