In Arabic treatises on algebra, Book II of Euclid’s Elements quickly became a traditional work of reference, especially for justifying quadratic equations. However, in many of these treatises we find a representation of Euclid’s notions that deviates from the “original Euclid.” In this article, I focus on the way in which propositions of Book II were understood and reported by al-Karaǧī (11th c.) in two of his algebraic writings. Inspired by the variety of arithmetical practices of his time, al-Karaǧī transposed these Euclidean propositions from geometrical objects to numbers and applied them to an algebraic context. This allowed him to combine various argumentative strategies deriving from different fields. Building upon al-Karaǧī’s work, al-Zanǧānī (13th c.) no longer needed to mention Euclid and instead conceived of a justification of quadratic equations (the “cause” of the equation) which is completely internal to algebra. These case studies provide evidence for the use of the Elements as a toolbox for the development of algebra. More importantly, they shed further light upon a typical feature of medieval mathematics, namely the existence of a plurality intrinsic in the name “Euclid.”

Nous entendons dans cet article éditer, traduire et analyser un texte datant du xiiie siècle dans lequel figurent des preuves arithmétiques de la proposition selon laquelle la somme des carrés de deux nombres impairs ne peut pas être un carré. Cette proposition avait déjà été démontrée par al-Ḫāzin au xe siècle par le biais des propositions 3 et 5 du livre II et de la proposition 22 du livre IX des Éléments d’Euclide.

Avicenna is well-known for rejecting Aristotle’s dichotomy between perception and the intellect by introducing the so-called estimative power, which connects perception and the intellect. The estimative power is similar to sensory cognition because what is estimated is always mixed with the sensibles. Additionally, the proper object of estimation is the individualised macnā, which seems similar to the object of the intellect as the intelligible macnā. Given the special role of estimation, scholars have recently begun debating whether Avicenna has a conceptualist theory of perception. This article contributes to that debate by focusing on Avicenna’s discussions about the perception of externals in Al-taclīqāt. I argue for a reading that steers between Mohammad Azadpur’s conceptualist reading and Luis Farjeat’s anti-conceptualist reading. For Avicenna, the presence of the sensible form in a sensory power is non-conceptual, but the perceptual judgement exhibits a weak epistemic conceptualism.

This study tries to shed further light on Avicenna’s (d. 1037) philosophical and linguistic innovations as suggested in his various accounts of the problem of individuation. To better contextualize his discussions, a background is given from both Porphyry’s (d. 305) Isagoge and Fārābī’s (d. 950) remarks in his Isāġūǧī. I have also enumerated all the candidates for the principle of individuation in Avicenna’s œuvre. It is argued in this paper that the pre-Avicennian Peripatetic tradition hardly engaged, both epistemologically and ontologically, with individual per se as having its own unique identity. Instead, individual was ontologically treated as instantiation of universals and epistemologically it was inquired about to the extent that it could be only told apart. Introducing the notion of individuation as tašaḫḫuṣ, instead of the traditional individuation as tamayyuz, Avicenna offers a new way of looking at intra-species differences for a more complex understanding of the individual per se. According to this view, individual with its unique šaḫṣiyya must be understood on its own through sense perception. This approach appears to propose that the individual should not be deemed as subordinate to Aristotelian universals whose assemblage, in Peripatetic thought, was vainly expected to lead to the knowledge and definition of the individual.

Avicenna’s distinction between external existence and mental existence is seminal to logic and philosophy in the Islamic tradition. This article examines philosophers who depart from Avicenna’s external-mental existence framework. They view the former as failing to support a general analysis of reality and truth, as mental existence is neither necessary nor sufficient for analyzing propositional truths, i.e., true propositions are true irrespective of “the very existence of minds” and “the perceptual acts of perceivers.” They propose that Avicenna’s semantics for categorical propositions needs revision, as there are true metathetic and hypothetical propositions, i.e., subject terms need not exist – in external reality or in a mind – for such propositions to be true. This counter-Avicennan current of thought articulates a third distinction in the analysis of reality, which focuses on the mind-independent nature of propositional content – particularly propositions with empty, hypothetical, or impossible subject terms – as a way to think generally about reality, in contrast to the Avicennan emphasis on the existential status of terms and essences. Notably, the analysis of mind-independent reality is supported by a novel semantics of “real” (ḥaqīqī) categorical propositions, which avoids external and mental existence conditions.