Insolubilia

Last updated April 09, 2019

In the Middle Ages, variations on the liar paradox were studied under the name of insolubilia ("insolubles").

Middle Ages Period of European history from the 5th through the 15th centuries

In the history of Europe, the Middle Ages lasted from the 5th to the 15th century. It began with the fall of the Western Roman Empire and merged 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.

In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that he or she is 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 is lying. 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.

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.

Ancient history as a term refers to the aggregate of past events from the beginning of writing and recorded human history and extending as far as the post-classical history. The phrase may be used either to refer to the period of time or the academic discipline.

Sophistical Refutations is a text in Aristotle's Organon in which he identified thirteen fallacies. According to Aristotle, this is the first work to treat the subject of deductive reasoning.. The fallacies Aristotle identifies are the following:

Equivocation
Amphibology
Composition
Division
Accent
Figure of speech or form of expression

Aristotle was a philosopher during the Classical period in Ancient Greece, the founder of the Lyceum and the Peripatetic school of philosophy and Aristotelian tradition. Along with his teacher Plato, he is considered the "Father of Western Philosophy". His writings cover many subjects – including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him, and it was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion.

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, especially by Jean Buridan.^[1]

Adam of Balsham was an Anglo-Norman scholastic and churchman.

Thomas Bradwardine 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.

Jean Buridan was an influential 14th century French philosopher.

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.

In the foundations of mathematics, Russell's paradox, discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction. The same paradox had been discovered in 1899 by Ernst Zermelo but he did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other members of the University of Göttingen. At the end of the 1890s Cantor himself had already realized that his definition would lead to a contradiction, which he told Hilbert and Richard Dedekind by letter.

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References

↑ 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, ISBN 0-521-28864-9.

Bibliography

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

External links

Spade, Paul Vincent. "Insolubles". In Zalta, Edward N. Stanford Encyclopedia of Philosophy .

Edward N. Zalta is a senior research scholar at the Center for the Study of Language and Information. He received his PhD in philosophy from the University of Massachusetts Amherst in 1980. Zalta has taught courses at Stanford University, Rice University, the University of Salzburg, and the University of Auckland. Zalta is also the Principal Editor of the Stanford Encyclopedia of Philosophy.

The Stanford Encyclopedia of Philosophy (SEP) combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Each entry is written and maintained by an expert in the field, including professors from many academic institutions worldwide. Authors contributing to the encyclopedia give Stanford University the permission to publish the articles, but retain the copyright to those articles.

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[1] 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, ISBN 0-521-28864-9.