1. _Judgment and Conception._--The emphasis now laid on judgment, the
recovery from Hume's confusion of beliefs with ideas and the association
of ideas, and the distinction of the mental act of judging from its
verbal expression in a proposition, are all healthy signs in recent
logic. The most fundamental question, before proceeding to the
investigation of inference, is not what we say but what we think in
making the judgments which, whether we express them in propositions or
not, are both the premises and the conclusion of inference; and, as this
question has been diligently studied of late, but has been variously
answered, it will be well to give a list of the more important theories
of judgment as follows:--
a. It expresses a relation between the content of two ideas, not a
relation of these ideas (Lotze).
b. It is consciousness concerning the objective validity of a
subjective combination of ideas, i.e. whether between the
corresponding objective elements an analogous combination exists
(Ueberweg).
c. It is the synthesis of ideas into unity and consciousness of their
objective validity, not in the sense of agreement with external
reality but in the sense of the logical necessity of their synthesis
(Sigwart).
d. It is the analysis of an aggregate idea (_Gesammtvorstellung_) into
subject and predicate; based on a previous association of ideas, on
relating and comparing, and on the apperceptive synthesis of an
aggregate idea in consequence; but itself consisting in an
apperceptive analysis of that aggregate idea; and requiring will in
the form of apperception or attention (Wundt).
e. It requires an idea, because every object is conceived as well as
recognized or denied; but it is itself an assertion of actual fact,
every perception counts for a judgment, and every categorical is
changeable into an existential judgment without change of sense
(Brentano, who derives his theory from Mill except that he denies the
necessity of a combination of ideas, and reduces a categorical to an
existential judgment).
f. It is a decision of the validity of an idea requiring will
(Bergmann, following Brentano).
g. Judgment (_Urtheil_) expresses that two ideas belong together:
"by-judgment" (_Beurtheilung_) is the reaction of will expressing the
validity or invalidity of the combination of ideas (Windelband,
following Bergmann, but distinguishing the decision of validity from
the judgment).
h. Judgment is consciousness of the identity or difference and of the
causal relations of the given; naming the actual combinations of the
data, but also requiring a priori categories of the understanding, the
notions of identity, difference and causality, as principles of
thought or laws, to combine the plurality of the given into a unity
(Schuppe).
i. Judgment is the act which refers an ideal content recognized as
such to a reality beyond the act, predicating an idea of a reality, a
what of a that; so that the subject is reality and the predicate the
meaning of an idea, while the judgment refers the idea to reality by
an identity of content (Bradley and Bosanquet).
k. Judgment is an assertion of reality, requiring comparison and ideas
which render it directly expressible in words (Hobhouse, mainly
following Bradley).
These theories are of varying value in proportion to their proximity to
Aristotle's point that predication is about things, and to Mill's point
that judgments and propositions are about things, not about ideas. The
essence of judgment is belief that something is (or is not) determined,
either as existing (e.g. "I am," "A centaur is not") or as something in
particular (e.g. "I am a man," "I am not a monkey"). Neither Mill,
however, nor any of the later logicians whose theories we have quoted,
has been able quite to detach judgment from conception; they all suppose
that an idea, or ideas, is a condition of all judgment. But judgment
starts from sensation (_Empfindung_) and feeling (_Gefühl_), and not
from idea (_Vorstellung_). When I feel pleased or pained, or when I use
my senses to perceive a pressure, a temperature, a flavour, an odour, a
colour, a sound, or when I am conscious of feeling and perceiving, I
cannot resist the belief that something sensible is present; and this
belief that something exists is already a judgment, a judgment of
existence, and, so far as it is limited to sense without inference, a
true judgment. It is a matter of words whether or not we should call
this sensory belief a judgment; but it is no matter of choice to the
logician, who regards all the constituents of inference as judgments;
for the fundamental constituents are sensory beliefs, which are
therefore judgments in the logical sense. Sense is the evidence of
inference; directly of analogical and inductive, directly or indirectly
of deductive, inference; and therefore, if logic refuses to include
sensory beliefs among judgments, it will omit the fundamental
constituents of inference, inference will no longer consist of judgments
but of sensory beliefs plus judgments, and the second part of logic, the
logic of judgment, the purpose of which is to investigate the
constituents of inference, will be like _Hamlet_ without the prince of
Denmark. If, on the other hand, all the constituents of inference are
judgments, there are judgments of sense; and the evidence of the senses
means that a judgment of sense is true, while a judgment of inference is
true so far as it is directly or indirectly concluded from judgments of
sense. Now a sensory judgment, e.g. that a sensible pressure is
existing, is explained by none of the foregoing theories, because it
requires nothing but sensation and belief. It requires no will, but is
usually involuntary, for the stimulus forces one's attention, which is
not always voluntary; not all judgment then requires will, as Wundt
supposes. It requires no reference to reality beyond the sensible
