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Insolubilia
In the Middle Ages, variations on the liar paradox were studied under the name of ''insolubilia'' ("insolubles"). Overview Although the liar paradox was well known in antiquity, interest seems to have lapsed until the twelfth century, when it appears to have been reinvented independently of ancient authors. Medieval interest may have been inspired by a passage in the ''Sophistical Refutations'' of Aristotle. Although the ''Sophistical Refutations'' are consistently cited by medieval logicians from the earliest ''insolubilia'' literature, medieval studies of ''insolubilia'' go well beyond Aristotle. Other ancient sources which could suggest the liar paradox, including Saint Augustine, Cicero, and the quotation of Epimenides appearing in the Epistle to Titus, were not cited in discussions of ''insolubilia''. Adam of Balsham mentioned, in passing, some paradoxical statements (dated to 1132), but he did not dwell on the difficulties raised by these statements. Alexander Neckham, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas Bradwardine
Thomas Bradwardine (c. 1300 – 26 August 1349) was an English cleric, scholar, mathematician, physicist, courtier and, very briefly, Archbishop of Canterbury. As a celebrated scholastic philosopher and doctor of theology, he is often called ''Doctor Profundus'' ( medieval epithet, meaning "the Profound Doctor" or "the Profound Teacher"). Life Sources vary about Bradwardine's early life before receiving his degree in 1321. His exact date of birth is unknown but sources point to a date between 1290 and 1300. His place of birth is also unknown but some sources point to it being near Chichester, Sussex, or Harfield. The first concrete sources of his do not appear until he received his degree in 1321 from Balliol College, Oxford. Thomas Bradwardine became a Fellow of Merton College in Oxford, and was awarded his B.A. in August 1321. Bradwardine stayed at Merton College until 1333, when he was appointed Canon of Lincoln, and in 1337 he was appointed the chaplain of St Paul's ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middle Ages
In the history of Europe, the Middle Ages or medieval period lasted approximately from the 5th to the late 15th centuries, similarly to the post-classical period of global history. It began with the fall of the Western Roman Empire and transitioned into the Renaissance and the Age of Discovery. The Middle Ages is the middle period of the three traditional divisions of Western history: classical antiquity, the medieval period, and the modern period. The medieval period is itself subdivided into the Early, High, and Late Middle Ages. Population decline, counterurbanisation, the collapse of centralised authority, invasions, and mass migrations of tribes, which had begun in late antiquity, continued into the Early Middle Ages. The large-scale movements of the Migration Period, including various Germanic peoples, formed new kingdoms in what remained of the Western Roman Empire. In the 7th century, North Africa and the Middle East—once part of the Byzantine Empire� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adam Of Balsham
Adam of Balsham ( or ') (c. 1100/1102 – c. 1157/1169) was an Anglo-Norman scholastic and churchman. Life Adam was born in Balsham, near Cambridge, England. He studied with Peter Lombard at the University of Paris. He later taught in Paris, teaching John of Salisbury and William of Tyre. Further, he may have been a contemporary of Rainald of Dassel (c. 1120 – 14 August 1167) there. Gabriel Nuchelmans surmises that he may have been the first person to introduce the term ''enuntiabile'', which came to be used in the same sense as dictum.Nuchelmans, p. 169. Many sources have surmised that Adam of Balsham and Adam, Bishop of St Asaph (or Adam the Welshman) are the same person, but Raymond Klibansky concludes that they were two different men. The Petit-Pont attached to Adam's name and which crosses the Seine linking the west front of Notre-Dame Cathedral in Paris (and the site of a former bishop's palace) to the Left Bank In geography, a bank is the land alongs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russell's Paradox
In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox published by the British philosopher and mathematician, Bertrand Russell, in 1901. Russell's paradox shows that every set theory that contains an unrestricted comprehension principle leads to contradictions. According to the unrestricted comprehension principle, for any sufficiently well-defined property, there is the set of all and only the objects that have that property. Let ''R'' be the set of all sets that are not members of themselves. (This set is sometimes called "the Russell set".) If ''R'' is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The resulting contradiction is Russell's paradox. In symbols: : Let R = \. Then R \in R \iff R \not \in R. Russell also showed that a version of the paradox co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Self–referential Paradoxes
This list includes well known paradoxes, grouped thematically. The grouping is approximate, as paradoxes may fit into more than one category. This list collects only scenarios that have been called a paradox by at least one source and have their own article in this encyclopedia. These paradoxes may be due to fallacious reasoning (falsidical), or an unintuitive solution (Veridical paradox, veridical). The term ''paradox'' is often used to describe a counter-intuitive result. However, some of these paradoxes qualify to fit into the mainstream viewpoint of a paradox, which is a self-contradictory result gained even while properly applying accepted ways of reasoning. These paradoxes, often called ''antinomy,'' point out genuine problems in our understanding of the ideas of truth and Definite description, description. Logic * : The supposition that, "if one of two simultaneous assumptions leads to a contradiction, the other assumption is also disproved" leads to paradoxical conseq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Edward Hughes
