Luitzen Egburtus Jan Brouwer founded a school of thought whose aim was to include mathematics within the framework of intuitionistic philosophy; mathematics was to be regarded as an essentially free development of the human mind. What emerged diverged considerably at some points from tradition, but intuitionism has survived well the struggle between contending schools in the foundations of mathematics and exact philosophy. Originally published in 1981, this monograph contains a series of lectures dealing with most of the fundamental topics such (...) as choice sequences, the continuum, the fan theorem, order and well-order. Brouwer's own powerful style is evident throughout the work. (shrink)

What became of Erasmus' books? The most famous scholar of his day died in peaceful prosperity and in the company of celebrated and responsible friends. His zeal for useful books was insatiable. Indeed, he had taken care to insure that after his death they would pass to an appreciative noble owner, yet after his death their fate was unknown. Erasmus and His Books provides the most comprehensive evidence available about the books of Erasmus of Rotterdam - the books he owned (...) and his attitude towards them, when and how he acquired them, how he housed, used, and cared for them, and how, from time to time, he disposed of them. Part 1 details the formation, growth, scope, and arrangement of Erasmus' library and opens the door to a new understanding of the more intimate side of his daily life as a scholar at home with his books, friends, publishers, and booksellers. Part 2 presents a carefully annotated catalogue, the Versandliste, of the more than 400 books in Erasmus' possession at one point. Drawing upon his command of bibliographical data and his extensive knowledge of Erasmus' correspondence and related records, Egbertus van Gulik proposes as precise an identification of each of the titles as the evidence will allow."-- Provided by publisher. (shrink)

In hisLife of Aemilius Paulus, Plutarch (quite naturally) rehearses the initial phase of Aemilius Paulus' campaign against Perseus, when the Macedonian had occupied a position on the northern bank of the river Elpeus so strongly fortified that any direct assault could only be disastrous for the attackers. Aemilius instead resorted to a cunning strategy of synchronized surgical strikes, while a detachment, the departure and direction of which were successfully disguised, managed to round the Macedonian camp. Perseus' position (...) was thus compromised, and in reaction the monarch hastily retreated to Pydna, where in the end his luck was even worse. Embedded in this narrative is the report that, prior to Aemilius' dislodging of Perseus, the morale of the legions was sorely depressed. The reason was simple and straightforward: they were suffering from a shortage of satisfactorily potable water. This difficulty Aemelius resolved by digging wells. (shrink)

In hisLife of Aemilius Paulus, Plutarch (quite naturally) rehearses the initial phase of Aemilius Paulus' campaign against Perseus, when the Macedonian had occupied a position on the northern bank of the river Elpeus so strongly fortified that any direct assault could only be disastrous for the attackers. Aemilius instead resorted to a cunning strategy of synchronized surgical strikes, while a detachment, the departure and direction of which were successfully disguised, managed to round the Macedonian camp. Perseus' position (...) was thus compromised, and in reaction the monarch hastily retreated to Pydna, where in the end his luck was even worse. Embedded in this narrative is the report that, prior to Aemilius' dislodging of Perseus, the morale of the legions was sorely depressed. The reason was simple and straightforward: they were suffering from a shortage of satisfactorily potable water. This difficulty Aemelius resolved by digging wells. (shrink)

Friedrich Nietzsche and Luitzen Egbertus Jan Brouwer had strong personalities and freely expressed unconventional opinions. In particular, they dared to challenge the traditional view that considered Aristotelian logic as being absolute and intrinsic to man. Although they formed this opinion in different ways and in different contexts, they both based it on a view of life that considered it as a struggle for power in which logic was a weapon. Therefore, it is interesting to carry out an in-depth analysis (...) on the origins, the core of their opinions concerning logic and the consequences. As a matter of fact, a detailed analysis and a comparison of their contributions to the philosophy of logic have not yet been carried out. In this paper, I intend to present the results of my research.. (shrink)

