The History of Continua

Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially; a continuum is a unified whole. The most dominant account today, traced to Cantor and Dedekind, is in stark contrast with this, taking a continuum to be composed of infinitely many points. The opening chapters cover the ancient and medieval worlds: the pre-Socratics, Plato, Aristotle, Alexander, and a recently discovered manuscript by Bradwardine. In the early modern period, mathematicians developed the calculus the rise of infinitesimal techniques, thus transforming the notion of continuity. The main figures treated here include Galileo, Cavalieri, Leibniz, and Kant. In the early party of the nineteenth century, Bolzano was one of the first important mathematicians and philosophers to insist that continua are composed of points, and he made a heroic attempt to come to grips with the underlying issues concerning the infinite. The two figures most responsible for the contemporary hegemony concerning continuity are Cantor and Dedekind. Each is treated, along with precursors and influences in both mathematics and philosophy. The next chapters provide analyses of figures like du Bois-Reymond, Weyl, Brouwer, Peirce, and Whitehead. The final four chapters each focus on a more or less contemporary take on continuity that is outside the Dedekind–Cantor hegemony: a predicative approach, accounts that do not take continua to be composed of points, constructive approaches, and non-Archimedean accounts that make essential use of infinitesimals.

Author(s):  
Wiederin Ewald

This chapter presents an overview and history of the Austrian administrative state. It shows how the traditional form of the Austrian administration evolved in the second half of the nineteenth century. After defeat in World War I, the Republic of Austria succeeded the extinct Danube Monarchy; it took over the Viennese central administrative departments and their personnel and remained a ‘typical administrative state’. In the early modern period, the fundamental elements of Austria's administration developed on three different levels that still exist and to this day continue to characterize the administration's structure. Most notably, the state's dominant administrative feature is expressed by the equality of the judiciary and the administrative branch in both standing and rights.


Hypatia ◽  
2006 ◽  
Vol 21 (4) ◽  
pp. 1-19 ◽  
Author(s):  
Joan Gibson

Before women could become visible as philosophers, they had first to become visible as rational autonomous thinkers. A social and ethical position holding that chastity was the most important virtue for women, and that rationality and chastity were incompatible, was a significant impediment to accepting women's capacity for philosophical thought. Thus one of the first tasks for women was to confront this belief and argue for their rationality in the face of a self-referential dilemma.


2017 ◽  
Vol 5 (1) ◽  
pp. 56-79
Author(s):  
Sara Zandi Karimi

This article is a critical translation of the “History of the Ardalānids.” In doing so, it hopes to make available to a wider academic audience this invaluable source on the study of Iranian Kurdistan during the early modern period. While a number of important texts pertaining to the Kurds during this era, most notably the writings of the Ottoman traveler Evliya Chalabi, focus primarily on Ottoman Kurdistan, this piece in contrast puts Iranian Kurdistan in general and the Ardalān dynasty in particular at the center of its historical narrative. Thus it will be of interest not only to scholars of Kurdish history but also to those seeking more generally to research life on the frontiers of empires.Keywords: Ẕayl; Ardalān; Kurdistan; Iran.ABSTRACT IN KURMANJIDîroka Erdelaniyan (1590-1810)Ev gotar wergereke rexneyî ya “Dîroka Erdelaniyan” e. Bi vê yekê, merema xebatê ew e ku vê çavkaniya pir biqîmet a li ser Kurdistana Îranê ya di serdema pêş-modern de ji bo cemawerê akademîk berdest bike. Hejmareke metnên girîng li ser Kurdên wê serdemê, bi taybetî nivîsînên Evliya Çelebî yê seyyahê osmanî, zêdetir berê xwe didine Kurdistana di bin hukmê Osmaniyan de. Lê belê, di navenda vê xebatê de, bi giştî Kurdistana Îranê û bi taybetî jî xanedana Erdelaniyan heye. Wisa jî ew dê ne tenê ji bo lêkolerên dîroka kurdî belku ji bo ewên ku dixwazin bi rengekî berfirehtir derheq jiyana li ser tixûbên împeretoriyan lêkolînan bikin jî dê balkêş be.ABSTRACT IN SORANIMêjûy Erdellan (1590-1810)Em wutare wergêrranêkî rexneyî “Mêjûy Erdellan”e, bew mebestey em serçawe girînge le ser Kurdistanî Êran le seretakanî serdemî nwê bixate berdest cemawerî ekademî. Jimareyek serçawey girîng le ser kurdekan lew serdeme da hen, diyartirînyan nûsînekanî gerîdey ‘Usmanî Ewliya Çelebîye, ke zortir serincyan le ser ‘Kurdistanî ‘Usmanî bûwe. Em berheme be pêçewanewe Kurdistanî Êran be giştî, we emaretî Erdelan be taybetî dexate senterî xwêndinewekewe. Boye nek tenya bo twêjeranî biwarî mêjûy kurdî, belku bo ewaney le ser jiyan le sinûre împiratoriyekan twêjînewe deken, cêgay serinc debêt.


