Handbook of the History of Logic: - Fordham University Faculty

580 Mikko Yrjönsuuri
but even with the truth-predicate analogous paradoxes were constructed in significantly
differing ways. The semantic paradoxes of self-reference seem to have
been discussed in both Arabic and Latin logic well before the thirteenth century
so that the standard example was ‘what I utter is false’, but various authors developed
versions that in many cases were interestingly different in terms of the
solutions given for the core paradox. Roughly at the beginning of the fourteenth
century treatments of the topic became really a flourishing genre of logic. The
most original work seems to have been done in the 1320s and 1330s in Oxford
by authors like Richard Kilvington, William Heytesbury and Roger Swyneshed.
Especially Thomas Bradwardine’s treatment accrued well-deserved fame in the
following centuries. These logicians really can be said to have undertaken the task
of giving a consistent, theoretically satisfactory solution to the Liar paradox and
its associates rather than simply having the interest of studying various logical
aspects of the Liar and other congenial paradoxes.
In the following I will go through a selection of medieval texts. The choice of the
texts is not straightforwardly based on the historical importance or even quality
in logic. The aim is, rather, that the sample gives a picture of the multiplicity and
theoretical richness of this particular medieval discussion.
INSOLUBILIA MONACENSIA
The oldest known Latin tract dedicated to the paradoxes of self-reference is an
anonymous text written about at the end of the twelfth century, called Insolubilia
Monacensia according to the current location of the manuscript in Munich.
Scholars know about occasional references to the Liar paradox already long before
that, like in Adam of Balsham’s Ars disserendi, which was written in 1132 [Adam
of Balsham, 1956, 107]. However, the scarcity of the surviving early treatments of
the paradox has made it difficult to give a story how the medieval Latin discussions
got started. One alternative is that they originate from Byzantine Greek or
medieval Arabic logical texts, which are not known either. 1
In any case, Insolubilia Monacensia presents a theory that is already relatively
developed. The word for these paradoxes is insolubilia, or “insolubles”, and the
author explains that this is due to the difficulty in giving a truth value evaluation
of the paradoxical sentences. In a manner typical for medieval logicians, he puts
the problem in a disputational context. “A solution is,” as he says, “an appropriate
determination of a thing”, which means that the semantic value of a proposition
is evaluated in a satisfactory way, typically by saying “yes” (ita) or“no”(non),
or “it is true” or “it is false” [De Rijk, 1966, 104]. That the author is thinking
of disputations in fairly technical terms becomes obvious from his comment that
1 Cf. [De Rijk, 1966, 83–86, 103]; edition of the Insolubilia Monacensia on pp. 104–115.
The text has been discussed also by, e.g. [Spade, 1973]; see also [Spade, 1987; Martin, 1993;
Bottin, 1976]. For a listing of medieval texts, see [Spade, 1975]. For other interesting early
treatments, see [Braakhuis, 1967; De Rijk, 1976; Roure, 1970]. Discussions are also to be found
in commentaries on Aristotle’s Sophistical Refutations.