pressure, because it is merely a belief that this exists without
inference of the external stimulus or any inference at all: not all
judgment then requires the reference of subjective to objective supposed
by Ueberweg, or the consciousness of logical necessity supposed by
Sigwart. It requires in addition to the belief that something exists, no
consideration as to whether the belief itself be true, because a man who
feels pressure believes in the thing without further question about the
belief: not all judgment then requires a decision of validity, as
Bergmann supposes. It requires nothing beyond the sensation and belief
in the given existence of the given pressure: not all judgment then
requires categories of understanding, or notions of identity, difference
and causality, or even of existence, such as Schuppe supposes. It
requires no comparison in order to express it in words, for a judgment
need not be expressed, and a sensory judgment of pressure is an
irresistible belief that a real pressure exists, without waiting for
words, or for a comparison which is wanted not to make a sensation a
judgment, but to turn a judgment into language: not all judgment then
requires comparison with a view to its expression, as supposed by
Hobhouse. Lastly, all the authors of the above-quoted theories err in
supposing that all judgment requires conception; for even Mill thinks a
combination of ideas necessary, and Brentano, who comes still nearer to
the nature of sensory judgment when he says, "Every perception counts
for a judgment," yet thinks that an idea is necessary at the same time
in order to understand the thing judged. In reality, the sensation and
the belief are sufficient; when I feel a sensible pressure, I cannot
help believing in its reality, and therefore judging that it is real,
without any _tertium quid_--an idea of pressure, or of existence or of
pressure existing--intervening between the sensation and the belief.
Only after sensation has ceased does an idea, or representation of what
is not presented, become necessary as a substitute for a sensation and
as a condition not of the first judgment that there is, but of a second
judgment that there was, something sensible. Otherwise there would be no
judgment of sensible fact, for the first sensation would not give it,
and the idea following the sensation would be still farther off. The
sensory judgment then, which is nothing but a belief that at the moment
of sense something sensible exists, is a proof that not all judgment
requires conception, or synthesis or analysis of ideas, or decision
about the content, or about the validity, of ideas, or reference of an
ideal content to reality, as commonly, though variously, supposed in the
logic of our day.
Not, however, that all judgment is sensory: after the first judgments of
sense follow judgments of memory, and memory requires ideas. Yet memory
is not mere conception, as Aristotle, and Mill after him, have
perceived. To remember, we must have a present idea; but we must also
have a belief that the thing, of which the idea is a representation, was
(or was not) determined; and this belief is the memorial judgment.
Originally such judgments arise from sensory judgments followed by
ideas, and are judgments of memory after sense that something sensible
existed, e.g. pressure existed: afterwards come judgments of memory
after inference, e.g. Caesar was murdered. Finally, most judgments are
inferential. These are conclusions which primarily are inferred from
sensory and memorial judgments; and so far as inference starts from
sense of something sensible in the present, and from memory after sense
of something sensible in the past, and concludes similar things,
inferential judgments are indirect beliefs in being and in existence
beyond ideas. When from the sensible pressures between the parts of my
mouth, which I feel and remember and judge that they exist and have
existed, I infer another similar pressure (e.g. of the food which
presses and is pressed by my mouth in eating), the inferential judgment
with which I conclude is a belief that the latter exists as well as the
former (e.g. the pressure of food without as well as the sensible
pressures within). Inference, no doubt, is closely involved with
conception. So far as it depends on memory, an inferential judgment
presupposes memorial ideas in its data; and so far as it infers
universal classes and laws, it produces general ideas. But even so the
part played by conception is quite subordinate to that of belief. In the
first place, the remembered datum, from which an inference of pressure
starts, is not the conceived idea, but the belief that the sensible
pressure existed. Secondly, the conclusion in which it ends is not the
general idea of a class, but the belief that a class, represented by a
general idea, exists, and is (or is not) otherwise determined (e.g. that
things pressing and pressed exist and move). Two things are certain
about inferential judgment: one, that when inference is based on sense
and memory, inferential judgment starts from a combination of sensory
and memorial judgment, both of which are beliefs that things exist; the
other, that in consequence inferential judgment is a belief that similar
things exist. There are thus three primary judgments: judgments of
sense, of memory after sense, and of inference from sense. All these are
beliefs in being and existence, and this existential belief is first in
sense, and afterwards transferred to memory and inference. Moreover, it
is transferred in the same irresistible way: frequently we cannot help
either feeling pressure, or remembering it, or inferring it; and as
there are involuntary sensation and attention, so there are involuntary
memory and inference. Again, in a primary judgment existence need not be
expressed; but if expressed, it may be expressed either by the
predicate, e.g. "I exist," or by the subject, e.g. "I who exist think."
