Handbook of the History of Logic: - Fordham University Faculty

254 Terence Parsons
8.5 Modes caused by infinitizing negation
Infinitizing negation was sometimes held to be a cause of distribution. 112 Buridan
claims that in ‘[A] non-man runs’ the term ‘man’ is distributed by the infinitizing
negation, but this distribution is cancelled out by the ‘every’ in‘Every non-man
runs’. This would fit in with the above rules for the causes of modes of supposition:
INF-NEG: An infinitizing negation distributes the term to which it is
adjoined if that term is not distributed; if it is distributed, it makes
the term determinate. It has no effect at all on any other term in the
proposition.
This rule predicts the examples given by Buridan. In the case of ‘[A] non-man
runs’ the term ’man’ is distributed by the ‘non’, and no further rules apply to
it, so it is distributed. In the case of ‘Every non-man runs’ the ‘every’ changes
the distribution back to determinacy, provided that the rule UA is expanded to
say that if it is adjoined to a distributed term it makes it determinate. Since at
present rule UA is silent about such a case, this does not alter its other applications.
Buridan actually argues for this by appeal to “the traditionally posited rule ...,
i.e. that which has the power to distribute an undistributed term removes the
distribution of a distributed one.” [SD 4.3.7.3 (271)]
The rule also insures that iterated infinitizing negations cancel one another, so
that the mode of supposition of ‘non-non-man’ in any given occurrence would be
the same as it would be if the two negations were absent.
There is however something odd about this view. Buridan defends the view
by appeal to the definitions of the modes, arguing implicitly that the term ’man’
is distributed in ‘[A] non-man runs’ because one may descend to ‘Non-Socrates
runs’. The descent is valid, but the application of the definition to this case is quite
different from other cases. Typically you produce a descended form by erasing the
term in question along with its quantifier sign and inserting a singular term. But in
the descent above the term is erased and no other changes are made. In particular,
the ‘non’ is retained, as is any quantifier sign preceding the ‘non’. The context
of the term is thus different from that of other terms that we have considered.
One might then suppose that the definition of the modes does not apply to a term
prefixed by ‘non’. Or one may take the definition to be broader than what was
proposed above. The latter view is probably better, not just because some logicians
did indeed take this application to be a case of distribution, but also because if
we count negated terms as having modes of supposition, then the principles of
inference discussed in the section after next appear to apply correctly to these
terms. So it is logically useful.
112 Peter of Spain SL XII.24 (198) discusses this as if it were a well-known view, and he rejects it.
However, Buridan SD 4.3.7.3 (271) writes as if Peter holds the view. This may not be important
since Buridan elsewhere says that some of the views he attributes to Peter’s work he is actually
making up for his own convenience. In any event, Buridan himself holds the view.