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LOGIC
Aristotelian forms of judgment, A, E, I, O, into tho
following existential forms :—
A. “There is not an immortal man.”
E. “ There is not a live stone.”
I. “ There is a sick man.”
0. “ There is an unlearned man.”
This reconstruction, which merges subject and predicate
in one expression, in order to combine it with the verb of
existence, is repeated in similar proposals of recent English
logicians. Venn, in his Symbolic Logic, proposes the four
forms, xy = 0, xy = 0, xy>0, xy>0 (where y means “ not-?/ ”),
but only as alternative to the ordinary forms. Bradley
says that “ ‘ S-P is real ’ attributes S-P, directly or in¬
directly, to the ultimate reality,” and agrees with Bren-
tano that “ £ is ’ never stands for anything but ‘ exists ’ ” ;
while Bosanquet, who follows Bradley, goes so far as to
define a categorical judgment as “ that which affirms the
existence of its subject, or, in other words, asserts a fact.”
Now, it is true that our primary judgments do contain a
belief in existence; but they do not all contain it in the
same way, but are beliefs sometimes that something is
determined as existing, and sometimes that something
existing is particularly determined. Brentano’s forms do
not express such a judgment of existence, as “ All existing
men are mortal.” Nor does Bradley’s form, “B,eality
includes S-P.” Metaphysically, all realities are parts of
one ultimate reality ; but logically, even philosophers think
more often only of finite realities, existing men, dogs,
horses, &c.; so that the normal form of a judgment of
■existence is either “S is a real P,” or “A real S is P.”
Hence the reconstruction of all categorical judgments
by merging subject and predicate, either on Brentano’s
or on Bradley’s plan, is a misrepresentation even of
normal categorical judgments of existence. Secondly,
it is much more a misrepresentation of categorical
judgments of non-existence. No existential form suits
a judgment such as “A centaur is a fiction,” when
we do not believe that there is a centaur, or that
reality includes a centaur. As Mill pointed out, it cannot
be implied that a centaur exists, since the very thing
asserted is that the thing has no real existence. In a
correspondence with Mill, Brentano rejoined that the
centaur exists in imagination; Bradley says, “ inside our
heads.” According to one, then, the judgment becomes
“ There is an imaginary centaur ” ; according to the other
“Reality includes an imaginary centaur.” The rejoinder,
however, though partly true, is not to the point. The
idea of the centaur does exist in our imagination, and
inside our heads, and the name of it in our mouths.
But the point is that the centaur conceived and named
does not exist beyond the idea of it and the name
for it; it is not, like a man, a real thing which is neither
the idea of it nor the name for it; it is not an existing
thing in the ordinary sense. Accordingly, no amount of
subtlety will remove the difference between a categorical
judgment of existence, e.g., “An existing man is mortal,”
and a categorical judgment of non-existence, e.g., “A con¬
ceivable centaur is a fiction,” because in the former we
believe and mean that the thing exists beyond the idea,
and in the latter we do not. If, contrary to usage, we
choose to call the latter a judgment of existence, there is
no use in quarrelling about words ; but we must insist
that new terms must in that case be invented to express
so fundamental a difference as that between judgments
about real men and judgments about ideal centaurs. So
long, however, as we use words in the natural sense, and
call the former judgments of existence, and the latter
judgments of non-existence, then “ is ” will not be, as
Bradley supposes, the same as “exists,” for we use “is”
in both judgments, but “exists” only in the first kind.
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Bosanquet’s definition of a categorical judgment contains
a similar confusion. To assert a fact and to affirm the
existence of a subject are not, as he makes out, the same
thing : a judgment often asserts a fact and denies existence
in the same breath, e.g., “ Jupiter is non-existent.” Here,
as usual in logic, tradition is better than innovation. All
categorical judgment is an unconditional belief in the fact,
signified by the copula, that a thing of some sort is (or is
not) determined ; but some categorical judgments are also
beliefs that the thing is an existing thing, signified by the
subject or by the predicate, while others are not beliefs
that the thing exists at all, but are only beliefs in some¬
thing conceivable, or nameable, or in something or other,
without particularizing what. Judgment then always
signifies being, but not always existence.
(3) Particular and Universal Judgments.—Aristotle, by
distinguishing affirmative and negative, particular and
universal, made the fourfold classification of judgments,
A, E, I, and O, the foundation both of opposition and
of inference. With regard to inference, he remarked that a
universal judgment means by “ all,” not every individual
we know, but every individual absolutely; so that, when
it becomes a major premiss, we know in it every individual
universally, not individually, and often do not know a
given individual individually until we add a minor premiss
in a syllogism. Whereas, then, a particular judgment is
a belief that some, a universal judgment is a belief that
all the individuals of a kind, or total of similar individuals,
are similarly determined, whether they are known or un¬
known individuals. Now, as we have already seen, what
is signified by the subject may be existing or not, and in
either case a judgment remains categorical so long as it is
a belief without conditions. Thus, “ Some existing men
are poets,” ‘‘All existing men are mortal,” “ Some conceiv¬
able centaurs are human in their forequarters,” “ All con¬
ceivable centaurs are equine in their hindquarters,” are
all categorical judgments. Nevertheless these obvious
applications of Aristotelian traditions have been recently
challenged, especially by Sigwart, who holds in his Logic
(secs. 27, 36) that while a particular is a categorical
judgment of existence, a universal is hypothetical, on
the ground that it does not refer to a definite number of
individuals, or to individuals at all, but rather to general
ideas, and that the appropriate form of “ all M is P ” is
“if anything is M it is P.” This view, which has in¬
fluenced not only German but also English logicians, such
as Venn, Bradley, and Bosanquet, destroys the fabric of
inference, and reduces scientific laws to mere hypotheses.
In reality, however, particular and universal judgments
are too closely connected to have such different imports.
In opposition, a categorical particular is the contradictory
of a universal, which is also categorical, not hypothetical,
e.g., “ not all M is P ” is the contradictory of “ all M is P,”
not of “ if anything is M it is P.” In inference, a particular
is an example of a universal, which in its turn may become
a particular example of a higher universal. For instance,
in the history of mechanics it was first inferred from some
that all terrestrial bodies gravitate, and then from these
as some that all ponderable bodies, terrestrial and celestial,
gravitate. How absurd to suppose that here we pass from
a particular categorical to a universal hypothetical, and
then treat this very conclusion as a particular categorical
to pass to a higher universal hypothetical ! Sigwart,
indeed, is deceived both about particulars and universals.
On the one hand, some particulars are not judgments of
existence, e.g., “some imaginary deities are goddesses”;
on the other hand, some universals are not judgments of
non-existence, e.g., “ every existing man is mortal.”
Neither kind is always a judgment of existence, but each
is sometimes the one and sometimes the other. In no