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According to the standard and largely traditional interpretation, Aristotle’s conception of nous, at least as it occurs in the Posterior Analytics, is geared against a certain set of skeptical worries about the possibility of scientific knowledge, and ultimately of the knowledge of Aristotelian first principles. On this view, Aristotle introduces nous as an intuitive faculty that grasps the first principles once and for all as true in such a way that it does not leave any room for the skeptic to (...) |
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This paper reconstructs the account of concept formation developed in the 4th Century A.D. by Themistius in the most ancient extant commentary on Aristotle’s Posterior Analytics. Themistius’ account can be contrasted with two widespread modern interpretations of Aristotle. Unlike psychological empiricists, Themistius ascribes an active role in concept formation to our innate capacity of understanding. Unlike intuitionists, he would not be satisfied by saying that νοῦς “intuits” or “spots” concepts. Rather, the question is what makes our νοῦς capable of “finding” (...) |
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With the systematic aim of clarifying the phenomenon sometimes described as “the intellectual apprehension of first principles,” Descartes’ first principle par excellence is interpreted before the historical backcloth of Aristotle’s Posterior Analytics. To begin with, three “faces” of the cogito are distinguished: (1) the proto-cogito (“I think”), (2) the cogito proper (“I think, therefore I am”), and (3) the cogito principle (“Whatever thinks, is”). There follows a detailed (though inevitably somewhat conjectural) reconstruction of the transition of the mind from (1) (...) |
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Dans un célèbre ouvrage surContemplation et Vie contemplative selon Platon, A.J. Festugière donnait de la dialectique platonicienne une interprétation selon laquelle celle-ci constituait une véritable expérience mystique possédant presque tous les traits de la contemplation chrétienne. La dialectique platonicienne y était présentée, surtout dans son acte final, comme une sorte d'extase, une union d'ordre mystique, un contact de l'âme perdue dans son objet, contact qui suscite en elle un sentiment qui dépasse tout l'ordre normal de la connaissance. Le Bien ou (...) |
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Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this reason, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the concept (...) |
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The article comments on the epistemological foundations of medieval Arabic science and philosophy, as presented in five earlier communications, and attempts to draw some guidelines for the study of its social history. At the very beginning the notion of "Islam" is discounted as a meaningful explanatory category for historical investigation. A first part then looks at the applied sciences and notes three major characteristics of their epistemological approach: they were functionalist and based on experience and observation. The second part looks (...) |
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Newton's Principia begins with eight formal definitions and a scholium, the so-called scholium on space and time. Despite a history of misinterpretation, scholars now largely agree that the purpose of the scholium is to establish and defend the de fi nitions of key concepts. There is no consensus, however, on how those definitions differ in kind from the Principia's formal definitions and why they are set-off in a scholium. The purpose of the present essay is to shed light on the (...) |
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This article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully general, (...) |
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Book 1 of Euclid's Elements opens with a set of unproved assumptions: definitions, postulates, and ‘common notions’. The common notions are general rules validating deductions that involve the relations of equality and congruence. The attested postulates are five in number, even if a part of the manuscript tradition adds a sixth, almost surely spurious, that in some manuscripts features as the ninth, and last, common notion. The postulates are called αἰτήματα both in the manuscripts of the Elements and in the (...) |
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Although there are many questions to be asked about philosophy of mathematics, the fundamental questions to be asked will be questions about what the mathematical object is in view of being and what the mathematical reasoning is in view of knowledge. It is clear that other problems will develop in parallel within the framework of the answers to these questions. For this rea son, when we approach Aristotle's philosophy of mathematics over these two basic problems, we come up with the (...) |
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I argue that these inconsistencies in wording and practice reflect the existence of two distinct Aristotelian views of inquiry, one peculiar to the Posterior Analytics and the other put forward in the Physics and practiced in the Physics and in other treatises. Although the two views overlap to some degree (e.g. both regard a rudimentary understanding of the subject as an essential first stage), the view of the syllogism as the workhorse of scientific investigation and the related view of inquiry (...) |
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