Handbook of the History of Logic: - Fordham University Faculty

The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 341
predicate to either (i) at least one thing of each kind under the subject, or (ii)
to each individual thing belonging to the subject. William is not explicit as to
which of (i) and (ii) he prefers. The example ‘Every dog is an animal’ is analyzed
in (i) into a conjunction of ‘A collie is an animal’, and ‘A puddle is an animal’,
etc. In (ii), it is analyzed into ‘Fido is an animal’, and ‘Spot is an animal’, etc.
William’s discussion of ‘Every’ or ‘All’ is very detailed and goes through all cases
and examples in which this term functions as a syncategorematic term.
William seems to be one of the first logicians to treat ‘is’ as a syncategorematic
term. The first question he addresses is whether ‘is’ pertains to the composition of
the subject and the predicate or if it pertains to the predicate. To explain this he
recalls the distinction between ‘signification’ and ‘consignification’, and explains
that ‘is’ is not really a third part of the proposition, that is, a composition, since it
signifies that which is said of something other than itself and this is the predicate,
but it does consignify the composition, which is the function of the copula.
‘Is’ is also equivocal for sometimes it indicates actual being (esse actuale) and
at other times conditional being (esse habituale), which is something with some
nature, but which does not actually exist although it could. If in ‘Every human
being is an animal’ ‘is’ is taken in the first way, then it is false when no humans
exist. If it is taken in the second way, then it is true no matter whether there
are any human or not. In this way, William commits himself to possibilia or to
things that could exist but does not. He notes himself that this amounts to saying
that things that do not exist but could have a diminished kind of being (esse
diminutum).
I will end by noting some interesting things said by William about modal terms
like ‘necessarily’ and ‘contingently’. These can be taken both as categorematic and
syncategorematic terms. If they are taken in the first sense, then they determine
the predicate and if they are taken in the second sense then they determine the
composition of the subject and the predicate, but as we just saw, if something
determines the composition then it also determines the predicate. He writes further
that:
If necessarily’ is an adverb, then it determines something that is an
act and is in the manner of an act. But the composition belonging
to the verb in a sentence is not consignified in the manner of an act;
therefore an adverb does not determine it. The assumption is clear, for
the thing belonging to the verb to which the composition belongs per
se is signified not in the manner of a substance but in the manner of an
act proceeding from the subject, while that to which the act belongs is
always signified in the manner of a substance. And thus it seems that
‘necessarily’ determines the predicate in the second case just as in the
first. 96
The argument is really interesting. In the proposition ‘Socrates runs’, ‘runs’ signifies
the act of running, but it consignifies the composition of the act with the
96 See William of Sherwood, Introduction to Logic, 100-1.