Lapo da Castiglionchio the Younger was a Florentine Renaissance humanist who died in 1438 at the age of thirty-three. He took part in one of the most interesting phases of Italian Renaissance humanism and achieved in his short lifetime a modest reputation as a first-rate Greek to Latin translator. Less well known is the fact that he wrote a fair amount of prose works. One of the most interesting of these is a treatise which he composed in the year (...) of his death, entitled De curie commodis, or, On the Benefits of the Curia, a portrait of the papal Curia which is written elegantly, learnedly, earnestly, and angrily. ;The goal of this study is to discuss this dialogue in its intellectual and social contexts; there are three chapters. The first is a general introduction to Lapo's life and work, to the dialogue itself, and to the historiography on the De curie commodis. The second chapter discusses the manner in which Lapo employs the virtues in a Stoicizing fashion as persuasive tools in the environment of Italian humanism. It is argued that his particular treatment of the virtues can serve as a key for interpreting the dialogue as a whole. The third chapter touches both on social historical issues in the De curie commodis and on Lapo's defense or curial wealth. ;There has been no adequate edition of the Latin text, based on a wide enough variety of extant manuscripts, nor has the De curie commodis ever been translated into English . Therefore, a thorough critical edition of the Latin text along with an annotated English translation follows the discussion. ;The treatise has been notoriously difficult to interpret and seems often to prevaricate. The interpretive conclusion of this study is that Lapo wrote as a well-informed but liminal figure in the socio-cultural environment of the papal Curia--as an outsider who desired to become a full-fledged insider. The De curie commodis is not the parting shot of a fed-up hanger-on; it is instead Lapo's last-ditch, highly critical but nonetheless sincere attempt to find a patron who would allow him to join a cultural ambient at which he marvelled but from which he felt himself unjustly excluded. (shrink)

SummaryRussell's vicious‐circle principle is an endeavour to express a general principle of mathematics which, as the author feels, is fundamental for mathematics. This principle, in a sense warranty of formal consistency, interdicts in some form or other the selfapplication of mathematical entities. It is shown that the VCP is a vicious‐circle fallacy; that, although it can't be given an expression which is simultaneously formal and generally valid, it is generally presupposed by mathematics as far as a consistent formalism is concerned; (...) that this paradoxical situation refers to an essentially informal and non‐mathematical domain which forms a necessary condition for mathematics, but can't exhaustively be expressed in any mathematical formalism. Finally the distinction between semantical and syntactical import and the character of negation are restated in view of these results.RésuméLe principe du cercle vicieux de Russell a, selon l'auteur, une portée générale et fondamentale en mathématiques: il interdit, sous quelque forme que ce soit, lapos;application dapos;entités mathématiques à elles‐mêmes. Ce principe est équivalent au paradoxe de Russell; on ne peut pas le formaliser sous peine de compromettre sa validite universelle, et pourtant il constitue une présupposition de tout formalisme qui veut éviter la contradiction. Cette situation paradoxale nous renvoie à un domaine essentiellement in‐formel et non‐mathématique, qui embrasse le formalisme mathématique, en constitue une condition nécessaire, mais ne peut être exprimé dans aucun formalisme dapos;une manière exhaustive. Finalement le problème logique de la négation et celui de la distinction entre les rapports sémantiques et syntactiques sont repris à la lumière de ces résultats.ZusammenfassungRussells Zirkelprinzip ist der Versuch, ein allgemeingültiges Prinzip der Mathematik auszudrücken, das, wie der Verfasser meint, von grundsätzlicher Bedeutung ist. Dieses Prinzip, das in einem gewissen Sinne die formale Widerspruchsfreiheit verbürgt, verbietet die Selbstbezüglichkeit mathematischer Entitäten. Der Artikel zeigt, dass es mit Russells Paradox äquivalent ist, und dass es eine allgemeine Voraussetzung der Mathematik als eines konsistenten Formalismus darstellt, obwohl man ihm selbst keinen zugleich allgemeingültigen und formellen Ausdruck geben kann; es wird des weiteren gezeigt, dass diese paradoxale Situation auf ein wesentlich informelles und nicht‐mathematisches Gebiet verweist, das eine notwendige Bedingung für die Mathematik darstellt, jedoch selber nicht erschöpfend im Formalismus dargestellt werden kann. Schliesslich werden a) die Unterscheidung zwischen semantischen und syntakti‐schen Beziehungen und b) die Negation im Lichte dieser Ergebnisse neu überdacht. (shrink)