There are indeed differences between primary judgments, in that the
sensory is a belief in present, the memorial in past, and the
inferential in present, past and future existence. But these differences
in detail do not alter the main point that all these are beliefs in the
existing, in the real as opposed to the ideal, in actual things which
are not ideas. In short, a primary judgment is a belief in something
existing apart from our idea of it; and not because we have an idea of
it, or by comparing an idea with, or referring an idea to, reality; but
because we have a sensation of it, or a memory of it or an inference of
it. Sensation, not conception, is the origin of judgment.
2. _Different Significations of Being in different Kinds of
Judgment._--As Aristotle remarked both in the _De Interpretatione_ and
in the _Sophistici Elenchi_, "not-being is thinkable" does not mean
"not-being exists." In the latter treatise he added that it is a
_fallacia a dicto secundum quid ad dictum simpliciter_ to argue from the
former to the latter; "for," as he says, "it is not the same thing to be
something and to exist absolutely." Without realizing their debt to
tradition, Herbart, Mill and recently Sigwart, have repeated Aristotle's
separation of the copula from the verb of existence, as if it were a
modern discovery that "is" is not the same as "exists." It may be added
that they do not quite realize what the copula exactly signifies: it
does not signify existence, but it does signify a fact, namely, that
something is (or is not) determined, either absolutely in a categorical
judgment, or conditionally in a conditional judgment. Now we have seen
that all primary judgments signify more than this fact; they are also
beliefs in the existence of the thing signified by the subject. But, in
the first place, primary judgments signify this existence never by the
copula, but sometimes by the predicate, and sometimes by the subject;
and, secondly, it does not follow that all judgments whatever signify
existence. Besides inference of existence there is inference of
non-existence, of things inconsistent with the objects of primary
judgments. Hence secondary judgments, which no longer contain a belief
that the thing exists, e.g. the judgment, "not-being is thinkable,"
cited by Aristotle; the judgment, "A square circle is impossible," cited
by Herbart; the judgment, "A centaur is a fiction of the poets," cited
by Mill. These secondary judgments of non-existence are partly like and
partly unlike primary judgments of existence. They resemble them in that
they are beliefs in being signified by the copula. They are beliefs in
things of a sort; for, after all, ideas and names are things; their
objects, even though non-existent, are at all events things conceivable
or nameable; and therefore we are able to make judgments that things,
non-existent but conceivable or nameable, are (or are not) determined in
a particular manner. Thus the judgment about a centaur is the belief, "A
conceivable centaur is a fiction of the poets," and the judgment about a
square circle is the belief, "A so-called square circle is an
impossibility." But, though beliefs that things of some sort are (or are
not) determined, these secondary judgments fall short of primary
judgments of existence. Whereas in a primary judgment there is a further
belief, signified by subject or predicate, that the thing is an existing
thing in the sense of being a real thing (e.g. a man), different from
the idea of it as well as from the name for it; in a secondary judgment
there is no further belief that the thing has any existence beyond the
idea (e.g. a centaur), or even beyond the name (e.g. a square circle):
though the idea or name exists, there is no belief that anything
represented by idea or name exists. Starting, then, from this
fundamental distinction between judgments of existence and judgments of
non-existence, we may hope to steer our way between two extreme views
which emanate from two important thinkers, each of whom has produced a
flourishing school of psychological logic.
