Roger Swyneshed, in his treatise on insolubles, dating from the early 1330s, drew three notorious corollaries from his solution. The third states that there is a contradictory pair of propositions both of which are false. This appears to contradict what Whitaker, in his iconoclastic reading of Aristotle’s De Interpretatione, dubbed “The Rule of Contradictory Pairs”, which requires that in every such pair, one must be true and the other false. Whitaker argued that, immediately after defining the notion of a contradictory (...) pair, in which one statement affirms what the other denies of the same thing, Aristotle himself gave counterexamples to the rule. This gives some credence to Swyneshed’s claim that his solution to the logical paradoxes is not contrary to Aristotle’s teaching, as many of Swyneshed’s contemporaries claimed. Insolubles are false, he said, because they falsify themselves; and their contradictories are false because they falsely deny that the insoluble itself is false. Swyneshed’s solution depends crucially on the revision he makes to the acount of truth and falsehood, brought out in his first thesis: that a false proposition can signify as it is, or as Paul of Venice, who took up and developed Swyneshed’s solution some sixty years later, puts it, a false proposition can have a true significate. Swyneshed gave a further counterexample to when he claimed that some insolubles, like future contingents, are neither true nor false. Dialetheism, the contemporary claim that some propositions are both true and false, is wedded to the Rule, and in consequence divorces denial from the assertion of the contradictory negation. Consequently, Swyneshed’s logical heresy is very different from that found in dialetheism. (shrink)

This new edition of Aristotle s De interpretatione provides an improved text compared to the 1949 Oxford edition, based upon an evaluation of the seven earliest surviving medieval manuscripts as well as many translations and commentaries from late antiquity. A text-critical apparatus provides information about the different readings.".

John Mair was an influential post-medieval scholar. This paper focuses on his Tractatus insolubilium, in which he proposed semantic analysis of self-referential phenomena, in particular on his solution to alethic and correspondence paradoxes and his treatment of their general semantic aspects as well as particular applications. His solution to paradoxes is based on the so-called “network evaluation”, i.e. on a semantics which defines the concepts of truth and correspondence with reality in contextual terms. Consequently, the relation between semantic valuation, synonymy (...) and contradiction must be redefined. (shrink)