We prove that the Cutting Plane proof system based on Gomory–Chvátal cuts polynomially simulates the lift-and-project system with integer coefficients written in unary. The restriction on the coefficients can be omitted when using Krajíček’s cut-free Gentzen-style extension of both systems. We also prove that Tseitin tautologies have short proofs in this extension.

While Aristotle adverts in the Politica to those who have declared themselves about the aristē or best politeia without qualification, he actually devotes much of his attention here to telling his intended audience how to establish and maintain the aristē politeia for each of the different places in which each of them is engaged, given the circumstances. In the face of this contrast in the Politica, scholars look to EN 1135a5 for clarification. According to the established interpretation of EN 1135a5, (...) Aristotle means that there is only one politeia that is best by nature for every place. According to the alternative interpretation, Aristotle means that, for every place, there is only one politeia that is best by nature for it. In this paper it is argued that the alternative interpretation fits both works better than does the established interpretation. (shrink)

Islamic philosophy; philosophy, Ancient.

In this article, I claim that the treatise known as περὶ πνεύματος/De spiritu (481a-486b Bekker) was written by Theophrastus. My overall argument unfolds in three stages: first, I briefly summarize the arguments against De spiritu’s authenticity in Aristotle’s corpus. This summary will lead to my first argument which uses the very same reasons that prove the non-Aristotelian authorship to claim the Theophrastean one, in particular linguistic aspects of the text (§2). Next, I will focus on chronology, by discussing the mention (...) of one Aristogenes to show that Aristotle could not have known this individual (§3). Third and last, I will examine various aspects of the work that demonstrate stylistic and argumentative connections (§4), as well as doctrinal affinities with the works of Theophrastus, although some have attributed it to Strato (§5). On the basis of these arguments, I conclude that the weight of the evidence makes On Breath a work by Theophrastus (or his circle) rather than one composed by Aristotle. (shrink)

The two slaves, Xanthias and Sosias, posted by their master's son to guard his ‘sick’ father Philocleon, challenge the audience to guess the nature of the mysterious and strange disease &nuó&sgr&ogr&nu &lambda&lambdaó&kappa&ogr&tau&ogr&nu, 71) on account of which the father must be kept inside the house. When the correct answer to the riddle is finally disclosed, Philocleon is revealed to beis revealed to be φιληλιαστσ , namely a man ‘who loves to be a juror’ and to spend his days in the (...) law-courts passionately pursuing the infatuation of which his son tries to cure him by locking him up away from the law-courts and from his fellow jurors. The joke owes its comic effect to incongruity, termed the ‘humour of inappropriateness’ by MacDowell, who writes: ‘It is funny when addiction to being a juror is called a disease , because “disease” is a word which is not generally applied to such conditions’. It should, however, be stressed that in order to create this sense of incongruity the previously mentioned diseases must form a class with certain common characteristics fundamentally different from those of Philocleon's, thus gradually moulding the audience's expectations and channelling them in a completely different direction. (shrink)

This article aims at elucidating the logic of Arist. SE 22, 178b36–179a10 and, in particular, of the sophism labelled "Third Man" discussed in it. I suggest that neither the sophistic Walking Man argument, proposed by ancient commentators, nor the Aristotelian Third Man of the , suggested by modern interpreters, can be identified with the fallacious argument Aristotle presents and solves in the passage. I propose an alternative reconstruction of the Third Man sophism and argue that an explanation of the (...) lines regarding the identity of Coriscus and Coriscus the musician (178b39–179a3) is indispensable for its correct understanding, since they hint at another sophism in some important aspects analogous. Finally, I show that two contradictions concerning spotted by scholars in the passage are only apparent and can be dissolved once the assumption that the anti-Platonic Third Man argument is at stake here is discarded, and once the passage is read in the light of its agonistic context. (shrink)

Several features of this compact passage have puzzled scholars ever since the discovery of the Aristotelian Constitution of the Athenians a century ago. First, did the Athenian Assembly really deliberate on all these disparate matters in the chief meeting of the sixth prytany, and if so, why? Second, why did it limit complaints against sycophants to a total of six divided equally between citizens and metics? Since the answers we give to these questions are fundamental to our understanding of basic (...) Athenian institutions, they deserve careful consideration. This paper will argue that the Assembly did deliberate on these matters at the same meeting and indeed that this was natural, since they are all symbolic, as well as practical, instruments for controlling behaviour inimical to the demos' interests. It will also suggest that the limitation on probolai against citizen and metic sycophants was introduced to safeguard against the sort of abuse of the label ‘sycophant’ that took place under the regime of the Thirty, and that the measures described in Ath. Pol. 43.5 were, therefore, most likely linked together in the early years of the restored democracy. (shrink)

