Handbook of the History of Logic: - Fordham University Faculty

464 Catarina Dutilh Novaes
(2 ′ ) would no longer be preserved: B would have merely confused supposition in
(2 ′ ), whereas it ought to have determinate supposition, as in (1).
Thus, neither of these rules is able to preserve both equivalences: thus formulated,
a rule concerning the effect of the negation upon a term originally with
confused and distributive supposition either preserves the equivalence between (1)
and (2 ′ ) (Ockham’s rule) or it preserves the equivalence between (3) and (4 ′ )(Buridan’s
rule). This is due to the following asymmetry: in the case of contradiction 1,
the opposition in the supposition of B in each proposition is between determinate
supposition and confused and distributive supposition, whereas in contradiction
2 the same opposition is between merely confused supposition and confused and
distributive supposition. Therefore, it would seem impossible to provide a homogeneous
account of the effect of the negation (or other distributive term) upon
terms with confused and distributive supposition (for a systematic approach to
this problem, see part 8 of Parson’s contribution to this volume).
However (and fortunately for the general robustness of supposition theory as a
semantic framework), later masters were well aware of this difficulty and proposed
ways to deal with it. Already at the end of the 14 th century, in his popular
commentary to Buridan’s Summulae, John Dorp [1499] proposed a method to
determine the supposition of terms following a negation based on the idea that
the proposition should be rephrased in such a way that the negation would be
all the way at the end of the proposition, in which case the usual (i.e. positive)
rules for the determination of the personal supposition of a term could be applied.
On this approach, ‘[t]he problem of assigning the mode of supposition to a term
following a negation becomes that of determining a procedure for bringing negative
sentences into a non-ordinary form [one where the negation only precedes the verb]
such that the mode of supposition of each term remains unchanged.’ [Karger, 1993,
419]
On the basis of Dorp’s examples, Karger proposes a reconstruction of what this
procedure would be like, essentially based in the idea of bringing the negation
towards the end of the proposition, immediately before the verb, and introducing
universally quantifying signs (to recover the distributive effect of the negation)
where there was none, and deleting such universally quantifying terms previously
present. Here is an example (cf. [Karger, 1993, 419], and [Read, 1991a, fn. 8] for
Dorp’s text):
Nullum animal omnis homo est (No animal is every man) is rephrased
as
Omne animal homo non est (Every animal a man is not).
Nullum is replaced by Omne, omnis preceding homo in the original proposition is
deleted, and the negation comes to be followed only by the verb est. Now, it is clear
that animal has confused and distributive supposition (which was clear already in
the original proposition), but moreover it becomes apparent that homo has merely
confused supposition (as it follows mediately the universal sign), whereas in the
original proposition it would have been unclear (from 3o and 3b alone) whether it