§ 383. The violation of Rule 4 is known as 'ignotum per ignotius' or
'per aeque ignotum.' This rule also may seemingly be violated when it
is not really so. For a definition may be correct enough from a
special point of view, which, apart from that particular context,
would appear ridiculous. From the point of view of conic sections, it
is correct enough to define a triangle as that section of a cone which
is formed by a plane passing through the vertex perpendicularly to the
base, but this could not be expected to make things clearer to a
person who was inquiring for the first time into the meaning of the
word triangle. But a real violation of the fourth rule may arise, not
only from obscurity, but from the employment of ambiguous language or
metaphor. To say that 'temperance is a harmony of the soul' or that
'bread is the staff of life,' throws no real light upon the nature of
the definiend.
§ 384. The material correctness of a definition is, as we have already
seen, a matter extraneous to formal logic. An acquaintance with the
attributes which terms imply involves material knowledge quite as much
as an acquaintance with the things they apply to; knowledge of the
intension and of the extension of terms is alike acquired by
experience. No names are such that their meaning is rendered evident
by the very constitution of our mental faculties; yet nothing short of
this would suffice to bring the material content of definition within
the province of formal logic.
CHAPTER VIII.
_Of Division._
§ 385. To divide a term is to unfold its extension, that is, to set
forth the things of which it is a name.
§ 386. But as in definition we need not completely unfold the
intension of a term, so in division we must not completely unfold its
extension.
§ 387. Completely to unfold the extension of a term would involve
stating all the individual objects to which the name applies, a thing
which would be impossible in the case of most common terms. When it is
done, it is called Enumeration. To reckon up all the months of the
year from January to December would be an enumeration, and not a
division, of the term 'month.'
§ 388. Logical division always stops short at classes. It may be
defined as the statement of the various classes of things that can be
called by a common name. Technically we may say that it consists in
breaking up a genus into its component species.
§ 389. Since division thus starts with a class and ends with classes,
it is clear that it is only common terms which admit of division, and
also that the members of the division must themselves be common terms.
§ 390. An 'individual' is so called as not admitting of logical
division. We may divide the term 'cow' into classes, as Jersey,
Devonshire, &c., to which the name 'cow' will still be applicable, but
the parts of an individual cow are no longer called by the name of the
whole, but are known as beefsteaks, briskets, &c.
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