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The Unity of Science in the Arabic Tradition: Science, Logic, Epistemology and their Interactions

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Abstract

the demise of the logical positivism programme. The answers given to these qu- tions have deepened the already existing gap between philosophy and the history and practice of science. While the positivists argued for a spontaneous, steady and continuous growth of scientific knowledge the post-positivists make a strong case for a fundamental discontinuity in the development of science which can only be explained by extrascientific factors. The political, social and cultural environment, the argument goes on, determine both the questions and the terms in which they should be answered. Accordingly, the sociological and historical interpretation - volves in fact two kinds of discontinuity which are closely related: the discontinuity of science as such and the discontinuity of the more inclusive political and social context of its development. More precisely it explains the discontinuity of the former by the discontinuity of the latter subordinating in effect the history of science to the wider political and social history. The underlying idea is that each historical and - cial context generates scientific and philosophical questions of its own. From this point of view the question surrounding the nature of knowledge and its development are entirely new topics typical of the twentieth-century social context reflecting both the level and the scale of the development of science.

Chapters (11)

We try to find the answers to two main questions of philosophy of mathematics Philosophy of mathematics in Ibn Sīnā’s philosophy, i.e. what and where are mathematical objects Mathematical objects? And how can we know mathematical objects? Ibn Sīnā’s ontology implies that mathematical objects are mental objects. In his epistemology, Ibn Sīnā emphasises on intuition andthinking as two main ways of attaining mathematical knowledge Mathematical knowledge. Moreover, Ibn Sīnā’s analysis of mathematical propositions implies that they are synthetic a priori judgements Synthetic!a priori judgements in the sense of Kant.
One of the most well-known elements of Avicenna’s philosophy is the famous thought experiment known as the “Flying Man.” The Flying Man argument attempts to show that the soul possesses innate awareness of itself, and it has often been viewed as forerunner to the Cartesian cogito. But Avicenna’s reflections on the nature of self-awareness and self-consciousness are by no means confined to the various versions of the Flying Man. Two of Avicenna’s latest works, the Investigations and the Notes, contain numerous discussions of the soul’s awareness of itself. From an examination of these works I show that Avicenna recognizes two distinct levels of self-knowledge: (1) primitive self-awareness, which is illustrated by the Flying Man; and (2) reflexive self-awareness, which comes from our awareness of cognizing some object other than ourselves. While Avicenna assigns primitive self-awareness a central role in ensuring the unity of the soul’s operations, he encounters a number of difficulties in his efforts to explicate the relation of primitive self-awareness to the reflexive varieties of self-knowledge that he inherits from the Aristotelian tradition.
Arabic algebra derives its epistemic value not from proofs but from correctly performing calculations using coequal polynomials. This idea of ‘mathematics as calculation’ had an important influence on the epistemological status of European mathematics until the seventeenth century. We analyze the basic concepts of early Arabic algebra such as the unknown and the equation and their subsequent changes within the Italian abacus tradition. We demonstrate that the use of these concepts has been problematic in several aspects. Early Arabic algebra reveals anomalies which can be attributed to the diversity of influences in which the al-jabr practice flourished. We argue that the concept of a symbolic equation as it emerges in algebra textbooks around 1550 is fundamentally different from the ‘equation’ as known in Arabic algebra.
This study provides a survey of Avicenna’s theoretical or abstract discussions of the methods of science and the psychological processes laying behind them as they appear in his Kitāb al-Burhān. Since that text has not been studied in-depth, the chapter is primarily exegetical, focusing what might be termed Avicenna’s ‘naturalized epistemology’. The study is divided into two sections. The first treats Avicenna’s theory of demonstrative knowledge, and how Avicenna envisions the relation between logic and science, where it is argued that one of the primary functions of Kitāb al-Burhān is to provide heuristic aids to the scientist in his investigation of the world. The second half concerns Avicenna’s empirical attitude in Kitāb al-Burhān towards acquiring the first principles of a science, where such cognitive processes as abstraction, induction and methodic experience are considered.