On the one hand, early in the 19th century Herbart started the view that
a categorical judgment is never a judgment of existence, but always
hypothetical; on the other hand, in the latter part of the century
Brentano started the view that all categorical judgments are
existential. The truth lies between these contraries. The view of
Herbart and his school is contradicted by our primary judgments of and
from sense, in which we cannot help believing existence; and it gives an
inadequate account even of our secondary judgments in which we no longer
indeed believe existence, but do frequently believe that a non-existent
thing is (or is not) somehow determined unconditionally. It is true, as
Herbart says, that the judgment, "A square circle is an impossibility,"
does not contain the belief, "A square circle is existent"; but when he
goes on to argue that it means, "If a square circle is thought, the
conception of impossibility must be added in thought," he falls into a
_non-sequitur_. To be categorical, a judgment does not require a belief
in existence, but only that something, existent or not, is (or is not)
determined; and there are two quite different attitudes of mind even to
a non-existent thing, such as a square circle, namely, unconditional and
conditional belief. The judgment, "A non-existent but so-called square
circle is an impossibility," is an unconditional, or categorical
judgment of non-existence, quite different from any hypothetical
judgment, which depends on the conditions "if it is thought," or "if it
exists," or any other "if." On the other hand, the view of Brentano and
his school is contradicted by these very categorical judgments of
non-existence; and while it applies only to categorical judgments of
existence, it does so inadequately. To begin with the latter objection,
Brentano proposed to change the four Aristotelian forms of judgment, A,
E, I, O, into the following existential forms:--
A. "There is not an immortal man."
E. "There is not a live stone."
I. "There is a sick man."
O. "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-y"), but only as alternative to the ordinary forms.
Bradley says that "'S-P is real' attributes S-P, directly or indirectly,
to the ultimate reality," and agrees with Brentano 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, "Reality 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.; and children know that their parents exist long
before they apprehend ultimate reality. The normal form, then, 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. 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 conceivable 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. 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 either
by the subject or by the predicate, while others are not beliefs that
the thing exists at all, but are only beliefs in something 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 premise,
we know therein every individual universally, not individually, and
often do not know a given individual individually until we add a minor
premise 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 unknown 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 conceivable centaurs are human in their
forequarters," "All conceivable centaurs are equine in their
hindquarters," are all categorical judgments, while the two first are
also categorical judgments of existence. 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 influenced 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 case is a universal hypothetical, unless we
think it under a condition; for in a universal judgment about the
non-existing, e.g. about all conceivable centaurs, we do not think, "If
anything is a centaur," because we do not believe that there are any;
and in a universal judgment about the existent, e.g. about all existing
men, we do not think, "If anything is a man," because we believe that
there is a whole class of men existing at different times and places.
The cause of Sigwart's error is his misconception of "all." So far as he
follows Aristotle in saying that "all" does not mean a definite number
of individuals he is right; but when he says that we mean no individuals
at all he deserts Aristotle and goes wrong. By "all" we mean every
individual whatever of a kind; and when from the experience of sense and
memory we start with particular judgments of existence, and infer
universal judgments of existence and scientific laws, we further mean
those existing individuals which we have experienced, and every
individual whatever of the kind which exists. We mean neither a definite
number of individuals, nor yet an infinite number, but an incalculable
number, whether experienced or inferred to exist. We do not mean
existing here and now, nor yet out of time and place, but at any time
and place (_semper et ubique_)--past, present and future being treated
as simply existing, by what logicians used to call _suppositio
naturalis_. We mean then by "all existing" every similar individual
whatever, whenever, and wherever existing. Hence Sigwart is right in
saying that "All bodies are extended" means "Whatever is a body is
extended," but wrong in identifying this form with "If anything is a
body it is extended." "Whatever" is not "if anything." For the same
reason it is erroneous to confuse "all existing" with a general idea.
