Handbook of the History of Logic: - Fordham University Faculty

312 Henrik Lagerlund
Instead Boethius provides us with a systematic way of searching for the middle
term.
A syllogism contains three terms called a major extreme, a middle and a minor
extreme, and for the syllogism to be valid the two extremes need to bare the right
relation to the middle term. The topical differentiae provide a classification of
these relations. The differentiae are the distinguishing features of these relations.
For example, species of such relations are ‘is the definition of’ and ‘is the meaning
of’, and their differnetiae are ‘from a whole’ and ‘from a sign’.
An example that Boethius has is the following: I want to answer the question:
Are trees animals? I run through the different sorts of relations in the list of topics
or loci for one suitable for relating the extremes ‘tree’ and ‘animal’. Once I come
to the relation of definition I find that the definition of animal is ‘living substance
with sense perception’ and I immediately see that I can deny this of trees, which
means that I have shown that trees are not animals.
The practical question for a theorist of the topics is of course how to organise
the list of differentiae and there are various lists in the commentary tradition.
Boethius’ list is based on Cicero’s and the tradition after Boethius follow him
closely. The character of the discussion did not chance when one started to comment
on Aristotle’s original book in the thirteenth century instead of commenting
on his.
The status of the loci, however, gradually became the overarching problem, and
it is also in that discussion that some new problems and developments can be seen
in the thirteenth century. 73 Most authors from this period described the locus as
a relation, but what is it a relation between? It is not a relation between terms
taken as term, but between the things that the terms stand for. This, of course,
touches upon a much larger question, namely what is logic about? The discussion
we find in thirteenth century commentaries on the Topics is highly interesting.
In 1240 to 1250, in Paris a consensus about the status on the loci start to
emerge. These authors, one of which is Robert Kilwardby, define a locus as a
relation of one thing to another (habitudo rei ad rem). The logician here meets
the metaphysician, which so often is the case in thirteenth century logic as we have
seen, that is, logic is about things and their relations.
The loci are not just any relation between things, but they are of a general
character and could hence equally well apply to various things. This means that
they are external and accidental in comparison to any particular thing to which
they apply. They do not belong essentially to any kind of species of a thing. This
explains the difference between dialectics and demonstrative science. Demonstrative
science regard the thing which is the cause or is defined as the thing which
it actually is. Dialectics only applies to the general concept without specifying
which cause, but concerns causes in general.
73 The discussion in the rest of this section is foremost based on [Green-Pedersen, 1984, 223-40].
See also [Stump, 1982] for a careful overview of the tradition of the Topics.