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We can divide medieval discussions of the insolubles—logical paradoxes such as the Liar—into two main periods, before and after Bradwardine, who wrote his treatise on Insolubles in Oxford in the early 1320s. Bradwardine's aim was to develop a solution to the insolubles which, unlike the then dominant theories, restrictio and cassatio, placed no restriction on self-reference or the theory of truth. He claimed to be able to prove that insolubles signify not only that they are false but also that they are true, and so are false. Few subsequent writers on insolubles followed him completely. Nonetheless, Heytesbury's solution agrees with Bradwardine's that there is an additional signification, though he was agnostic what that additional signification was; and a popular solution commonly found in the teaching manuals at Oxford modified Heytesbury's solution to incorporate aspects of Bradwardine's. There were remarkably similar developments at Paris, where Buridan's solution also claimed that propositions have an additional signification or implication of their own truth. Gregory of Rimini claimed that (spoken and written) insolubles correspond to a conjunction of two mental propositions, one of which says that the other is false. Gregory's solution was taken up and adapted by Peter of Ailly, arguing that the phenomena are better explained by realising that insolubles are equivocal, both true and false, corresponding to two different mental propositions. In contrast, Roger Swyneshed's aim was to provide a solution without the postulation of hidden meanings, but taking the expressions at face value. At the end of the century, Paul of Venice subscribes to the modified Heytesbury solution in his Logica Parva, but in his Logica Magna he defends a version of Swyneshed's solution.
|Title of host publication
|Theories of paradox in the Middle Ages
|Stephen Read, Barbara Bartocci
|Place of Publication
|Number of pages
|Published - 12 Jan 2023
|Studies in logic
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