L’étude d’un document épigraphique antinoïte, jusqu’ici négligé, suggère que le géomètre Serenus, auteur de deux traités "Sur la section du cylindre" et "Sur la section du cône", vivait au début du IIIe siècle. Le réexamen plus précis d’un certain nombre d’éléments tirés tant des traités de Serenus que de la tradition indirecte permet de faire de celui-ci le continuateur tardif d’une tradition de recherches sur les coniques très liée à la catoptrique, remontant aux travaux pré-apolloniens sur la question menés autour (...) de Conon de Samos et de Pythion de Thasos. Cette hypothèse pose, corrélativement, le problème de la nature du platonisme de Serenus: on l’examine à la lumière du constructivisme de Ménechme. Enfin, la prise en compte d’un détail de la tradition arabe des "Coniques" d’Apollonius permet de préciser un élément dans la transmission textuelle des deux traités de Serenus. (shrink)

I discuss the exact meaning of the thesis according to which the object of scientific knowledge is necessary. The thesis is expressed by Aristotle in the Posterior Analytics, in his definition of scientific knowledge. The traditional interpretation understands this definition as depending on two parallel and independent requirements, the causality requirement and the necessity requirement. Against this interpretation, I try to show, through the examination of several passages that refer to the definition of scientific knowledge, that the necessity requirement specifies (...) more exactly the causality requirement: what cannot be otherwise is the explanatory relation between the explanandum and the cause by which it is what it is. (shrink)

In this article, I tackle a heretofore unnoticed difficulty with the application of Pyrrhonian scepticism to science. Sceptics can suspend belief regarding a dogmatic proposition only by setting up opposing arguments for and against that proposition. Since Sextus provides arguments exclusively against particular geometrical definitions in Adversus Mathematicos III, commentators have argued that Sextus’ method is not scepticism, but negative dogmatism. However, commentators have overlooked the fact that arguments in favour of particular geometrical definitions were absent in ancient geometry, and (...) hence unavailable to Sextus. While this might explain why they are also absent from Sextus’ text, I survey and evaluate various strategies to supply arguments in support of particular geometrical definitions. (shrink)

At Topics 8.11 161b19–33 Aristotle lists five criticisms () which may be leveled against a dialectical argument ‘in itself’ (). The five criticisms correspond in many respects to the familiar conditions Aristotle places on syllogism and refutation. However, begging the question —the violation of the condition that the conclusion of a syllogism be something different () from the premises—seems not to appear on the list of five criticisms. That this omission is only apparent becomes clear once it is seen that (...) the five criticisms are not independent but rather amount to five successive filters through which an argument may be passed before its non-genuineness is exposed. This result sheds light on Aristotle's curious insistence, in the face of the heterogeneity of his examples of BTQ in Topics 8.13, that every question-begging refutation contains a premise that is ‘the same’ as the conclusion. The fact that the five criticisms expose BTQ as a defect in syllogistic reasoni.. (shrink)

In this paper, I examine how the Mode of Infinite Regress functions in Pyrrhonian scepticism. I argue that it is used both to generate an infinite regress of reasons and to show that such infinite regresses are epistemically defective. I clarify precisely how this occurs while examining the Mode’s efficaciousness and whether ancient philosophers might have accepted infinite regresses of reasons. I ultimately argue that they would not for reasons which have hitherto not been adequately appreciated and which shed further (...) light on how the Mode of Infinite Regress functions, its efficacy, and the relevant notions of justification at stake. (shrink)

In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prior Analytics 2.5 he gives a more complex, syllogistic account. My aim is to show that these problems can be solved, and that (...) Aristotle’s third argument in 1.3 is successful. I argue that both chapters are concerned with the same conception of circular proof, namely the propositional one. Contrary to what is often thought, the syllogistic conception provides an adequate analysis of the internal deductive structure of the propositional one. Aristotle achieves this by employing a kind of multiple-conclusion logic. (shrink)

