Insolubilia
Encyclopedia
In the Middle Ages
, variations on the liar paradox
were studied under the name of insolubilia (insolubles).
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, writing later in the twelfth century, explicitly recognized the paradoxical nature of insolubilia, but did not attempt to resolve the inconsistent implications of the paradox. The first resolution was given by an anonymous author at the end of the twelfth or beginning of the thirteenth century. There was an established literature on the topic by about 1320, when Thomas Bradwardine
prefaced his own discussion of insolubilia with nine views then current. Interest in insolubilia continued throughout the fourteenth century.
The medieval insolubilia literature seems to treat these paradoxes as difficult but not truly "insoluble", and, though interesting and meriting investigation, not central to the study of logic. This may be contrasted with modern studies of self-referential paradoxes such as Russell's paradox
, in which the problems are seen as fundamentally insoluble, and central to the foundations of logic.
Middle Ages
The Middle Ages is a periodization of European history from the 5th century to the 15th century. The Middle Ages follows the fall of the Western Roman Empire in 476 and precedes the Early Modern Era. It is the middle period of a three-period division of Western history: Classic, Medieval and Modern...
, variations on the liar paradox
Liar paradox
In philosophy and logic, the liar paradox or liar's paradox , is the statement "this sentence is false"...
were studied under the name of insolubilia (insolubles).
Although the liar paradox was well known in antiquity
Ancient history
Ancient history is the study of the written past from the beginning of recorded human history to the Early Middle Ages. The span of recorded history is roughly 5,000 years, with Cuneiform script, the oldest discovered form of coherent writing, from the protoliterate period around the 30th century BC...
, 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
Aristotle
Aristotle was a Greek philosopher and polymath, a student of Plato and teacher of Alexander the Great. His writings cover many subjects, including physics, metaphysics, poetry, theater, music, logic, rhetoric, linguistics, politics, government, ethics, biology, and zoology...
. 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
Augustine of Hippo
Augustine of Hippo , also known as Augustine, St. Augustine, St. Austin, St. Augoustinos, Blessed Augustine, or St. Augustine the Blessed, was Bishop of Hippo Regius . He was a Latin-speaking philosopher and theologian who lived in the Roman Africa Province...
, Cicero
Cicero
Marcus Tullius Cicero , was a Roman philosopher, statesman, lawyer, political theorist, and Roman constitutionalist. He came from a wealthy municipal family of the equestrian order, and is widely considered one of Rome's greatest orators and prose stylists.He introduced the Romans to the chief...
, and the quotation of Epimenides
Epimenides
Epimenides of Knossos was a semi-mythical 6th century BC Greek seer and philosopher-poet. While tending his father's sheep, he 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...
appearing in the Epistle to Titus
Epistle to Titus
The Epistle of Paul to Titus, usually referred to simply as Titus, is one of the three Pastoral Epistles , traditionally attributed to Saint Paul, and is part of the New Testament...
, 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, writing later in the twelfth century, explicitly recognized the paradoxical nature of insolubilia, but did not attempt to resolve the inconsistent implications of the paradox. The first resolution was given by an anonymous author at the end of the twelfth or beginning of the thirteenth century. There was an established literature on the topic by about 1320, when Thomas Bradwardine
Thomas Bradwardine
Thomas Bradwardine was an English scholar, scientist, courtier and, very briefly, Archbishop of Canterbury. As a celebrated scholastic philosopher and doctor of theology, he is often called Doctor Profundus, .-Life:He was born either at Hartfield in Sussex or at Chichester, where his family were...
prefaced his own discussion of insolubilia with nine views then current. Interest in insolubilia continued throughout the fourteenth century.
The medieval insolubilia literature seems to treat these paradoxes as difficult but not truly "insoluble", and, though interesting and meriting investigation, not central to the study of logic. This may be contrasted with modern studies of self-referential paradoxes such as Russell's paradox
Russell's paradox
In the foundations of mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction...
, in which the problems are seen as fundamentally insoluble, and central to the foundations of logic.