George Edward Hughes (8 June 1918 – 4 March 1994) was an Irish-born New Zealand philosopher and logician whose principal scholarly works were concerned with modal logic and medieval philosophy. Biography Hughes was born on 8 June 1918 in Waterford city, Ireland. His English parents George James Hughes and Gertrude Sparks moved to Scotland in the early 1920s, as a result of the Irish War of Independence. George graduated MA with First Class Honours in Philosophy and English, and then in pure Philosophy, from the University of Glasgow. He then studied for a year at the University of Cambridge, before being called back to Glasgow as an assistant lecturer. Subsequently, he held lectureships at the University College of South Wales at Cardiff, and then the University College of North Wales at Bangor. In 1951 he was appointed to the first Chair in Philosophy at the Victoria University of Wellington in New Zealand, a position from which he retired in 1984. He died in Wellington on 4 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Buridan
Jean Buridan (; ; Latin: ''Johannes Buridanus''; – ) was an influential 14thcentury French scholastic philosopher. Buridan taught in the faculty of arts at the University of Paris for his entire career and focused in particular on logic and on the works of Aristotle. Buridan sowed the seeds of the Copernican Revolution in Europe. He developed the concept of impetus, the first step toward the modern concept of inertia and an important development in the history of medieval science. His name is most familiar through the thought experiment known as Buridan's ass, but the thought experiment does not appear in his extant writings. Life Education and career Buridan was born sometime before 1301, perhaps at or near the town of Béthune in Picardy, France,Zupko 2015, §1 or perhaps elsewhere in the diocese of Arras. He received his education in Paris, first at the Collège du Cardinal Lemoine and then at the University of Paris, receiving his Master of Arts degree and formal l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Neckham
Alexander Neckam (8 September 115731 March 1217) was an English poet, theologian, and writer. He was an abbot of Cirencester Abbey from 1213 until his death. Early life Born on 8 September 1157 in St Albans, Alexander shared his birthday with King Richard I. For this reason, his mother, Hodierna of St Albans, was hired by the royal household under Henry II to serve as a wet nurse for the future monarch. As a result, Alexander was raised as Richard's foster-brother in their early years. Works ''Speculum speculationum'' The ''Speculum speculationum'' (edited by Rodney M. Thomson, 1988) is Neckam's major surviving contribution to the science of theology. It is unfinished in its current form, but covers a fairly standard range of theological topics derived from Peter Lombard's ''Sentences'' and Augustine. Neckam is not regarded as an especially innovative or profound theologian, although he is notable for his early interest in the ideas of St. Anselm of Canterbury. His outlook ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epistle To Titus
The Epistle to Titus is one of the three pastoral epistles (along with 1 Timothy and 2 Timothy) in the New Testament, historically attributed to Paul the Apostle. It is addressed to Saint Titus and describes the requirements and duties of presbyters/bishops. Harris, Stephen L., ''Understanding the Bible''. Palo Alto: Mayfield. 1985. Text The epistle is divided into three chapters, 46 verses in total. Recipient Not mentioned in the Acts of the Apostles, Saint Titus was noted in Galatians (cf. Galatians 2:1, 3) where Paul wrote of journeying to Jerusalem with Barnabas, accompanied by Titus. He was then dispatched to Corinth, Greece, where he successfully reconciled the Christian community there with Paul, its founder. Titus was later left on the island of Crete to help organize the Church there, and later met back with the Apostle Paul in Nicopolis. He soon went to Dalmatia (now Croatia). According to Eusebius of Caesarea in the ''Ecclesiastical History'', he served as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liar Paradox
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie", the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction. Assume that "this sentence is false" is true, then we can trust its content, which states the opposite and thus causes a contradition. Similarly, we get a contradiction when we assume the opposite. History The Epimenides paradox (c. 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. The semi-mythica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epimenides
Epimenides of Knossos (or Epimenides of Crete) (; ) was a semi-mythical 7th- or 6th-century BC Greek seer and philosopher-poet, from Knossos or Phaistos. Life While tending his father's sheep, Epimenides is said to have fallen asleep for fifty-seven years in a Cretan cave sacred to Zeus, after which he reportedly awoke with the gift of prophecy (Diogenes Laërtius i. 109–115). Plutarch writes that Epimenides purified Athens after the pollution brought by the Alcmeonidae, and that the seer's expertise in sacrifices and reform of funeral practices were of great help to Solon in his reform of the Athenian state. The only reward he would accept was a branch of the sacred olive, and a promise of perpetual friendship between Athens and Knossos (Plutarch, ''Life of Solon'', 12; Aristotle, '' Ath. Pol''. 1). Athenaeus also mentions him, in connection with the self-sacrifice of the ''erastes'' and ''eromenos'' pair of Aristodemus and Cratinus, who were believed to have given their ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cicero
Marcus Tullius Cicero ( ; ; 3 January 106 BC – 7 December 43 BC) was a Roman statesman, lawyer, scholar, philosopher, orator, writer and Academic skeptic, who tried to uphold optimate principles during the political crises that led to the establishment of the Roman Empire. His extensive writings include treatises on rhetoric, philosophy and politics. He is considered one of Rome's greatest orators and prose stylists and the innovator of what became known as "Ciceronian rhetoric". Cicero was educated in Rome and in Greece. He came from a wealthy municipal family of the Roman equestrian order, and served as consul in 63 BC. He greatly influenced both ancient and modern reception of the Latin language. A substantial part of his work has survived, and he was admired by both ancient and modern authors alike. Cicero adapted the arguments of the chief schools of Hellenistic philosophy in Latin and coined a large portion of Latin philosophical vocabulary via ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