With regard to Aristotle’s discussion of chance and fortune in Phys. II.5–6, interpreters maintain that, after having provided a specific definition of fortune, applicable to intentional chance processes, in ch. 5, Aristotle is, in ch. 6, seeking to identify a specific meaning of αὐτόματον, which exclusively applies to strictly natural chance processes. When understood in such terms, however, ch. 6 turns out to be problematic, insofar as the examples Aristotle uses to illustrate αὐτόματον refer to mixed natural and intentional chance (...) processes. To show that ch. 6 is internally consistent, I will argue that Aristotle’s goal simply is to emphasise the generic quality of the notion of αὐτόματον compared to that of τύχη and that the examples are chiefly geared towards this aim. I will also explain why such a treatment of chance is relevant within his critical analysis of Empedocles’ and Democritus’ theories of τύχη and αὐτόματον. (shrink)

Aristotle; ifluences; Arabic language; Arabic criticism; history and criticism, 14th century; master's thesis.

Aristophanes' description of the stages of promotion in the Athenian navy recently received renewed attention, when Mastromarco and Halliwell enlisted it in their battle against the traditional opinion that Aristophanes' early career fell into two stages, a secret one of writing plays but not producing them, and a public one in which he undertook both activities. Mastromarco argues for a tripartite career, and Halliwell, who is against a too strict correlation, for a gradual development, a sort of a complex apprenticeship, (...) which eventually he divides also into three stages similar to those discerned by Mastromarco. In summing up their position, MacDowell paraphrases the above passage according to its prevalent interpretation: ‘The nautical metaphor , with its progression from oarsman to prow-officer to helmsman, indicates that Aristophanes did not take over his task all at once, but by stages. But what were the stages?’. (shrink)

Contributions in the concept of the divine; influence; Islamic philosophy.

t. 1. Texto inédito de los doce primeros capítulos. Facsímil de la segunda versión suareciana (Lyon 1621).

صدر عن المركز العربي للأبحاث ودراسة السياسات كتاب المنطق الإسلامي: حضور المنطق الأرسطي لدى مفكري المشرق الإسلامي، وهو من تأليف محمد بن يعيش. يقع الكتاب في 272 صفحة، شاملةً ببليوغرافيا وفهرسًا عامًّا. أمام ما يعرِّفه مؤلفُ الكتاب بـ "حقيقتين تاريخيتين"؛ هما أوّلًا: كثرة من اشتغلوا بعلم المنطق في الحضارة العربية الإسلامية من أفذاذ العلماء، وانتشارهم في أصقاع البلاد الإسلامية، وتنوّع أديانهم، وأصناف تخصصاتهم العلمية ونتاجاتهم، تأليفًا وحواشيَ مسهبةً وترجماتٍ ومختصراتٍ وشروحًا وأرجوزات، وثانيًا: إقراره بما لقيه هؤلاء العلماء من مضايقات وتجريح (...) واتهامات وملاحقات. يطرح الكتاب إشكاليةَ البحث، المتمثلةَ بالحيثيات التي رافقت استقبال المسلمين علمًا دخيلًا على العلوم الإسلامية كالمنطق وتعاملهم معه، ومراحل تردده بين الرفض والقبول في البيئة الجديدة، وأوجه الجِدّة لدى العلماء الذي ساهموا في تكريسه لغويًّا (الفارابي وابن سينا) ودينيًّا (الغزالي). وقد دفع "الحضور" الأرسطي لدى مناطقة الشرق الإسلامي الكاتبَ إلى تبيان مساهمة أرسطو - ضمن عناصرَ مساهِمة كثيرة - في تكريس خطاب إسلامي عقلاني جديد، وتشكيل المعالم الكبرى والجزئية لفلسفة هؤلاء المناطقة، التي تعبّر برأيه عن "تواصل" بين الفكرين اليوناني والإسلامي بدلًا مما يُحكى عن الانفصال والقطيعة والطلاق البائن، متجنِّبًا الانحياز إلى أحد طرفي الأزمة، المشنِّعين الذين يقذفون المنطق بشتى التهم، كإثارة الشبهات والباطل والرجم بالغيب من جهة، والقائلين بمادية فيلسوف اليونان وعقلانيته في مقابل لاعقلانية المسلمين وظلامية فكرهم، مع تشديده على تميز خطاب مفكري المشرق ضمن تاريخ الفلسفة المرافِق لهذا التواصل. وقد أتاح الجهد البحثي المبذول الانفتاحَ على أفق منطقي غير مدرسي اتبعته مجموعة من مفكري العالم الإسلامي، في محاولة لتكريس نظرة جديدة إلى التراثين اليوناني والإسلامي، متوسِّلًا لبلوغها كثرة الاستشهاد بنصوص المناطقة المشرقيين التي يُستدعى فيها أرسطو وسيلةً لإثبات حقيقة العلاقة بين الخطابين بطريقة علمية أمينة. (shrink)

-- -- ḥeleḳ 2. Sofisṭim. Soḳraṭes. Aflaṭon.