Handbook of the History of Logic: - Fordham University Faculty

TREATMENTS OF THE PARADOXES OF
SELF-REFERENCE
Mikko Yrjönsuuri
In chapter II, 51 of Don Quixote, Miguel de Cervantes describes a curious case
presented to Sancho Panza as the governor of the island Barataria. There was a
river, a bridge, a gallows — and a law. According to the law, everyone crossing the
bridge must first tell under oath where he is going. If he is truthful, he may pass
freely, but if he lies, he will be hanged on the gallows. Now, a man is brought to
Sancho after having taken the oath that he was going to be hanged on the gallows.
The judges had been unable to solve the case, for if he was hanged, he had spoken
the truth and thus should not have been hanged. And if he was not hanged, he
lied, and thus should have been hanged. Even Sancho with his meager intellectual
powers is able to see that the case is paradoxical. No solution would accord to the
law.
Cervantes did not invent the paradox himself. Instead it was developed in the
medieval literature concerning the paradoxes of self-reference, and the formulation
is so similar to certain medieval formulations that Cervantes must have got it in
some way or other from the logicians. This is, of course, no surprise. Don Quixote
draws upon many other philosophical discussions of the schools as well.
Aristotle considers in Sophistical Refutations 25 (180a27–180b7) whether and
in what sense a person who “swears that he will break his oath” can keep his oath,
and claims that there are parallel arguments “as regards the problem whether the
same man can at the same time say what is both false and true”. Although it is
very difficult to judge whether Aristotle really had in mind genuine paradoxes of
self-reference like the Liar, ‘this sentence is false’, many medieval authors refer to
this passage as the context where Aristotle offers his solution of such paradoxes.
There was, thus, a very authoritative source for connecting oaths to the context
of self-referential paradoxes.
It is a very distinctive characteristic of the general manner in which medieval
authors discuss paradoxes of self reference that they are put into the framework of
a supposed situation. In a typical, simple fourteenth-century version of the Liar,
there is a person, Socrates, who begins speaking with the sentence ‘what Socrates
says is false’, and says nothing more (cf., e.g. [Ockham, 1974, p. 744]). In this
way, the paradoxes of self-reference are supposed to arise from something people
do, not from linguistic constructions in abstracto. In this sense, an oath is a quite
natural element to use in constructing a self-referential paradox.
Clearly, oaths were not at the core of medieval discussions of these paradoxes.
The core was the truth-predicate applied in such a way as to produce a paradox,
Handbook of the History of Logic. Volume 2: Mediaeval and Renaissance Logic
Dov M. Gabbay and John Woods (Editors)
c○ 2007 Elsevier BV. All rights reserved.