Handbook of the History of Logic: - Fordham University Faculty

Treatments of the Paradoxes of Self-reference 585
cannot be, because from conceding only the sentence ‘a falsehood is conceded’ and
nothing else, a paradox would follow. [Anonymous, 2001, 203].
In both of these cases, the paradox can be avoiding by the respondent’s refusal
to go into such situation, since the rules of obligations allow such a move. Without
respondent’s acceptance nothing can be posited, and without him conceding the
crucial sentence nothing dangerous is conceded, and no self-reference arises.
After discussing the case of positing ‘a falsehood is posited’ (let us call it ‘p’)
alone, the author goes into a discussion of the opponent wishing to posit a molecular
sentence containing ‘p’. The rules concerning these situations are quite simple,
and again the idea is to avoid the paradox. The disjunction p ∨ q can be posited
if q is true but not if it is false. Similarly, the conjunction p&q can be posited if
q is false but not if it is true. The underlying idea is, of course, that it should be
possible to assign truth values without problems. In the case of the disjunction
that is true because of q, it can be entertained that the positum is true and thus
‘a falsehood is posited’ is false. Similarly, in the case of positing the conjunction
having an unambiguously false conjunct, it can be entertained that ‘a falsehood is
posited’ is true [Anonymous, 2001, 200–201]. At this point it may also be pointed
out that Insolubilia Monacensia too addresses the issue and resolves it similarly.
According to that text, ‘I utter a falsehood or God exists’ can be granted because
of the latter disjunct, while ‘I utter a falsehood and God exists’ is insoluble and
must be cancelled because its truth would require the truth of the first conjuct
[De Rijk, 1966, 109–111].
According to a further rule in the Emmeran Treatise, if the opponent wants to
posit a material equivalence between the positum and some other sentence, the
respondent must check whether the sentence at issue is true or false: if it is false,
the positum may not be accepted. If the opponent wants to posit something like
“the positum and [the first sentence] put forward are similar [in truth value]”, the
respondent can only accept the positum in case the first sentence will be true.
Unfortunately the author does not recognize that this ruling allows the opponent
to trap the respondent who maybe does not know what the opponent is going to
put forward as the first sentence [Anonymous, 2001, 201–202].
These rules about molecular sentences containing self-reference show that the
intention is not to prohibit reference to the positum in the positum itself. It is
not the self-reference that is taken to be problematic, but the possibly ensuing
paradoxes. Thus, the suggestions do not amount to even trying to give a solution
to the paradox. Rather, the author sketches ways of seeing how it could arise and
how it can be avoided in advance. The picture gets very complicated because of the
two-tier structure involving the technical disputational context and the discussion
outside the disputation. Somewhat interestingly, the author does not pay attention
to how self-referential paradoxes could arise within the technical disputation itself.
In the later treatments of the obligations technique self-referential structures
become more rare or merely apparent. 5 Occurrences of the sentence ‘the positum
5 As an outstanding exception, Obligationes Parisiensis contains material similar to that found
in the Emmeran Treatise. Cf. [De Rijk, 1975].