Is there a philosophy of mathematics in classical Islam? If so, what are the conditions and the scope of its presence? To answer these questions, hitherto left unnoticed, it is not sufficient to present the philosophical views on mathematics, but one should examine the interactions between mathematics and theoretical philosophy. These interactions are numerous, and mainly foundational. Mathematics has provided to theoretical philosophy some of its central themes, methods of exposition and techniques of argumentation. The aim of this chapter is to study some of these interactions, in an effort to give some answers to the questions raised above. The themes which will be successively discussed are mathematics as a model for the philosophical activity (al-Kindī, Maimonides), mathematics in the philosophical syntheses (Ibn Sīnā, Nasīr al-Dīn al-Tūsī), and finally the constitution of ars analytica (Thābit ibn Qurra, Ibn Sinān, al-Sijzī, Ibn al-Haytham).
The so-called Copernican revolution is Kuhn’s most cherished example in his conception of the non-cumulative development of science. Indeed, in his view not only has the Copernican model introduced a major discontinuity in the history of science but the new paradigm and the old paradigm are incommensurable, i.e. the gap between the two models is so huge that the changes introduced in the new model cannot be understood in terms of the concepts of the old one. The aim of this chapter is to show on the contrary that the study of the Arabic tradition can bridge the gap assumed by Kuhn as a historical fact precisely in the case of Copernicus. The changes involved in the work of Copernicus arise, in our view, as a result of interweaving epistemological and mathematical controversies in the Arabic tradition which challenged the Ptolemaic model. Our main case study is the work of Ibn al-Haytham who devotes a whole book to the task of refuting the implications of the Almagest machinery. Ibn al-Haytham’s al-Shukūkhad such an impact that since its disclosure the Almagest stopped being seen as the suitable model of the heavenly bodies. Numerous attempts have been made to find new alternative models based on the correct principles of physics following the strong appeal launched by both Ibn al-Haytham and, after him, Ibn Rushd. The work of Ibn al-Shāir, based exclusively on the concept of uniform circular motion, represents the climax of the intense theoretical research undertaken during the thirteenth and the fourteenth centuries by the Marāgha School (which owes its name to the observatory of Marāgha in north-western Iran). The connection point, in our view, between the works of Ibn al-Haytham and Ibn al-Shā ir is that while the al-Shukūk gives the elements to build a countermodel to the Almagest, the work of Ibn al-Shā ir offers a model which takes care of the objections triggered by the work of Ibn al-Haytham. Furthermore, not only has the basic identity of the models of Ibn al-Shā ir and Copernicus been established by recent researches, but it was also found out that Copernicus used the very same mathematical apparatus which was developed by the Marāgha School over at least two centuries. Striking is the fact that Copernicus uses without proof mathematical results already geometrically proven by the Marāgha School three centuries before. Our paper will show that Copernicus was in fact working under the influence of the two streams of the Arabic tradition: the well known more philosophical western stream, known as physical realism, and the newly discovered eastern mathematical stream. The first relates to the idea that astronomy must be based on physics and that physics is about the real nature of things. The second relates to the use of mathematics in the construction of models and countermodels in astronomy as developed by the Marāgha School. The case presented challenges the role of the Arabic tradition assigned by the standard interpretation of the history of science and more generally presents a first step towards a reconsideration of the thesis of discontinuity in the history of science. Our view is that major changes in the development of science might sometimes be non-cumulative, though this is not a case against continuity understood as the result of a constant interweaving of a net of controversies inside and beyond science itself.
The word, tropos, translated in Arabic as jiha, is understood in the field of logic as mode. Though investigations of modals in the medieval Arabo-Islamic logical tradition trace their lineage back to Aristotle, the Greek word designating this concept was never used in this manner by the Stagirite. The closest word that the Arabic jiha translates from Greek is tropos, which was a technical term that gradually developed with Aristotle’s commentators. The word came to be understood as part of a dichotomy, tropos-hûlç, which was inherited by the Arabs as jiha-mādda This dichotomy seems to have become a determining factor for conversion rules of modal propositions and thus for modal syllogistic. After an investigation outlining the evolution of the term tropos and the development of the dichotomy tropos-hûlç in the Commentary tradition of modal logic, the article presents philological evidence for their influence on Avicenna. It then briefly discuss the ramifications of this influence for his modal conversion rules and syllogistic. In sum, the article argues that the jiha-mādda (tropos-hûlç) division was part of a larger dichotomy that allowed Avicenna to construe propositions in various ways. How he understood a given proposition determined the validity of its conversion and so of its place in his modal syllogistic.