Nor does the use of abstract ideas and terms make any difference. When
Bosanquet says that in "Heat is a mode of motion" there is no reference
to individual objects, but "a pure hypothetical form which absolutely
neglects the existence of objects," he falls far short of expressing the
nature of this scientific judgment, for in his _Theory of Heat_ Clerk
Maxwell describes it as "believing heat as it exists in a hot body to be
in the form of kinetic energy." As Bacon would say, it is a belief that
all individual bodies _qua_ hot are individually but similarly moving in
their particles. When, again, Bradley and Bosanquet speak of the
universal as if it always meant one ideal content referred to reality,
they forget that in universal judgments of existence, such as "All men
existing are mortal," we believe that every individually existing man
dies his own death individually, though similarly to other men; and that
we are thinking neither of ideas nor of reality; but of all existent
individual men being individually but similarly determined. A universal
is indeed one whole; but it is one whole of many similars, which are not
the same with one another. This is indeed the very essence of
distribution, that a universal is predicable, not singly or
collectively, but severally and similarly of each and every individual
of a kind, or total of similar individuals. So also the essence of a
universal judgment is that every individual of the kind is severally but
similarly determined. Finally, a universal judgment is often
existential; but whether it is so or not it remains categorical, so long
as it introduces no hypothetical antecedent about the existence of the
thing signified by the subject. It is true that even in universal
judgments of existence there is often a hypothetical element; for
example, "All men are mortal" contains a doubt whether every man
whatever, whenever and wherever existing, must die. But this is only a
doubt whether all the things signified by the subject are similarly
determined as signified by the predicate, and not a doubt whether there
are such things at all. Hence the hypothetical element is not a
hypothetical antecedent "If anything is a man," but an uncertain
conclusion that "All existing men are mortal." In other words, a
categorical universal is often problematic, but a problematic is not the
same as a hypothetical judgment.
4. _The Judgment and the Proposition._--Judgment in general is the
mental act of believing that something is (or is not) determined. A
proposition is the consequent verbal expression of such a belief, and
consists in asserting that the thing as signified by the subject is (or
is not) determined as signified by the predicate. But the expression is
not necessary. Sensation irresistibly produces a judgment of existence
without needing language. Children think long before they speak; and
indeed, as mere vocal sounds are not speech, and as the apprehension
that a word signifies a thing is a judgment, judgment is originally not
an effect, but a cause of significant language. At any rate, even when
we have learnt to speak, we do not express all we think, as we may see
not only from the fewness of words known to a child, but also from our
own adult consciousness. The principle of thought is to judge enough to
conclude. The principle of language is to speak only so far as to
understand and be understood. Hence speech is only a curtailed
expression of thought. Sometimes we express a whole judgment by one
word, e.g. "Fire!" or by a phrase, e.g. "What a fire!" and only usually
by a proposition. But even the normal proposition in the syllogistic
form _tertii adjacentis_, with subject, predicate and copula, is seldom
a complete expression of the judgment. The consequence is that the
proposition, being different from a judgment arising after a judgment,
and remaining an imperfect copy of judgment, is only a superficial
evidence of its real nature. Fortunately, we have more profound
evidences, and at least three evidences in all: the linguistic
expression of belief in the proposition; the consciousness of what we
mentally believe; and the analysis of reasoning, which shows what we
must believe, and have believed, as data for inference. In these ways we
find that a judgment is both different from, and more than, a
proposition. But recent logicians, although they perceive the
difference, nevertheless tend to make the proposition the measure of the
judgment. This makes them omit sensory judgments, and count only those
which require ideas, and even general ideas expressed in general terms.
Sigwart, for example, gives as instances of our most elementary
judgments, "This is Socrates," "This is snow"--beliefs in things
existing beyond ourselves which require considerable inferences from
many previous judgments of sense and memory. Worse still, logicians seem
unable to keep the judgment apart from the proposition. Herbart says
that the judgment "A is B" does not contain the usually added thought
that A is, because there is no statement of A's existence; as if the
statement mattered to the thought. So Sigwart, in order to reduce
universals to hypotheticals, while admitting that existence is usually
thought, argues that it is not stated in the universal judgment; so also
Bosanquet. But in the judgment the point is not what we state, but what
we think; and so long as the existence of A is added in thought, the
judgment in question must contain the thought that A exists as well as
that A is B, and therefore is a judgment that something is determined
both as existing and in a particular manner. The statement only affects
the proposition; and whenever we believe the existence of the thing, the
belief in existence is part of the judgment thought, whether it is part
of the proposition stated or not.