Dutch Mathematician Luitzen Egbertus Jan Brouwer (1881-1966) was a rebel. His doctoral thesis... was the manifesto of an angry young man taking on the mathematical establishment on all fronts. In a short time he established a world-wide reputation for himself; his genius and originality were acknowledged by the great mathematicians of his time... The Intuitionist-Formalist debate became a personal feud between the mathematical giants Brouwer and Hilbert, and ended in 1928 with the expulsion of Brouwer from the editorial board (...) of the Mathematische Annalen by dictat of Hilbert. Forsaken, humiliated and disillusioned Brouwer abandoned his Intuitionist Programme and withdrew into silence just about the time when the Formalist Programme appeared to be fundamentally flawed and major opposition collapsed... This book attempts to follow the `genetic' development of Brouwer's ideas, linking the man Brouwer, his Weltanschauung, his philosophy of mathematics and his reconstruction of mathematics. Brouwer's own writings, his publications as well as his unpublished papers, are its immediate and main source of reference. It is the second volume in the new series Studies in the History and Philosophy of Mathematics, and is written for the specialist as well as for the general reader interested in mathematics and the interpretation of its status and function. (shrink)

Marcus Cato, Sulla, Aemilius Paullus, Pompey, The Gracchi, Marius, Julius Caesar, Anthony 'I treat the narrative of the Lives as a kind of mirror...The experience is like nothing so much as spending time in their company and living with them: I receive and welcome each of them in turn as my guest.' In the eight lives of this collection Plutarch introduces the reader to the major figures and periods of classical Rome. He portrays virtues to be emulated and vices (...) to be avoided, but his purpose is also implicitly to educate and warn those in his own day who wielded power. In prose that is rich, elegant and sprinkled with learned references, he explores with an extraordinary degree of insight the interplay of character and political action. While drawing chiefly on historical sources, he brings to biography a natural story-teller's ear for a good anecdote. Throughout the ages Plutarch's Lives have been valued for their historical value and their charm. This new translation will introduce new generations to his urbane erudition. The most comprehensive selection available, it is accompanied by a lucid introduction, explanatory notes, bibliographies, maps and indexes. (shrink)

Introduction Life, art and mysticism Luitzen Egbertus Jan Brouwer Logic and ethics as the limits of the world Anthony Rudd To what extent is solipsism a truth? Michael Kremer Frege at therapy Kelly Dean Jolley 'Making sense' of nonsense Conant and Diamond read Wittgenstein's Tractatus Diarmuid Costello More making sense of nonsense: from logical form to forms of life Daniel D. Hutto Saying and showing: an example from Anscombe Cora Diamond Why worry about the Tractatus? James Conant Transcendence and (...) contradiction in the Tractatus Barry Stocker Wittgenstein's onto-logic Barry Allen Bibliography Index. (shrink)

Publication d'une loi de Delphes qui ne peut être antérieure à 132-135 ap. J.-C, d'après la mention du corrector Aemilius Iuncus. La loi règle la répartition des terres sur une partie du territoire de la cité, après un premier lotissement dont les bénéficiaires voient leurs droits protégés. Cette seconde répartition, qui privilégie les damiurges et les bouleutes au détriment des simples demotes, montre l'existence dans le corps civique de Delphes d'une hiérarchie qui trouve des parallèles dans les cités de (...) la Grèce insulaire et micrasiatique de l'époque impériale. La concession des terres se rapproche de l'« emphytéose », puisque les bénéficiaires auront non pas la pleine propriété, mais la possession illimitée et héréditaire de terres vacantes, qui recevront des améliorations, susceptibles de revenir à la cité avec le fonds faute d'une dévolution successorale normale; cette concession paraît cependant être accordée à titre gratuit. Examen des rapprochements possibles avec les distributions de terres romaines et avec la politique économique impériale, en particulier celle que l'on a attribuée à Hadrien : il est toutefois difficile d'affirmer l'influence et l'intervention directes de Rome à Delphes. (shrink)

En este trabajo presentamos la traducción del latín al español, con introducción y breves notas, del octavo de los denominados Carmina Profana o Romulea escritos por el poeta cristiano Blosio Emilio Draconcio durante el siglo V y transmitido por la tradición textual bajo el título De Raptu Helenae. In this paper, we offer the translation from latin to spanish, with introduction and short notes, of the eighth of the so-called Carmina Profana or Romulea, written by the poet Blossius Aemilius (...) Dracontius during the 5th Century and transmitted by textual tradition under the title De Raptu Helenae. (shrink)

