Handbook of the History of Logic: - Fordham University Faculty

584 Mikko Yrjönsuuri
that they were closely connected from the very beginning, and many later authors
chose to present insolubles as obligational disputations in the technical sense.
As they were known in the thirteenth and fourteenth centuries, the technical
obligational disputations consisted of encounters between an opponent and a respondent,
with the opponent first assigning the respondent some special duty (obligatio),
typically that of accepting a sentence known to be false, and then putting
forward sentences for the respondent to concede, deny or doubt in a consistent
manner. The idea was that the respondent had to pay attention to inferential
relationships between different sentences. In the standard form, the disputation
would start with the opponent “positing” a sentence, or laying down as the basis
of reasoning a false, perhaps impossible sentence, the positum as it was called. The
respondent should accept the positum if he thought that it could be maintained
consistently. Then he should answer other sentences so that he concedes consistently
everything that logically follows from the presented positum. In a way, this
technique served for the Latin medieval period as a paradigm of how one should
deal with false assumptions in a disputational context. 3
In the medieval manuscripts from thirteenth century onwards, treatises on insolubles
were very often associated with treatises of obligational disputations. Furthermore,
paradoxical or at least complicated types of self-reference were often
constructed in the obligations treatises. It seems that already the very earliest
obligations treatises address issues that are of genuine relevance to the topics
discussed in the treatises on insolubles. One such is the anonymous “Emmeran
Treatise on False Positio”, which seems to date from the first half of the thirteenth
century. 4
The author of this text takes considerable effort to discuss exact rules for what
the respondent should do if the opponent wishes to lay down as the positum something
containing ‘a falsehood is posited’. As the text tells, the respondent ought
not to accept this sentence as the positum, since “a contradiction would follow”.
Interestingly, the author does not say that a contradiction would follow technically
in the disputation, but outside it. As he says, the opponent would then say “time
is finished”, which in these disputations means that one must turn into real discussion
of truth values and not care anymore about the duty to grant the positum
and anything following from it [Anonymous, 2001, 199–200]. The idea is simple:
when ‘a falsehood is posited’ is posited, it becomes a sentence that claims itself to
be false. The resulting paradox is quite near the standard Liar.
In another interesting move the author considers ‘a falsehood is conceded’ as
the positum. It can be accepted, as he points out, since no contradiction follows at
this stage. The sentence is not paradoxical as a positum, because the response to
the positum is not called ‘conceding’ but ‘accepting’. However, if it is posited and
accepted, and the opponent puts it forward as a proposition, the respondent loses
the disputation. The proposition put forward follows directly from the positum
as a repetition of the same sentence. Therefore, it should be conceded, but it
3 For deeper discussion of the genre, see, e.g. [Yrjönsuuri, 1994; 2001; Keffer, 2001].
4 Edition in [De Rijk, 1974], translation [Anonymous, 2001].