§ 421. Since definition and division are concerned with the intension
and extension of terms, they are commonly treated of under the first
part of logic: but as the treatment of the subject implies a
familiarity with the Heads of Predicables, which in their turn imply
the proposition, it seems more desirable to deal with them under the
second.
§ 422. We have already had occasion to distinguish division from
Enumeration. The latter is the statement of the individual things to
which a name applies. In enumeration, as in division, the wider term
is predicable of each of the narrower ones.
§ 423. Partition is the mapping out of a physical whole into its
component parts, as when we say that a tree consists of roots, stem,
and branches. In a partition the name of the whole is not predicable
of each of the parts.
§ 424. Distinction is the separation from one another of the various
meanings of an equivocal term. The term distinguished is predicable
indeed of each of the members, but of each in a different sense. An
equivocal term is in fact not one but several terms, as would quickly
appear, if we were to use definitions in place of names.
§ 425. We have seen that a logical whole is a genus viewed in relation
to its underlying species. From this must be distinguished a
metaphysical whole, which is a substance viewed in relation to its
attributes, or a class regarded in the same way. Logically, man is a
part of the class, animal; metaphysically, animal is contained in
man. Thus a logical whole is a whole in extension, while a
metaphysical whole is a whole in intension. From the former point of
view species is contained in genus; from the latter genus is contained
in species.
PART III.--OF INFERENCES.
CHAPTER I.
_Of Inferences in General_.
§ 426. To infer is to arrive at some truth, not by direct experience,
but as a consequence of some truth or truths already known. If we see
a charred circle on the grass, we infer that somebody has been
lighting a fire there, though we have not seen anyone do it. This
conclusion is arrived at in consequence of our previous experience of
the effects of fire.
§ 427. The term Inference is used both for a process and for a product
of thought.
As a process inference may be defined as the passage of the mind from
one or more propositions to another.
As a product of thought inference may be loosely declared to be the
result of comparing propositions.
§ 428. Every inference consists of two parts--
(1) the truth or truths already known;
(2) the truth which we arrive at therefrom.
The former is called the Antecedent, the latter the Consequent. But
this use of the terms 'antecedent' and 'consequent' must be carefully
distinguished from the use to which they were put previously, to
denote the two parts of a complex proposition.
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