Handbook of the History of Logic: - Fordham University Faculty

Some A is B (1)
Every A is B (3)
Logic in the 14 th Century after Ockham 463
is the contradictory of
is the contradictory of
No A is B (2)
Some A is not B (4)
(contradiction 1)
(contradiction 2)
‘Some A is B’ (1) should be equivalent to ‘Not: No A is B’(2 ′ ) (the contradictory
of (2)) and ‘Every A is B’ (3) should be equivalent to ‘Not: Some A is not B’ (4 ′ )
(the contradictory of (4)). If these equivalences hold, then the supposition of the
terms in (1) and (2 ′ ) should be the same: A and B have determinate supposition
in (1), so they should have the same kind of supposition in (2 ′ ).
For this to happen, the effect of the negation in (2 ′ ) should be to turn the
confused and distributive supposition of A and B in ‘No A is B’ into determinate
supposition. This is indeed the rule proposed by Ockham: Nevertheless, it should
be noted that the aforementioned rules hold only in the case where the term in
question would not stand confusedly and distributively if the negation sign or the
relevant verb or name were taken away. For if the term were to stand confusedly
and distributively when one of these expressions [negation sign] were taken
away, then with the addition of such an expression it would stand determinately.
[Ockham, 1998, 214]
Ockham’s rule can be formulated as follows:
Rule 3o Dist(A)P &〈∼,A〉P∗ → Det(A)P ∗
But what about the equivalence between (3) and (4 ′ )? In (3) A has confused
and distributive supposition and B has merely confused supposition. So the same
should occur in (4 ′ ). However, in ‘Some A is not B’, A has determinate supposition
and B has confused and distributive supposition. According to rule 1, the negation
would make A have confused and distributive supposition in (4 ′ ), that is, the same
supposition of A in (3) (so far, so good). But what about B? According to the rule
proposed by Ockham, since it has confused and distributive supposition in ‘Some
A is not B’, it would have determinate supposition in (4 ′ ), under the effect of
the negation. But in fact it ought to have merely confused supposition, because
of the equivalence between (3) and (4 ′ ). So the rule stated by Ockham does not
safeguard this equivalence.
Buridan, on the other hand, presents a rule that does safeguard the equivalence
between (3) and (4 ′ ): A common term is confused nondistributively by two distributive
[parts of speech] preceding it, either of which would distribute it without
the other. [Buridan, 2001, 275]
Buridan’s rule can be formulated as follows:
Rule 3b Dist(A)P &〈∼,A〉P∗ → Conf(A)P ∗
That is, under the effect of two negations, B in (4 ′ ) would have merely confused
supposition, which is the desired result. But then the equivalence between (1) and