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Abstract

Building on observed similarities in uniqueness proofs for the empty set and the Necessary Existent (Wājib al-Wujūd), this study engages the meta-methodological issue of cross-system commensurability. It identifies four instances of structural commensurability between Zermelo-Fraenkel set theory with Choice (ZFC) and Mulla Sadra's Transcendent Wisdom (Ḥikmat al-Muta'āliyah). First, identity principles: the Axiom of Extensionality provides a formal operational criterion analogous to the philosophical principle of identity through absence of distinguishing features. Second, multiplicity mechanisms: ZFC's constructor axioms (bottom-up construction) and emanation principles (top-down explanation) address analogous problems with inverse orientations. Third, transcending limitation: the Axiom of Infinity ensuring quantitative extensional infinity addresses a problem formally parallel to (though ontologically distinct from) principles of gradation and nobler possibility demonstrating qualitative intensive perfection. Fourth, foundation principles: the Axiom of Regularity and impossibility of infinite regress both prohibit vicious circularity and guarantee well-foundedness through comparable logical patterns. The results suggest constraints on rational frameworks: while ZFC and Transcendent Wisdom are ontologically distinct, this analysis demonstrates they are relatively commensurable regarding their problem-solving strategies for universal challenges (identity, multiplicity, infinity, foundation), despite radical differences in content and epistemological status.

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