Here Sir William Hamilton did a real service to logic in pointing out
that "Logic postulates to be allowed to state explicitly in language
all that is implicitly contained in the thought." Not that men should
or can carry this logical postulate out in ordinary life; but it is
necessary in the logical analysis of judgments, and yet logicians
neglect it. This is why they confuse the categorical and the universal
with the hypothetical. Taking the carelessly expressed propositions of
ordinary life, they do not perceive that similar judgments are often
differently expressed, e.g. "I, being a man, am mortal," and "If I am
a man, I am mortal"; and conversely, that different judgments are
often similarly expressed. In ordinary life we may say, "All men are
mortal," "All centaurs are figments," "All square circles are
impossibilities," "All candidates arriving five minutes late are
fined" (the last proposition being an example of the identification of
categorical with hypothetical in Keynes's _Formal Logic_). But of
these universal propositions the first imperfectly expresses a
categorical belief in existing things, the second in thinkable things,
and the third in nameable things, while the fourth is a slipshod
categorical expression of the hypothetical belief, "If any candidates
arrive late they are fined." The four judgments are different, and
therefore logically the propositions fully expressing them are also
different. The judgment, then, is the measure of the proposition, not
the proposition the measure of the judgment. On the other hand, we may
go too far in the opposite direction, as Hamilton did in proposing the
universal quantification of the predicate. If the quantity of the
predicate were always thought, it ought logically to be always stated.
But we only sometimes think it. Usually we leave the predicate
indefinite, because, as long as the thing in question is (or is not)
determined, it does not matter about other things, and it is vain for
us to try to think all things at once. It is remarkable that in
_Barbara_, and therefore in many scientific deductions, to think the
quantity of the predicate is not to the point either in the premises
or in the conclusion; so that to quantify the propositions, as
Hamilton proposes, would be to express more than a rational man thinks
and judges. In judgments, and therefore in propositions, indefinite
predicates are the rule, quantified predicates the exception.
Consequently, A E I O are the normal propositions with indefinite
predicates; whereas propositions with quantified predicates are only
occasional forms, which we should use whenever we require to think the
quantity of the predicate, e.g. (1) in conversion, when we must think
that all men are some animals, in order to judge that some animals are
men; (2) in syllogisms of the 3rd figure, when the predicate of the
minor premise must be particularly quantified in thought in order to
become the particularly quantified subject of the conclusion; (3) in
identical propositions including definitions, where we must think both
that 1 + 1 are 2 and 2 are 1 + 1. But the normal judgment, and
therefore the normal proposition, do not require the quantity of the
predicate. It follows also that the normal judgment is not an
equation. The symbol of equality (=) is not the same as the copula
(is); it means "is equal to," where "equal to" is part of the
predicate, leaving "is" as the copula. Now, in all judgment we think
"is," but in few judgments predicate "equal to." In quantitative
judgments we may think x = y, or, as Boole proposes, x = vy = (0/0)y
or, as Jevons proposes, x = xy, or, as Venn proposes, x which is not y
= 0; and equational symbolic logic is useful whenever we think in this
quantitative way. But it is a byway of thought. In most judgments all
we believe is that x is (or is not) y, that a thing is (or is not)
determined, and that the thing signified by the subject is a thing
signified by the predicate, but not that it is the only thing, or
equal to everything signified by the predicate. The symbolic logic,
which confuses "is" with "is equal to," having introduced a particular
kind of predicate into the copula, falls into the mistake of reducing
all predication to the one category of the quantitative; whereas it is
more often in the substantial, e.g. "I am a man," not "I am equal to a
man," or in the qualitative, e.g. "I am white," not "I am equal to
white," or in the relative, e.g. "I am born in sin," not "I am equal
to born in sin." Predication, as Aristotle saw, is as various as the
categories of being. Finally, the great difficulty of the logic of
judgment is to find the mental act behind the linguistic expression,
to ascribe to it exactly what is thought, neither more nor less, and
to apply the judgment thought to the logical proposition, without
expecting to find it in ordinary propositions. Beneath Hamilton's
postulate there is a deeper principle of logic--_A rational being
thinks only to the point, and speaks only to understand and be
understood_.