Mainly based on the study of a hitherto neglected epigraphic document from Antinoë, the present article aims at showing that the geometer Serenus – the author of two treatises On the Section of a Cylinder and On the Section of a Cone – lived at the beginning of the 3rdcentury AD. On the ground of a renewed study of various elements taken both from the treatises and the indirect tradition, it also suggests that Serenus must be placed among a scientific tradition closely linking geometry of conics and catoptrics that can be traced back to the works of Conon of Samos and Pythion of Thasos. This hypothesis raises the problem of the nature of his alleged Platonism, which is examined in relation to Menaechmus' heterodox constructivism. Finally, the study of an element in the Arabic transmission of the treatise on Conics by Apollonius enables us to clarify some point regarding the textual tradition of the treatises On the Section of a Cylinder and On the Section of a Cone.

I examine the theory of conditional propositions (qaḍāyā šarṭiyya muttaṣila) and conditional syllogisms (qiyāsāt šarṭiyya) in the logical works of Alfarabi (d. 950). I contextualize Alfarabi's logical doctrines related to conditional reasoning against the backdrop of the context-theory of logic, which was developed by Aristotle's ancient commentators. I show that Alfarabi thought that conditional propositions have truth-conditions. I provide conjectural truth-conditions for conditional propositions, and conjectural validity-conditions for connective conditional syllogisms. These truth-conditions and validity-conditions are shown to be sensitive to the pragmatic conditions in which conditional propositions and arguments are deployed. I end by suggesting that Alfarabi's logical pragmatism is a consequence of his adoption of the late antique context-theory of logic rather than a result of his developing Aristotle's formal syllogistic theory adumbrated in the Prior Analytics.

The article aims to demonstrate that Avicenna's (d. 428/1037) centrality in Islamic intellectual history is not restricted to the branches of theoretical philosophy; rather, he also has had a deep and strong influence on the conception of practical philosophy until modern times. I will discuss the impact of Avicenna's view of practical philosophy by analyzing his different classifications of practical philosophy throughout his career and the factors behind his disregard for practical philosophy in his philosophical summas on the basis of his view of the relationship between philosophy and šarīʿa. To demonstrate my argument regarding Avicenna's influence on the conception of practical philosophy in Islamic tradition, I will refer to major works on the classification of sciences, and the commentaries (šurūḥ) and glosses (ḥāwāšī) on the two most important and widely circulated philosophical summas in the post-Avicennan philosophy, which are al-Abharī's (d. 663/1264) Hidāyat al-ḥikma and al-Kātibī's (d. 675/1276) Ḥikmat al-ʿayn.

Aristotle did not develop the quantification of the predicate, but, as shown in a recent paper by Hasnawi, Ibn Sīnā did. In fact, assuming the Aristotelian subject-predicate structure, Ibn Sīnā qualifies those propositions that carry a quantified predicate as deviating (muḥarrafa) propositions. A consequence of Ibn Sīnā’s approach is that the second quantification is absorbed by the predicate term. The clear differentiation between a quantified subject, that settles the domain of quantification, and a predicative part, that builds a proposition over this domain, corresponds structurally to the distinction, made in constructive type theory, between the type of sets and the type of propositions.

Neither did Aristotle combine his logical analysis of quantification with his ontological theory of relations or equality. But Ibn Sīnā makes use of syllogisms that require a logic of equality, and considered cases where quantification combines via equality with singular terms. Moreover these reflections provide the basis for his theory of numbers that is based on the interplay between the One and the Many. If we combine Ibn Sīnā’s metaphysical theory of equality with his work on the quantification of the predicate, a logic of equality comes out naturally. Indeed, the interaction between quantification of the predicate and equality can be applied to Ibn Sīnā’s own examples of syllogisms involving these notions. By using the formal instruments provided Martin-Löf's constructive type theory, the present paper establishes links between Ibn Sīnā’s metaphysics and his logical work: links that have been discussed in relation to other topics by Thom and Street. Ibn Sīnā did not develop a logic of identity, but he did develop the conceptual means to do so.