In the 50sb.c.the Roman republic faced serious challenges, not least among them the related problems of electoral bribery and provincial extortion. The year 54b.c., which this article takes as a case study, witnessed both the worst electoral scandal Rome had ever seen and the high-profile extortion trial of M. Aemilius Scaurus. These events defy analysis in terms of the political allegiances and prosopographical connections usually tracked. It is more helpful to think of problems and (attempted) solutions, in which the (...) younger M. Porcius Cato played a leading role. Scaurus’ prosecutor summed up a vicious circle: governors who had engaged in extortion would buy the consulship with the money they had stolen and go on to plunder other provinces. Cato countered from both sides: in the Senate, he proposed a new form of process to combat electoral corruption; as president of the extortion court, he allowed the prosecution to hurry through a case that was as much aboutambitusasrepetundae. These initiatives, while not immediately successful, helped lay the groundwork for future reforms. (shrink)

All our ancient sources agree on the basic sequence of events after the battle of Pydna on 22 June 168: the consul L. Aemilius Paullus advanced to take possession of the whole of Macedonia and finally managed to capture Perseus, the defeated king, who had taken refuge on Samothrace. Once in complete control of the situation he sent his troops into winter quarters and himself set off on a trip that was to take him round the most famous sights (...) of Greece. Only when he heard of the arrival of the customary senatorial commission did he return to Macedon, settle its affairs, hold magnificent games, and finally return to Italy. Thus far there is little cause for concern, but what most of these events lack is a properly established date. Livy, our only ancient source venturing to date them, places everything up to sending the troops into winter quarters in the same consular year as Pydna and assigns the remaining events to autumn and winter 167 . He thereby creates an awkward gap of somewhat more than a year between the battle of Pydna and the subsequent actions of Aemilius Paullus. A majority of scholars either seem to have ignored this point altogether or silently corrected Livy's chronology by simply shifting the events in question back to 168/ . Others, ranging from Miiller and Weissenborn to Hammond and Walbank in their magisterial History of Macedonia, have kept Livy's date,4 while only one scholar has actually attempted to argue for a correction of Livy. (shrink)

In the nineteenth and twentieth centuries many mathematicians referred to intuition as the indispensable research tool for obtaining new results. In this essay we will analyse a group of mathematicians who interacted with Luitzen Egbertus Jan Brouwer in order to compare their conceptions of intuition. We will see how to the same word “intuition” very different meanings corresponded: they varied from geometrical vision, to a unitary view of a demonstration, to the perception of time, to the faculty of considering (...) concepts that habitually occur in our thinking separately. Furthermore, we will discover that these different meanings had a philosophical, very relevant counterside: they passed from a racial characterization of mathematics to a pluralistic view of it. (shrink)

In 179 b.c. the censors M. Aemilius Lepidus and M. Fulvius Nobilior brought about a reform in the voting. The only evidence for this is a single sentence in Livy : mutarunt suffragia regionatimque generibus hominum causisque et quaestibus tribus discripserunt The meaning of these words has often been discussed but never in a fully systematic manner. Further, the attempts to discover their meaning have always been made in an effort to throw light upon some other problem. They are (...) thus transported into the historical context in question, such as the vicissitudes of the freedman vote or the reforms of the comitia centuriata. Yet the formulaic nature of the sentence and its virtual independence from its immediate context make it essential to examine it in its own right in order objectively to establish its meaning. Only then should the question of historical context be considered. The purpose here is to provide a systematic analysis of each element in this sentence. If the results of this are accepted it will become apparent that Livy 40.51.9 relates to central questions concerning the census and the centuriate assembly. As it stands the sentence is entirely divorced from what precedes and follows it, with the exception of the subject, the censors. Not only is there nothing in the surrounding context to explain it; there is nothing remotely comparable anywhere else in Livy. This, together with the precision of the language, the institutional content, and the formal and formulaic sound of the whole, suggests that Livy has either lifted the sentence out of an official document or is using the terminology characteristic of such documents. (shrink)

