The Semantic Paradoxes: critical edition and translation of Bradwardine's "Insolubilia"

One of the most challenging problems in philosophical logic is to give an account of truth and meaning which is not undermined by the logical paradoxes, in particular, the semantic paradoxes such as the Liar paradox. This paradox arises from considering such a sentence as 'This sentence is false', which seems to be true just when it is false and vice versa. Much attention has been given to these paradoxes throughout the past hundred years, without satisfactory agreement on a solution which does not make the cure worse than the disease. For example, Tarski's solution in the 1930s seemed to involve abandoning any attempt to define truth for natural languages, and Kripke's proposal in 1975 required not only the abandonment of Bivalence (concluding that the Liar sentence is neither true nor false) but also recognition that this fact could not be consistently stated. Both Tarski and Kripke resort to a hierarchy of object language (for which truth is defined) and metalanguage (defining truth for the object language), albeit in Kripke's case this is needed only for claims such as that the Liar sentence is paradoxical and neither true nor false. Much attention was also paid to the semantic paradoxes in the Middle Ages, especially in the thirteenth and fourteenth centuries. The theory presented by John Buridan around 1350 has been extensively discussed in the past sixty years, and was given its best treatment by George Hughes in an edition, translation and commentary published in 1982. But not only are there several problems with Buridan's proposal, but the central idea was anticipated in the discussion of the paradoxes by Thomas Bradwardine, writing in Oxford in the 1320s. This work was first edited in 1970, but exists only in Latin, and the test is based on just one manuscript, though the editor even then knew of three others. We now know of at least thirteen mss. In earlier publications, I have argued that Bradwardine's solution is not vulnerable to the objections which undermine Buridan's, and indeed, have presented Bradwardine's solution as worthy of contemporary examination and elaboration. I have also identified several passages where the existing text can be improved and clarified by consulting other mss. My aim has been to establish a critical edition of the Latin text from all thirteen mss., and to provide an English translation of the work, in order to bring it to a wider audience of both researchers and students. Like Buridan's, Bradwardine's treatise is a beautifully written work, closely argued and powerfully presented. In the first few chapters, Bradwardine considers the prevailing doctrines in his own day, notably those of the "nullifiers', who claim that such sentences say nothing, and the "restricters", who say that no expression can refer to the whole of which it is part. He dismisses these views incisively, views which have obvious parallels in contemporary philosophy. He then sets out the various assumptions on which his own solution depends, and shows clearly how the paradox is solved, before extending the solution to other paradoxical or "insoluble" cases such as the famous Plato/Aristotle paradox, where Plato says that what Aristotle says is true while Aristotle says that what Plato says is false, and the Knower paradox, 'No one knows this proposition'.

The fourteenth-century thinker Thomas Bradwardine is well known in both the history of science and the history of theology. The first of the Merton Calculators (mathematical physicists) and passionate defender of the Augustinian doctrine of salvation through grace alone, he was briefly Archbishop of Canterbury before succumbing to the Black Death in 1349. This new edition of his Insolubilia, made from all thirteen known manuscripts, shows that he was also a logician of the first rank. The edition is accompanied by a full English translation. In the treatise, Bradwardine considers and rejects the theories of his contemporaries about the logical puzzles known as “insolubles,” and sets out his own solution at length and in detail. In a substantial Introduction, Stephen Read describes Bradwardine’s analysis, compares it with other more recent theories, and sets it in its historical context. The text is accompanied by three Appendices, the first of which is an extra chapter found in two manuscripts (and partly in a third), which appears to contain further thoughts by Bradwardine himself. The second contains an extract from Ralph Strode’s Insolubilia, composed in the 1360s, repeating and enlarging on Bradwardine’s text; and the third consists of an anonymous text which applies Bradwardine’s solution to a succession of different insolubles.

The main objective was to provide an English translation of Thomas Bradwardine's 'Insolubilia' for the use of students and researchers in philosophical logic. This work was composed while Bradwardine was a young master at Oxford in the 1320s. He later went on to make original contributions to the theory of dynamics, for which he is justly famous in the history of science, and eventually to become Archbishop of Canterbury, shortly before succumbing to the Black Death in 1349. This early treatise by an outstanding thinker contains an original treatment of the semantic paradoxes, arguably a viable solution, and at all events a model of clarity and effectiveness in treating the nature of truth and tackling the "insolubles", problem cases in semantics and logic which defy easy solution. By making this text available to a wider audience I intend to complete work begun by Arthur Prior in the 1960s. Working in ignorance of Bradwardine (but influenced by John Buridan, writing in the generation after Bradwardine), Prior made a proposal for solving the semantic paradoxes which has remarkable similarities to Bradwardine's. The Latin text of Bradwardine's treatise was published in 1970 by Roure. Although she knew of four manuscripts, Roure based her edition on only one manuscript, with some corrections against a second. We now know of 13 mss. of the work, and the time has now arrived for a critical edition of the Latin text. There are numerous passages where Roure's text is incorrect and misleading. To establish a reliable text required a survey of the all the extant manuscripts, and the formulation of the basic text with variants. From that, a trustworthy English translation has now been made. Bradwardine's treatise runs to nearly 19,000 words in Latin (nearly 25,000 in the translation), including a newly discovered chapter not included in Roure's edition. The text and translation is accompanied by a substantial introduction of around 20,000 words describing the historical context in which the work was composed, and the contemporary context in which the logical paradoxes have to a very large extent put boundaries to research on truth and meaning over the past century. The three parts, text, translation and commentary, comprise a useful volume to introduce students to the issues and historical background, and provide other researchers with material for further reflection. I have been invited to contribute to an edited collection on the "revenge problem". This is exactly where Bradwardine's solution cuts in, blocking the move from the claim that the Liar sentence is false to the conclusion that it must then be true. This paper has been completed and accepted, and is due to appear in the spring of 2007.