Handbook of the History of Logic: - Fordham University Faculty

462 Catarina Dutilh Novaes
account the whole propositional context, and not only the syncategorematic term
immediately preceding a given term. For this reason, the occurrence of several
syncategorematic terms all having the same categorematic terms under their scope
posed the problem of the effect of those embedded syncategorematic terms over
each other with respect to the (personal 29 ) supposition of the categorematic terms
in question.
In particular, the treatment of the negation requires a great deal of ingenuity.
The basic problem is: what is the effect of a negating term over the supposition
of a term which, if the negating term was removed, would have such-and-such
personal supposition in a given proposition? In other words, rules determining
the kind of supposition that a term would have if a negation is added to the
proposition where it stands are required for all three cases, namely if the term
in the original proposition had determinate, confused and distributive or merely
confused supposition. And this is where the issue arises.
Buridan, for example, offers an explicit rule concerning the effect of the negation
over a term that, without the negation, would have determinate or merely confused
supposition: A negating negation distributes every common term following it that
without it would not be distributive and does not distribute anything that precedes
it. [Buridan, 2001, 269]
That means that, if in a proposition P, atermA has determinate supposition,
and if a negation is added to P (yielding P ∗ )insuchawaythatA follows the
negation (immediate or mediately), then A will have confused and distributive
supposition. For the purposes of clarity in the exposition, let me introduce a few
notations in order to express this rule more precisely:
Det(A)P ⇔ The term A has determinate supposition in proposition P .
Dist(A)P ⇔ The term A has confused and distributive supposition in
proposition P .
Conf(A)P ⇔ The term A has merely confused supposition in proposition
P .
〈∼,A〉P ⇔ The negation is followed by term A in proposition P .
Buridan’s rule can then be formulated as follows:
Rule 1 Det(A)P &〈∼,A〉P∗ → Dist(A)P ∗
Rule 2 Conf(A)P &〈∼,A〉P∗ → Dist(A)P ∗
There is, however, a serious problem concerning the effect of a negating sign upon a
term that, without the negation, would have confused and distributive supposition.
Given the structure of the theory, it seems at first sight impossible to provide a
general rule for the negation and for confused and distributive supposition, for the
following reason. Consider the four traditional kinds of categorical propositions:
29 Or material supposition, if one follows Marsilius of Inghen in applying the traditional modes
of personal supposition also to material supposition.