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International audience; The present study, focused on Shihāb al-Dīn Suhrawardī Ḥikmat al-Ishrāq, develops some preliminary explorations on his remarkable epistemology of presence, in light of his postulate of the priority of the experience of unity by presence. Furthermore, the paper should pave the way for responding to the challenges of Tony Street and others on the compatibility of Suhrawardī's critique of Ibn Sīnā with the development of a temporal and modal syllogism that seems quite close to that of Ibn Sīnā. Suhrawardī's modalities are to be understood as the different ways a predicate relates to its subject rather than as propositional operators. Necessarily necessary modality relates unconditionally the subject-term with the predicate-term; in contrast, necessarily contingent modality relates conditionally these terms. Moreover, necessarily necessary predication either admits simple conversion (corresponds to definition) or not (corresponds to genus). Necessarily contingent predication can also be declined in admitting simple conversion (corresponds to proprium) and not admitting this conversion (corresponds to accident). Necessarily contingent predication includes acquired potentialities or capacities such as literacy; and natural or not-acquired, such as breathing. Whereas predicating a not-acquired capacity of an actual individual involves time as focusing in one particular individual-e.g. laughing/breathing is necessarily but contingently said of humans since there must be at least one time when laughing is present, and one when it is absent concerning each individual; predicating an acquired capacity amounts to asserting such a contingency with regard to the whole genus-e.g., predicating literacy of humans assumes that at least one individual in at least one time actualizes literacy iff there is another human who does not-there are some variants related to commitment to either strong or Weak Plenitude (only acquired capacities seem to admit Weak Plenitude). We will put this at work in Suhrawardī's own (sketchy) framework for syllogism.