Anselm of Canterbury OSB (ˈænsɛlm; 1033/4–1109), also called Anselm of Aosta (Anselmo d'Aosta) after his birthplace and Anselm of Bec (Anselme du Bec) after his monastery, was an Italian Benedictine monk, abbot, philosopher and theologian of the Catholic Church, who held the office of Archbishop of Canterbury from 1093 to 1109. After his death, he was canonized as a saint; his feast day is 21 April.
As archbishop, he defended the church's interests in England amid the Investiture Controversy. For his resistance to the English kings William II and Henry I, he was exiled twice: once from 1097 to 1100 and then from 1105 to 1107. While in exile, he helped guide the Greek bishops of southern Italy to adopt Roman rites at the Council of Bari. He worked for the primacy of Canterbury over the bishops of York and Wales but, though at his death he appeared to have been successful, Pope Paschal II later reversed himself and restored York's independence.
Beginning at Bec, Anselm composed dialogues and treatises with a rational and philosophical approach, sometimes causing him to be credited as the founder of Scholasticism. Despite his lack of recognition in this field in his own time, Anselm is now famed as the originator of the ontological argument for the existence of God and of the satisfaction theory of atonement. He was proclaimed a Doctor of the Church by a bull of Pope Clement XI in 1720.
Anselm was born in or around Aosta in Upper Burgundy sometime between April 1033 and April 1034. The area now forms part of the Republic of Italy, but Aosta had been part of the post-Carolingian Kingdom of Burgundy until the death of the childless Rudolph III in 1032. The Emperor and the Count of Blois then went to war over his succession. Humbert the White-Handed, Count of Maurienne, so distinguished himself that he was granted a new county carved out of the secular holdings of the bishop of Aosta. Humbert's son Otto was subsequently permitted to inherit the extensive March of Susa through his wife Adelaide in preference to her uncle's families, who had supported the effort to establish an independent Kingdom of Italy under William V, Duke of Aquitaine.
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Sir Richard William Southern (8 February 1912 – 6 February 2001), who published under the name R. W. Southern, was a noted English medieval historian based at the University of Oxford. Southern was born in Newcastle-upon-Tyne on 8 February 1912, and educated at the Royal Grammar School, Newcastle, and at Balliol College, Oxford, where he graduated with a first-class honours degree in history. At Oxford, Southern's mentors were Sir Maurice Powicke and Vivian Hunter Galbraith.
Anselm of Laon (Anselmus; () 1117), properly Ansel (Ansellus), was a French theologian and founder of a school of scholars who helped to pioneer biblical hermeneutics. Born of very humble parents at Laon before the middle of the 11th century, he is said to have studied under Saint Anselm at Bec, though this is almost certainly incorrect. Other potential teachers of Anselm have been identified, including Bruno of Cologne and Manegold of Lautenbach.
Medieval philosophy is the philosophy that existed through the Middle Ages, the period roughly extending from the fall of the Western Roman Empire in the 5th century until after the Renaissance in the 13th and 14th centuries. Medieval philosophy, understood as a project of independent philosophical inquiry, began in Baghdad, in the middle of the 8th century, and in France, in the itinerant court of Charlemagne, in the last quarter of the 8th century.
In this paper we present rigorous a posteriori L2 error bounds for reduced basis approximations of the unsteady viscous Burgers equation in one space dimension. The key new ingredient is accurate solution-dependent (Online) calculation of the exponential-i ...
The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. An error estimate is derived in the ...