2020 ◽  
Vol 54 (1-3) ◽  
pp. 72-98
Author(s):  
Nikolaos Chrissidis

Abstract The article first surveys Greek interpretations of the creation of the Russian Holy Synod by Peter the Great. It provides a critical assessment of the historiographical paradigm offered by N.F. Kapterev for the analysis of Greek-Russian relations in the early modern period. Finally, it proposes that scholars should focus on a Greek history of Greek-Russian relations as a complement and possibly corrective to the Kapterev paradigm.


2017 ◽  
Vol 34 (1) ◽  
pp. 1-22
Author(s):  
Paul Shore

The manuscipt Animadversiones, Notae ac Disputationes in Pestilentem Alcoranum is an almost entirely unknown translation of the Qur'an into baroque Latin completed by the Jesuit priest Ignazio Lomellini in 1622, of which only one copy exists. It is accompanied by extensive commentaries and includes a complete text of the Qur’an in Arabic and numerous marginalia. It is, therefore, one of the earliest complete translations of the Qur’an into a western European language and a crucial document of the encounter between western Christianity and Islam in the early modern period. This essay examines Lomellini’s understanding of Arabic and, specifically, of the cultural and religious underpinnings of Qur’anic Arabic. Special attention is given to his lexical choices. This essay also deals with the document’s intended audience, the resources upon which he drew (including the library of his patron, Cardinal Alessandro Orsini), and the manuscript’s relationship to the Jesuits’ broader literary and missionary efforts. Finally, it asks why scholars, particularly those who study the history of the Jesuits, have ignored this manuscript and its author.


Author(s):  
Irene Fosi

AbstractThe article examines the topics relating to the early modern period covered by the journal „Quellen und Forschungen aus italienischen Archiven und Bibliotheken“ in the hundred volumes since its first publication. Thanks to the index (1898–1995), published in 1997 and the availability online on the website perpectivia.net (since 1958), it is possible to identify constants and changes in historiographical interests. Initially, the focus was on the publication of sources in the Vatican Secret Archive (now the Vatican Apostolic Archive) relating to the history of Germany. The topics covered later gradually broadened to include the history of the Papacy, the social composition of the Curia and the Papal court and Papal diplomacy with a specific focus on nunciatures, among others. Within a lively historiographical context, connected to historical events in Germany in the 20th century, attention to themes and sources relating to the Middle Ages continues to predominate with respect to topics connected to the early modern period.


Sederi ◽  
2009 ◽  
pp. 153-174
Author(s):  
Javier Ruano García

The analysis of regional dialects in the Early Modern period has commonly been disregarded in favour of an ample scholarly interest in the ‘authorised’ version of English which came to be eventually established as a standard. The history of regional ‘Englishes’ at this time still remains to a very great extent in oblivion, owing mainly to an apparent scarcity of sources which supply trustworthy data. Research in this field has been for the most part focused on phonological, orthographical and morphological traits by virtue of the rather more abundant information that dialect testimonies yield about them. Regional lexical diversity has, on the contrary, deserved no special attention as uncertainty arises with regard to what was provincially restricted and what was not. This paper endeavours to offer additional data to the gloomy lexical scene of Early Modern regional English. It is our aim to give a descriptive account of the dialect words collated by Bishop White Kennett’s glossary to Parochial Antiquities (1695). This underutilised specimen does actually widen the information furnished by other well known canonical word-lists and provides concrete geographical data that might help us contribute to complete the sketchy map of lexical provincialisms at the time.


2021 ◽  
pp. 609-634
Author(s):  
Carolyn J. Sharp

This chapter explores homiletical possibilities afforded by the book of Jeremiah to the Christian preacher. The earliest layers of contextualization are examined through consideration of preaching on Jeremiah in the early Church, focusing on sermons of Origen. In discussing the early modern period, the chapter attends to the preaching of Reformers Martin Luther and John Calvin. Finally, the chapter reflects on homiletical moves made by contemporary preachers in a variety of ecclesial contexts from the nineteenth century to the present, including Charles Spurgeon and Walter Brueggemann. Noteworthy in the homiletical reception of Jeremiah are four passages: first, the commissioning of Jeremiah (1:4–10), which foregrounds agonistic dimensions of prophetic witness and has served as a focus in liturgies of ordination; second, the lament, “Is there no balm in Gilead?” (8:22), transformed in a renowned African American spiritual into the asseveration that “there is a balm in Gilead,” namely, Jesus; third, Jeremiah’s depiction of the divine word as irresistible, “like a burning fire shut up in my bones” (20:9); and fourth, the promise of the new covenant that God will inscribe on the heart (31:31–34).


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