PROPOSITIONS
We have seen that the first step of Deductive Reasoning is that which we
call Concepts. The second step is that which we call Propositions.
In Logic, a _Proposition_ is: "A sentence, or part of a sentence,
affirming or denying a connection between the terms; limited to express
assertions rather than extended to questions and commands." Hyslop
defines a Proposition as: "any affirmation or denial of an agreement
between two conceptions."
_Examples of Propositions_ are found in the following sentences: "The
rose is a flower;" "a horse is an animal;" "Chicago is a city;" all of
which are affirmations of agreement between the two terms involved; also
in: "A horse is not a zebra;" "pinks are not roses;" "the whale is not a
fish;" etc., which are denials of agreement between the terms.
The _Parts of a Proposition_ are: (1) the _Subject_, or that of which
something is affirmed or denied; (2) the _Predicate_, or _the
something_ which is affirmed or denied regarding the _Subject_; and (3)
the _Copula_, or the verb serving as a link between the Subject and the
Predicate.
* * * * *
In the Proposition: "Man is an animal," the term _man_ is the Subject;
the term _an animal_ is the Predicate; and the word _is_, is the Copula.
The Copula is always some form of the verb _to be_, in the present tense
indicative, in an affirmative Proposition; and the same with the
negative particle affixed, in a negative Proposition. The Copula is not
always directly expressed by the word _is_ or _is not_, etc., but is
instead expressed in some phrase which implies them. For instance, we
say "he runs," which implies "he is running." In the same way, it may
appear at times as if the Predicate was missing, as in: "God is," by
which is meant "God is existing." In some cases, the Proposition is
inverted, the Predicate appearing first in order, and the Subject last,
as in: "Blessed are the peacemakers;" or "Strong is Truth." In such
cases judgment must be used in determining the matter, in accordance
with the character and meaning of the terms.
An _Affirmative Proposition_ is one in which the Predicate is _affirmed_
to agree with the Subject. A _Negative Proposition_ is one in which the
agreement of the Predicate and Subject is _denied_. Examples of both of
these classes have been given in this chapter.
Another classification of Propositions divides them in three classes, as
follows (1) Categorical; (2) Hypothetical; (3) Disjunctive.
A _Categorical Proposition_ is one in which the affirmation or denial is
made without reservation or qualification, as for instance: "Man is an
animal;" "the rose is a flower," etc. The fact asserted may not be
_true_, but the statement is made positively as a statement of reality.
A _Hypothetical Proposition_ is one in which the affirmation or denial
is made to depend upon certain conditions, circumstances or
suppositions, as for instance: "If the water is boiling-hot, it will
scald;" or "if the powder be damp, it will not explode," etc. Jevons
says: "Hypothetical Propositions may generally be recognized by
containing the little word 'if;' but it is doubtful whether they really
differ much from the ordinary propositions.... We may easily say that
'boiling water will scald,' and 'damp gunpowder will not explode,' thus
avoiding the use of the word 'if.'"
A _Disjunctive Proposition_ is one "implying or asserting an
alternative," and usually containing the conjunction "or," sometimes
together with "either," as for instance: "Lightning is sheet or forked;"
"Arches are either round or pointed;" "Angles are either obtuse, right
angled or acute."
Another classification of Propositions divides them in two classes as
follows: (1) Universal; (2) Particular.
A _Universal Proposition_ is one in which the _whole quantity_ of the
Subject is involved in the assertion or denial of the Predicate. For
instance: "All men are liars," by which is affirmed that _all_ of the
entire race of men are in the category of liars, not _some_ men but
_all_ the men that are in existence. In the same way the Proposition:
"No men are immortal" is Universal, for it is a _universal denial_.
A _Particular Proposition_ is one in which the affirmation or denial of
the Predicate involves only a _part or portion_ of the whole of the
Subject, as for instance: "_Some_ men are atheists," or "_Some_ women
are not vain," in which cases the affirmation or denial does not involve
_all_ or the _whole_ of the Subject. Other examples are: "A _few_ men,"
etc.; "_many_ people," etc.; "_certain_ books," etc.; "_most_ people,"
etc.
