In the

Middle Ages In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the post-classical period of global history. It began with the fall of the Western Roman Empire a ...

, variations on the

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 ...

were studied under the name of ''insolubilia'' ("insolubles").

Overview

Although the liar paradox was well known in

antiquity Antiquity or Antiquities may refer to: Historical objects or periods Artifacts *Antiquities, objects or artifacts surviving from ancient cultures Eras Any period before the European Middle Ages (5th to 15th centuries) but still within the histo ...

, 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 ''Sophistical Refutations'' ( el, Σοφιστικοὶ Ἔλεγχοι, Sophistikoi Elenchoi; la, De Sophisticis Elenchis) is a text in Aristotle's ''Organon'' in which he identified thirteen fallacies.Sometimes listed as twelve. According to A ...

'' of

Aristotle Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of phil ...

. 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 ( , ; la, Aurelius Augustinus Hipponensis; 13 November 354 – 28 August 430), also known as Saint Augustine, was a theologian and philosopher of Berber origin and the bishop of Hippo Regius in Numidia, Roman North Af ...

Cicero Marcus Tullius Cicero ( ; ; 3 January 106 BC – 7 December 43 BC) was a Roman statesman, lawyer, scholar, philosopher, and academic skeptic, who tried to uphold optimate principles during the political crises that led to the estab ...

, and the quotation of

Epimenides Epimenides of Cnossos (or Epimenides of Crete) (; grc-gre, Ἐπιμενίδης) 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 ...

appearing in the

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 elders ...

, were not cited in discussions of ''insolubilia''.

Adam of Balsham Adam of Balsham ( la, Adam Balsamiensis 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 ...

mentioned, in passing, some paradoxical statements (dated to 1132), but he did not dwell on the difficulties raised by these statements.

Alexander Neckham Alexander Neckam (8 September 115731 March 1217) was an English magnetician, 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 bi ...

, 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 (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 call ...

prefaced his own discussion of ''insolubilia'' with nine views then current. Interest in ''insolubilia'' continued throughout the fourteenth century, especially by

Jean Buridan Jean Buridan (; Latin: ''Johannes Buridanus''; – ) was an influential 14th-century French people, French Philosophy, philosopher. Buridan was a teacher in the Faculty (division)#Faculty of Art, faculty of arts at the University of Paris for hi ...

. Hughes, G.E. (1982). ''John Buridan on Self-Reference: Chapter Eight of Buridan's Sophismata.'' An edition and translation with an introduction, and philosophical commentary. Cambridge/London/New York: Cambridge University Press, . 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 mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. Russell's paradox shows that every set theory that contains a ...

, in which the problems are seen as fundamentally insoluble, and central to the foundations of logic.

References

Bibliography

, ''Insolubilia'' (Insolubles), Latin text and English translation by Stephen Read, Leuven, Peeters Editions (Dallas Medieval Texts and Translations, 10), 2010.

External links

*{{cite SEP , url-id=insolubles , title=Insolubles , last=Spade , first=Paul Vincent History of logic Paradoxes