There is little agreement about Aristotle’s philosophy of geometry, partly due to the textual evidence and partly part to disagreement over what constitutes a plausible view. I keep separate the questions ‘What is Aristotle’s philosophy of geometry?’ and ‘Is Aristotle right?’, and consider the textual evidence in the context of Greek geometrical practice, and show that, for Aristotle, plane geometry is about properties of certain sensible objects—specifically, dimensional continuity—and certain properties possessed by actual and potential compass-and-straightedge drawings qua quantitative and (...) continuous. For their part, the objects of stereometry are potential sensible three-dimensional figures qua quantitative and continuous. (shrink)

Aristotle’s account of epistēmē is foundationalist. In contrast, the web of dialectical argumentation that constitutes justification for scientific principles is coherentist. Aristotle’s account of explanation is structurally parallel to the argument for a foundationalist account of justification. He accepts the first argument but his coherentist accounts of justification indicate that he would not accept the second. Where is the disanalogy? For Aristotle, the intelligibility of a demonstrative premise is the cause of the intelligibility of a demonstrated conclusion and causation is (...) asymmetric. Within the Posterior Analytics itself, Aristotle does not account for this, but elsewhere he develops the resources for doing so: the cause is what acts on a substrate to actualize a potential in that substrate, resulting in the effect. On the other hand, it may well happen that two propositions entail each other, in which case one may as well justify the one on the basis of the other as vice versa. (shrink)

This is a translation, made by myself, of the paper to be published in Portuguese in the journal Discurso, 2020, in honour of the late professor Oswaldo Porchat. I discuss what Aristotle was trying to encode when he said that the object of scientific knowledge is necessary, or that what we know (scientifically) cannot be otherwise etc. The paper is meant as a continuation of previous papers—orientated towards a book on the Posterior Analytics—and thus does not discuss in much detail (...) key passages, as the very definition of scientific knowledge in APo I.2, or passages from APo I.4 and I.6 (for these, I refer to my previous papers). This paper is mainly focused on Aristotle’s references to his notion of scientific knowledge both in other passages from the APo and in other treatises. I intend to show that there is a progressive, intrinsic relation between the two requirements by which scientific knowledge is defined. It is not true that each of these requirements stems from a different source. The Causal-Explanatory requirements gives Aristotle the general heading. Then, the Necessity Requirement ranges over the explanatory relation between explanans and explanandum and thereby specifies what sort of cause is sctricly required for having scientific knowledge of a given explanandum. Now, Aristotle was also concerned with the necessary truth of the elemental predications that constitute a demonstration. My claim that the Necessity Requirement ranges over the explanatory relation does not ignore that concern, and does not deny it. My claim is that Aristotle’s main focus, and main concern, consists in stressing that the explanatory factor to be captured in scientific knowledge of a given explanandum is such that cannot be otherwise. (shrink)

One of the hardest questions to answer for a (Neo)platonist is to what extent and how the changing and unreliable world of sense perception can itself be an object of scientific knowledge. My dissertation is a study of the answer given to that question by the Neoplatonist Proclus (Athens, 411-485) in his Commentary on Plato’s Timaeus. I present a new explanation of Proclus’ concept of nature and show that philosophy of nature consists of several related subdisciplines matching the ontological stratification (...) of nature. Moreover, I demonstrate that for Proclus philosophy of nature is a science, albeit a hypothetical one, which takes geometry as its methodological paradigm. I also offer an explanation of Proclus’ view of what is later called the mathematization of physics, i.e. the role of the substance of mathematics, as opposed to its method, in explaining the natural world. Finally, I discuss Proclus’ views of the discourse of philosophy of nature and its iconic character. (shrink)

This chapter discusses the first part of Aristotle's Posterior Analytics A-33, 88b30-89a10. I claim that Aristotle is not concerned with an epistemological distinction between knowledge and belief in general. He is rather making a contrast between scientific knowledge (which is equivalent to explanation by the primarily appropriate cause) and some explanatory beliefs that falls short of capturing the primarily appropriate cause.