Logical division,
Hoffmann says, shares some similarities with definition, since, in a
sense, both are divisions – in definition, we divide a concept
(say, humanity) to more abstract concept (rationality and animality).
A third form of division is then mathematical division of quantities
into smaller quantities. The peculiar sort of division we now
investigate, on the other hand, is a division of genus into its
species. Its importance lies in providing premisses for disjunctive
deductions – if we know all the species of a genus, we know that a
member of the genus must belong to some species.
Compared to his
account of definition, Hoffmann's discourse on divisions is rather
straightforward. Just like in case of definition, Hoffmann
distinguishes between nominal and real division – in nominal
division, the different classes have merely a common name, but in
case of real division, they truly belong to same genus. A real
division presupposes then, obviously, idea of genus as a whole and idea
of species as separate from one another. Furthermore, division also
requires a ground for distinguishing the species from another and
also some element that is common to all the species – this latter
element should then be something essential to genus, or otherwise
there might be a species that wouldn't have this element. Species
should also fill the genus in the sense that no other species can
belong to the same genus. Finally, changing from one species to
another should affect thing in question in some essential manner –
thus, if a piece of iron from London changes into a piece of iron
from France, nothing of consequence happens to iron and therefore
iron from London and iron from Paris do not form a true division.
After division,
Hoffmann turns his attention to judgements, and we can be equally
quick with them also. Hoffmann counts various manners in which a
judgement can be imperfect. There are external reasons, such as when
the proposition is more restricted than it could be, that is, when we
say ”for some x”, when we could as well say ”for all x” –
in such a case, improving the proposition would require a change in
the subject. There might also be internal reasons, such as ambiguity
– improving such a proposition does not change the subject or
predicate, but merely modifies the connection between them.
Hoffmann describes
in more detail methods for improving ambiguous propositions. In many
cases, all it takes is to clarify the concepts or ideas that form the
judgement, which is something Hoffmann has already explained in
theoretical part of his work. There is also the possibility that the
ambiguity derives more from the manner of connection between ideas in
judgement. Hoffmann especially mentions comparative judgements, such
as ”A has more quality X than B”, where X is a quality that can
appear in many shapes – for instance, because intelligence is
something that can appear in many shapes, ”A is more intelligent
than B” might mean e.g. that A does crossword puzzles better than
B, makes calculations more reliably than B etc. In such cases,
Hoffmann notes, we should state clearly in what manner A exceeds B.
So much for
divisions and judgements, next time we shall see what Hoffmann has
to say about deductions in his practical division of logic.