LUW 4 pm CET Stephen Read: Swyneshed, Aristotle and the Rule of Contradictory Pairs

[jean-yves beziau]

https://www.springer.com/journal/11787/updates/18988758

April 21, 2021 – Stephen Read – Swyneshed, Aristotle and the Rule of
Contradictory Pairs
Chair: Jens Lemanski
Editor of the LU special issue The Cretan Square

Associate Organization: Square of Opposition Project
presented by Jean-Yves Beziau

Roger Swyneshed, in his treatise on insolubles (logical paradoxes), 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” (RCP), 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
account 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 (RCP) 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.
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