The paper studies Livy's account in Book 45 of the aftermath of Aemilius Paullus' conquest of Macedon employing two interpretative methods, both common in recent studies of historians. The first is “metahistory,” in other words interpreting events within a historical narrative as commenting covertly on the genre of history and on the work as an example of that genre. The second is seeing how internal audiences provide a guide for the reader's interpretation. These, though theoretically independent, are in practice (...) often related, with internal audiences being used as a trigger for wider reflections on the text and the genre. Four linked passages from Livy 45 are discussed in detail. One invites a systematic metahistorical reading without the use of an internal audience, partly to endorse Livy's own manner of “secondary” history, partly to promote a moral reading of the text. The other three employ internal audiences to similar effect: first, Aemilius' meeting with the defeated Perseus, and the lesson which he draws about the mutability of fortune; second, the spectacular games he organizes at Amphipolis; and third, his eventual triumph in Rome, along with the speech that Servilius gives in its support. The understanding of the genre of history that Livy promotes through these passages is, however, astonishingly narrow and didactic, ignoring even central aspects of his own work which do not conform to that understanding. The paper concludes by considering why Livy would wish to present himself and his genre as single-mindedly moralistic when neither he nor it actually was. (shrink)

In this paper I explore the character and role of stereoformulas and models of the atom that appeared in the early history of stereochemistry, including those of Jacobus Henricus van't Hoff, Aemilius Wunderlich, Johannes Wislicenus, Victor Meyer, Arthur Hantzsch, Alfred Werner, and Hermann Sachse. I argue that stereochemists constructed and used stereoformulas in a pragmatic way that ignored the physical implications of the spatial distribution of valence, and that the models of the atom were created to reconcile the physically (...) curious concept of valence with known physical laws. Although such models were explanatory at a deeper level, they had little impact on the theory and practice of chemistry, and were not serious attempts to reduce chemical theory to physical laws. (shrink)

Among the difficulties in Propertius is the question whether to retain ‘cecinit’ in 3. 3. 7 or to adopt the conjecture ‘cecini’. Propertius dreamed that he was reclining upon Helicon in a grove by Hippocrene and that he was able to compose a Roman historical epic: Visus eram molli recubans Heliconis in umbra, Bellerophontei qua fluit umor equi, Reges, Alba, tuos et regum facta tuorum neruis hiscere posse meis, Paruaque tam magnis admoram fontibus ora Vnde pater sitiens Ennius ante bibit, (...) Et cecinit Curios fratres et Horatia pila Regiaque Aemilia uecta tropaea rate Victricesque moras Fabii pugnamque sinistram Cannensem et uersos ad pia uota deos Hannibalemque Lares Romana sede fugantes, Anseris et tutum uoce fuisse Iouem, Cum me Castalia speculans ex arbore Phoebus Sic ait… According to the paradosis 7–12 constitute a summary of Ennius' Annales. In that I case Propertius' failure to observe historical sequence is peculiar; nor is it defended securely by I supposedly parallel passages. More damaging, however, is that 8 must describe the triumph of L. Aemilius Paullus in 167, two years after the accepted date of Ennius' death. Hertzberg and Postgate claimed that it alludes to the defeat of Demetrius of I Pharos by a L. Aemilius Paullus in 219 ; this is unlikely for some of the same reasons as the rival theory of Butler and Barber, which has found many adherents, that it refers to the victory over Antiochus' navy by L. Aemilius Regillus at Myonnesus in 190. (shrink)

'I will do as the Senate decrees.' These words from one of Rome's opponents encapsulate the authority Rome achieved by its subjugation of the Mediterranean. The Third Macedonian War, recounted in this volume, ended the kingdom created by Philip II and Alexander the Great and was a crucial step in Rome's eventual dominance. For Livy, the story is also a fascinating moral study of the vices and virtues that hampered and promoted Rome's efforts in the conflict. He presents the war (...) not so much as a battle against Perseus, Alexander's last and unworthy successor, than as a struggle within the Roman national character. Only traditional moral strength, embodied in Lucius Aemilius Paullus, the general who ultimately defeats Perseus, ensures the Roman victory. This edition also includes the Periochae, later summaries of Livy's entire original 142-book history of Rome from its founding to the age of Augustus. (shrink)