A current ideology has it that different cultural traditions have privileged sources of insight and ways of knowing. Prizing one tradition over another would reek of cultural imperialism. In this vein we have those pushing for a unique status for Islamic philosophy: it should have its rightful place alongside Western philosophy—and no doubt alongside Chinese philosophy, Indian philosophy, African philosophy…. I begin by examining what could be meant by ‘Islamic philosophy’. I argue that embracing a multiculturalism that makes the philosophic enterprise relative to particular cultural traditions ignores a quite important part of the Islamic philosophical tradition itself: the quest for a transcultural, universal objectivity. The major Islamic philosophers embraced this ideal: al-Fārābī and Ibn Sīnā (Avicenna), for instance. They held that some cultures are better than others at attaining philosophical wisdom, and some languages better than others at expressing it. They advocated selecting critically features from the different cultures for constructing a general theory. I illustrate their method by considering their treatment of paronymy and the copula. I end by advocating a return to this Islamic tradition.
Avicenna (Ibn Sīnā, d. 1037) devotes two chapters of al-‘Ibāra to the quantification of the predicate. Al-‘Ibāra is the third treatise of the logical collection of his philosophical encyclopedia entitled al-Shifā’ (The Cure). An English translation of these two chapters, the first in any language, is offered here. This translation is preceded by an analysis of the content of these chapters and is followed by an Appendix containing a translation of [Ibn Zur‘a]’s treatment of the same topic. (The name of Ibn Zur‘a, d. 1027, is bracketed to indicate a problem of authorship). The whole dossier is intended to pave the way for further studies of this subject. Avicenna’s treatment of the quantification of the predicate has the following distinctive features: he deals systematically with singular and indefinite propositions; he states correctly the contradictories of the eight doubly quantified proposition forms which he enumerates; he is aware of the equivalence between two of these forms but makes no attempt to reduce the number of these forms to a selected basic set of them. It is suggested that Avicenna thought of the logic of doubly quantified propositions on the model of propositions with an indefinite predicate (S is not-P). Contrary to his predecessors, Avicenna did not reject a priori these proposition forms and he countered arguments supporting such a rejection.
Recent studies on Avicenna’s modal syllogistic have pointed out the significance of his distinction between the understanding of predications ‘with regard to essence/essentially’ (dhātī) and ‘with regard to escription/descriptionally’ (wasfī) (Street 2000a, 2000b, 2005a, 2005b). In this chapter I investigate the grammatical, theological and metaphysical context of Avicenna’s understanding of that what is ‘derived’ (mushtaqq) either with regard to essence/essentially or with regard to description/descriptionally. I argue that this distinction is based on two different kinds of understanding ‘derivation’ (ishtiqāq). The Arabic grammarian Sibawayh distin-guished two classes of the ‘derived’: [a.] “[the name of] the agent” ([ism] al-fā’il) and [b.] “the description/attribute which is similar to [the name of] the agent” (al-sifa al-mushabbaha bi-l-fū’il). These terms can be understood as derived either logically or grammatically. I argue that Avicenna’s dhātī-reading is based on the logical derivation of the ‘name of an agent’ or the ‘description/attribute’ from a noun which signifies an abstracted essence, and that Avicenna’s wasfi-reading is based on their grammatical derivation from a verb/acting (fi’l) which indicates the occuring (hudūth) and the happening (husūl) of an acting (fi’l) or of an affection by a quality (sifa). Thus, Avicenna’s dhātī/wasfī distinction is a typical product of the mutual rapprochement between Neoplatonic and Peripatetic metaphysics and logic on one hand and Arabic grammar on the other hand. I further argue that the dhātī/wasfī distinction is not only basic for Avicenna’s syllogistic, but also for al-Ghazālī’s semantical-logical explanation of the names of God.
Recent discussions of Avicenna’s modal syllogistic by Street (2000), Street (2002) and Thom (2003) have adopted a simple de re reading of Avicenna’s dhātī propositions, and either ignored or rejected the possibility of metaphysical applications for his modal theory. In this chapter I seek to supplement these interpretations by exploring an interpretation of Avicenna’s dhātī propositions that incorporates a de dicto element. I argue that, given such a reading, his absolute and modal propositions have application to Aristotelian metaphysical theory.
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