Handbook of the History of Logic: - Fordham University Faculty

14 John Marenbon
in fact exist apart from a body, but it is thought of in abstraction from any body,
and this thought is not false.
Not only does the appeal to abstraction defeat the argument (1)–(11): it also
suggests a way of explaining what universals are, which we could label ‘Neutral Abstractionism’.
According to Neutral Abstractionism, particulars of a given species
each have a nature or, as Boethius calls it here, a ‘likeness’ (similitudo), which
exactly resembles the likeness of any other member of the species. The species is
constituted by the thought which brings together these likenesses, and the genus
by the thought that brings together the likenesses of the species. This solution is
one of those Boethius puts forward.
At the same time, and without marking the difference, Boethius proposes a
rather different solution. He starts by explaining that the likeness ‘is sensible
to the senses when it is in the singular things, but it is intelligible in universal
things, and in the same way when it is sensible it remains in singular things; when
it is thought in the intellect (intelligitur) it becomes universal’ [Boethius, 1906,
166:18-21]. Then he goes on to say — expanding this idea — that singulars and
universals are two things in the same subject. Just as the same line is convex or
concave depending on how it is regarded, and so it can be considered two things
in one subject, so there is the same subject (for instance, this human, John) for
singularity and universality. When John is perceived through the senses, among
the things in which he has his existence (esse suum habet), he is a singular; but
when he is grasped in thought (as a human), he is a universal [Boethius, 1966:23-
167:7]. This solution differs from Neutral Abstractionism and might be called
‘Realist Abstractionism’ since it suggests that the process of abstracting does not
merely provide a way of regarding a world that is made up only of singular things,
some similar, some diverse, but that it allows people to grasp real universals,
accessible only to thought. [Marenbon, Forthcoming-B].
Boethius’s Logical Treatises([Martin, 1991])
The short On Division (De divisione; probably 515-20) [Boethius, 1998 — with
translation and commentary] stands somewhat apart from Boethius’s other logical
treatises. Like much else in his logic, it is probably based on a work by Porphyry,
prolegomena to a now lost commentary by him on Plato’s Sophist. Despite the
Platonic text, the approach is Aristotelian. Using the language and concepts of
the Isagoge and Categories, Boethius explains the difference between accidental
division (dividing, for instance, humans in virtue of accidents of colour into black,
white and medium) and intrinsic division. Intrinsic division is of a whole into parts,
a genus into species and a word into its different meanings. In the twelfth century,
when this treatise was studied most carefully, the section on whole-part division
was especially important. Questions about genera and species were treated more
fully in the Isagoge, and on semantics in On Interpretation, but On Division was
alone in providing a brief introduction to mereology.
All of Boethius’s other logical treatises concern types of argument. Two of
them, On the Categorical Syllogism (SC ) [Boethius, 2001] and Introduction to