Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 581
sometimes refraining from an evaluation can be the correct determination. Thus,
if you are asked to doubt whatever is put forward to you first in the disputation,
answering with doubt is the correct determination for the first proposition, given
your obligation. Such an obligation clearly has the taste of a technical duty. 2
An insoluble is a proposition that cannot be solved in this way: no answer will
be satisfactory. Or further, “an insoluble is a circular and necessary deduction
to both sides of a contradiction” [De Rijk, 1966, 105]. The author compares two
propositions:
God is one in essence and three in persons
I utter a falsehood
In his view, the first of these propositions is insoluble absolutely (simpliciter). No
correct and consistent answer can be given to whether God is one or to whether he
is three. But on the other hand, the latter proposition is insoluble only in a certain
respect (secundum quid) and thus allows for a solution [De Rijk, 1966, 104–105].
This attitude shows strong optimism about finding a solution to the paradoxes of
self-reference, and indeed such optimism was to remain dominant throughout the
middle ages, even in two senses. First, authors thought that solving the paradoxes
is not impossible but only difficult, maybe difficult to the extent of admitting that
no solution had yet been found. And second, they did not consider it a problem
if no solution is in sight. It seems that no medieval logician saw the threat of the
logical systems collapsing in mere inconsistence in the face of the paradoxes. In
the eyes of medieval logicians, the Liar paradox was not a threat but a treasure.
It gave an especially interesting test case for semantical theories and was indeed
used for that work.
The main approach taken by the author of Insolubilia Monacensia is to look
at how putting a proposition forward relates to asserting it. His solution of the
paradox, as far he really presents a solution, is simply cancellation (cassatio). It
seems that the idea is that the paradoxes somehow fail to be such that they would
need to be answered, and thus they ought to be “cancelled”. The author divides
his treatment to three ways in which the paradox may arise: through a human
act (of asserting or such like), through a feature of the (linguistic) instrument, or
through the nature of what is asserted [De Rijk, 1966, 105]. The examples are as
follows.
The act of uttering is at issue when one considers a paradox like ‘I utter a
falsehood’, ‘I lie’, or something such. These utterances are such that they allow
for inferring a contradiction. Consider whether ‘I utter a falsehood’ is true or false.
If it is true, it can be proved to be false:
Proof.
That I utter a falsehood is true
I utter a falsehood and nothing other than this
This is a falsehood
2 [De Rijk, 1966, 104].