Avicenna's Philosophy of Mathematics

I discuss four different aspects of Avicenna’s philosophical views on mathematics, as scattered across his various works. I first explore the negative aspect of his ontology of mathematics, which concerns the question of what mathematical objects (i.e., numbers and geometrical shapes) are not. Avicenna argues that mathematical objects are not independent immaterial substances. They cannot be fully separated from matter. He rejects what is now called mathematical Platonism. However, his understanding of Plato’s view about the nature of mathematical objects differs from both Plato’s actual view and the view that Aristotle attributes to Plato. Second, I explore the positive aspect of Avicenna’s ontology of mathematics, which is developed in response to the question of what mathematical objects are. He considers mathematical objects to be specific properties of material objects actually existing in the extramental world. Mathematical objects can be separated, in mind, from all the specific kinds of matter to which they are actually attached in the extramental word. Nonetheless, inasmuch as they are subject to mathematical study, they cannot be separated from materiality itself. Even in mind they should be considered as properties of material entities. Third, I scrutinize Avicenna’s understanding of mathematical infinity. Like Aristotle, he rejects the infinity of numbers and magnitudes. But he does so by providing arguments that are much more sophisticated than their Aristotelian ancestors. By analyzing the structure of his Mapping Argument against the actuality of infinity, I show that his understanding of the notion of infinity is much more modern than we might expect. Finally, I engage with Avicenna’s views on the epistemology of mathematics. He endorses concept empiricism and judgment rationalism regarding mathematics. He believes that we cannot grasp any mathematical concepts unless we first have had some specific perceptual experiences. It is only through the ineliminable and irreplaceable operation of the faculties of estimation and imagination upon some sensible data that we can grasp mathematical concepts. By contrast, after grasping the required mathematical concepts, independently from all other faculties, the intellect alone can prove mathematical theorems. Other faculties, and in particular the cogitative faculty, can assist the intellect in this regard; but the participation of such faculties is merely facilitative and by no means necessary

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available

Michel Foucault : topologies of thought : thinking-otherwise between knowledge, power and self

If something new has appeared in philosophy and that "this work is as beautiful as those it challenges" we shall see that it all takes place in a new dimension, "which we might call a diagonal dimension, a sort of distribution of points, groups or figures that no longer simply act as an abstract framework but actually exist in space". The spaces that constitute this immanent dimension are topological or as Foucault says - "heterotopological". We shall designate these heterotopologies: Knowledge, Power and Self. Although these sites are irreducible to each other they seep into and 'capture' each other through a series of multiple and complex relations in such a way as to suspect, neutralise or invert the set of relations that they happen to designate, mirror or reflect. If within these sites subjects, objects and concepts disappear it is only in order to 'disperse' or 'distribute' them according to their variable functions and make them reappear again, released of their 'self-evidence', in a new space of immanence. Each heterotopology is capable of juxtaposing within itself and outside of itself, or rather across its folded surfaces, several formed spaces that are not isomorphic or even compatible but are heterogeneous and communicate with or 'encounter' each other through a pure transmission of elements

Creating Through Mind and Emotions

The texts presented in Proportion Harmonies and Identities (PHI) Creating Through Mind and Emotions were compiled to establish a multidisciplinary platform for presenting, interacting, and disseminating research. This platform also aims to foster the awareness and discussion on Creating Through Mind and Emotions, focusing on different visions relevant to Architecture, Arts and Humanities, Design and Social Sciences, and its importance and benefits for the sense of identity, both individual and communal. The idea of Creating Through Mind and Emotions has been a powerful motor for development since the Western Early Modern Age. Its theoretical and practical foundations have become the working tools of scientists, philosophers, and artists, who seek strategies and policies to accelerate the development process in different contexts

The Imaginary Context in Nahj al-Balāghah: Theory and Practice

Poetic language can make an epistemological contribution. It is the purpose of this thesis to argue that the poetic language employed by Nahj al-Balāghah makes such a contribution, through its uses of the “imaginary context”. While poetic imagery is described by some schools of thought as mere ornamentation within a text, it has been recognised by philosophers of language, such as Al-Fārābī (d.339/950) and his followers, as having an effect on the soul. This idea is part of Al-Fārābī’s logical system in which demonstration – intended to bring about assent – is the highest practice for the tools of logical thought, such as syllogism. Yet, takhyīl [the imaginary] which affects the soul is a result of the poetic syllogism; a syllogism appearing at the lowest level of logic. Al-Sharīf al-Raḍī (d.406/1016) was a well-known poet and Shīʿī exegete in tenth-century Baghdad. He compiled Nahj al-Balāghah, which consists of sermons, letters and aphorisms of ʿAlī ibn Abī Ṭālib (d.40/661), the first imam and fourth caliph. The time of Al-Sharīf al-Raḍī was one in which intellectual contributions in different fields reached their peak. Social gatherings, disputation and the emergence and development of different sects contributed to the enrichment of cultural and intellectual life in the Islamic world. The Muʿtazilite school was known for its rational approach, rather than reliance on the interpretation of revelation transmitted through generations; as such, the Muʿtazilī approach has had a profound and long-lasting impact on some major schools of Islamic thought. Al-Sharīf al-Raḍī was a scholar who followed this approach and utilised his own forms of interpretation based upon his linguistic and poetic knowledge. Through understanding Al-Sharīf al-Raḍī’s poetic approach, and via a reading of Al-Fārābī’s linguistic philosophy and thoughts on logic, I argue that Nahj al-Balāghah utilises the rational tools that were considered valid, not only to influence the soul by the power of language, but also to educate people through poetic language. This can only be proved through a recognition of the “imaginary context” present within the texts I discuss, a term I develop from Al-Fārābī’s takhyīl. This context, as this thesis attempts to show, has its own logic, constructed by building images upon each other, and by establishing poetic relationships between elements, which depend on predicative propositions that are also, in their essence, poetic

Computational intelligence approaches to robotics, automation, and control [Volume guest editors]

No abstract available