Hyslop says: "The signs of the Universal Proposition, when formally
expressed, are _all_, _every_, _each_, _any_, _and whole_ or words with
equivalent import." The signs of Particular Propositions are also
certain adjectives of quantity, such as _some_, _certain_, _a few_,
_many_, _most_ or such others as denote _at least a part_ of a class.
The subject of the Distribution of Terms in Propositions is considered
very important by Logicians, and as Hyslop says: "has much importance in
determining the legitimacy, or at least the intelligibility, of our
reasoning and the assurance that it will be accepted by others." Some
authorities favor the term, "Qualification of the Terms of
Propositions," but the established usage favors the term
"Distribution."
The definition of the Logical term, "Distribution," is: "The
distinguishing of a universal whole into its several kinds of species;
the employment of a term to its fullest extent; the application of a
term to its fullest extent, so as to include all significations or
applications." A Term of a Proposition is _distributed_ when it is
employed in its fullest sense; that is to say, _when it is employed so
as to apply to each and every object, person or thing included under
it_. Thus in the proposition, "All horses are animals," the term
_horses_ is distributed; and in the proposition, "Some horses are
thoroughbreds," the term _horses_ is not distributed. Both of these
examples relate to the distribution of the _subject_ of the proposition.
But the predicate of a proposition also may or may not be distributed.
For instance, in the proposition, "All horses are animals," the
predicate, _animals_, is not distributed, that is, _not used in its
fullest sense_, for all _animals_ are not _horses_--there are _some_
animals which are not horses and, therefore, the predicate, _animals_,
not being used in its fullest sense is said to be "_not distributed_."
The proposition really means: "All horses are _some_ animals."
There is however another point to be remembered in the consideration of
Distribution of Terms of Propositions, which Brooks expresses as
follows: "Distribution generally shows itself in the form of the
expression, but sometimes it may be determined by the thought. Thus if
we say, 'Men are mortal,' we mean _all men_, and the term men is
distributed. But if we say 'Books are necessary to a library,' we mean,
not 'all books' but 'some books.' The _test of distribution_ is whether
the term applies to '_each and every_.' Thus when we say 'men are
mortal,' it is true of each and every man that he is mortal."
The Rules of Distribution of the Terms of Proposition are as follows:
1. All _universals_ distribute the _subject_.
2. All _particulars_ do not distribute the _subject_.
3. All _negatives_ distribute the _predicate_.
4. All _affirmatives_ do not distribute the _predicate_.
The above rules are based upon logical reasoning. The reason for the
first two rules is quite obvious, for when the subject is _universal_,
it follows that the _whole subject_ is involved; when the subject is
_particular_ it follows that _only a part_ of the subject is involved.
In the case of the third rule, it will be seen that in every _negative_
proposition the _whole of the predicate_ must be denied the subject, as
for instance, when we say: "Some _animals_ are _not horses_," the whole
class of _horses_ is cut off from the subject, and is thus
_distributed_. In the case of the fourth rule, we may readily see that
in the affirmative proposition the whole of the predicate _is not
denied_ the subject, as for instance, when we say that: "Horses are
animals," we do not mean that horses are _all the animals_, but that
they are merely a _part or portion_ of the class animal--therefore, the
predicate, _animals_, is not distributed.
In addition to the forms of Propositions given there is another class of
Propositions known as _Definitive or Substitutive Propositions_, in
which the Subject and the Predicate are exactly alike in extent and
rank. For instance, in the proposition, "A _triangle_ is a _polygon of
three sides_" the two terms are interchangeable; that is, may be
substituted for each other. Hence the term "substitutive." The term
"definitive" arises from the fact that the respective terms of this kind
of a proposition necessarily _define_ each other. All logical
definitions are expressed in this last mentioned form of proposition,
for in such cases the subject and the predicate are precisely equal to
each other.