Handbook of the History of Logic: - Fordham University Faculty

The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 325
Things said of a subject, but which are not in a subject are thing like substantial
genera and species, and substantial differentiae, that is, human being, animal and
rational. Things like substantial individuals, like Socrates, are neither said of a
subject nor are they in a subject. Things said of a subject that are also in a
subject are the genera and species of the other nine categories. They are said of
inferiors and they are in a subject as accidents are in a subject, for example, as
colour is said of whiteness as of an inferior and it is also in a body as in a subject.
Finally there are also things which are in a subject, but not said of any subject,
like a particular piece of knowledge is in the soul, or this individual colour of the
wall, for example, is in a subject.
After this Peter turns to a discussion of the individual categories and first
is, of course, substance. Traditionally, it is divided into primary and secondary
substance. Primary substance is what is most properly called substance, and as
mentioned above it is neither said of a subject not in a subject, like individual
humans (Socrates, Plato etc.) and horses. Secondary substances are species and
genera, since they have primary substances under them. A secondary substance
can be used as a predicate, but a primary cannot, like ‘Socrates is a human being’,
but one cannot say ‘A human being is Socrates’. A primary substance is also a
hoc aliquid, that is a thing or an individual of which there is only one.
A quantity, which is the second category, is either discrete or continued. Number
or discourse are discrete quantities. There is no common terms to which either
numbers or discourse can be linked. They are separate and a multitude brought
together into a unit. Lines, body, time and place are continuous quantities. A line
is joined to a common term, namely a point, and hence continuous.
Relation is the next category treated. Contrariety is a relation, and more or
less as well as equal and unequal. Every relation is convertible like father and son
are convertible, that is, if A is the father of B, then B is the son of A. This means
that in a relation like father to son, which is asymmetrical, then one can always
find another asymmetrical relation that together makes up a symmetrical relation.
The fourth category discussed by Peter is quality. There are four subdivisions
of quality, namely, (i) habits and dispositions, (ii) capacity, (iii) passion, and (iv)
form. A habit differs from a disposition by being more permanent. Knowledge is a
habit while virtue is a disposition. Some have a natural capacity for health while
others have a natural capacity for sickness; some can play the piano while others
cannot. (iii) is a passivity or a quality of being affected, like sensations. The fourth
kind of quality is the form or shape of something stable, like the triangularity of
a body. The other categories are only mentioned by Peter.
On Syllogisms
After their treatment of the categories comes a discussion of syllogisms (William
jumps from the discussion of predicables to the syllogisms). The theory of the
syllogisms is the main part of logic for a thirteenth century logician and it is what
comes closest to what we now call logic. The other parts of medieval logic would