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, 1 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 removed by consulting other mss.
My aim is 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. My model would be Hughes's treatment of Buridan's similar text. 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 "restrictors", 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.