Elucidating the relationship between subject and predicate in demonstrative propositions (qaḍāyā burhāniyya) and applying the criterion of the essential accident (ʿaraḍ dhātiyya) to philosophical predicates (maḥmūlāt falsafiyya) have long remained among the most challenging and ambiguous issues in logic and philosophy. This study investigates an apparent duality in Allāmah Ṭabāṭabāʾī's view of the criterion for essential accidents. On the one hand, grounded in the concept of relational existence (wujūd rābiṭ), Ṭabāṭabāʾī considers the subject to be among the existential causes of the predicate. On the other hand, by advancing the theory of co-extensionality (tasāwuq), he emphasizes the mutual equality of all philosophical predicates with the subject of ultimate reality, thereby rejecting narrower or specific accidents (ʿāriḍ akhāṣṣ). Employing a descriptive-analytical methodology, this study reconciles these two accounts by establishing a clear distinction between quidditative demonstrative sciences (ʿulūm burhāniyya māhiyya) and metaphysics proper (ʿilm al-falsafa). The findings indicate that Ṭabāṭabāʾī’s framework in metaphysics rests upon tasāwuq, which entails the rejection of propter quid demonstration (burhān limmī) and its replacement with the method of general concomitances (mulāzamāt ʿāmma). In contrast, in other demonstrative sciences, his criterion aligns with the conventional Avicennan view—namely, inclusion in the definition (akhdh fī al-ḥadd). Finally, alongside explicating this dual framework, this paper provides well-founded responses to several objections raised by critics against the condition of equality (tasāwī) and the negation of specific accidents in philosophy.