The Art of Logical Thinking; Or, The Laws of ReasoningAtkinson, William Walker
Philosophy
The Art of Logical Thinking; Or, The Laws of Reasoning
Atkinson, William Walker
Logic; Reasoning
Some authorities also classify terms as _higher and lower_; also as
_broad and narrow_. This classification is meant to indicate the content
and extent of the term. For instance, when we classify, we begin with
the individuals which we then group into a small class. These classes we
then group into a larger class, according to their resemblances. These
larger classes then go to form a part of still larger classes, and so
on. As these classes advance they form _broader_ terms; and as we
retreat from the general class into the less general and more
particular, the term becomes _narrower_. By some, the _broader_ term
which includes the narrower is called the _higher term_, and the
narrower are called the _lower terms_. Thus _animal_ would be a higher
and broader term than dog, cat or tiger because it includes the latter.
Brooks says: "Since a concept is formed by the union of the common
attributes of individuals, it thus embraces both attributes and
individuals. The attributes of a concept constitute what is called its
_content_; the individuals it embraces constitute its _extent_."
Accordingly, the feature of including objects in a concept or term is
called its _extension_; while the feature of including attributes or
qualities is called its intension. It follows as a natural consequence
that the greater the _extension_ of a term, the less its _intension_;
the greater its _intension_, the less its _extension_. We will
understand this more clearly when we consider that the more individuals
contained in a term, the fewer _common_ properties or qualities it can
contain; and the more common properties, the fewer individuals. As
Brooks says: "The concept _man_ has more _extension_ than _poet_,
_orator_ or _statesman_, since it embraces more individuals; and less
_intension_, since we must lay aside the distinctive attributes of poet,
orator and statesman in order to unite them in a common class _man_." In
the same way the general term _animal_ is quite extended for it includes
a large number of individual varieties of very different and varied
characteristics and qualities; as for instance, the lion, camel, dog,
oyster, elephant, snail, worm, snake, etc. Accordingly its intension
must be small for it can include only the qualities common to all
animals, which are very few indeed. The definition of the term shows how
small is its _intension_, as: "_Animal._ An organic being, rising above
a vegetable in various respects, especially in possessing sensibility,
will and the power of voluntary motion." Another narrows the intension
still further when he defines _animal_ as: "a creature which possesses,
or has possessed, life." Halleck says: "_Animal_ is very narrow in
intension, very broad in extension. There are few qualities common to
all animals, but there is a vast number of animals. To give the full
meaning of the term in _extension_, we should have to name every animal,
from the microscopic infusoria to the tiger, from the angleworm to the
whale.
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