THE LOGIC OF NAMES.

THE LOGIC OF NAMES.

AN INTBODUCTION

BOOLE'S LAWS OF THOUGHT.

I. P. HUGHLINGS.

" The symbolic language of Algebra, framed wholly on notions
of number and quantity, is adequate, by what is certainly not an
accident, to the representation of all the laws of thought."— DE
MORGAN.

LONDON :
JAMES WALTON, 137, GOWER STREET.

1869.

LONDON I

PRINTED BY WEKTHEIMER, LEA AND CO.,
FI5JSBURY CIRCUS.

CONTENTS.

PAQE.

INTRODUCTION >. 1

i. Logic . . . . . ' i . ' . . 3

n. Mind 4

in. Thought 5

IT. Nervous Action ,,

v. Naming 8

vi. Sensations 11

vn. Compound Sensations ...... 12

vin. Abstraction 20

ix. Consciousness 26

x. Grammar 28

xi. "Words. ........ „

xii. Names ... . - 39

xin. Meaning . . . . • . . . 42

xiv. Relation . . . . . . . . 45

xv. Propositions . " . . . . . . 46

xvi. The Copula 47

xvn. Terms . . . 48

xvni. Logical Wholes . 49

xix. Logical Equality 53

xx. Numerical Values '. 54

xxi. Classification ........ 58

xxn. Logical Addition 71

xxni. Logical Subtraction 72

xxrv. Predication . . " . . . . 74

xxv. Predicables . . . . . . 77

xxvi. Logical Multiplication ...... 78

xxvii. Negative Propositions . . .... . 80

xxvui. Calculus of Logic . . . . . 82

2017249

ADVERTISEMENT.

PRIMARILY these pages are an attempt to inde-
pendently think out and popularly interpret
some of the principles characteristic of Mr.
John Stuart Mill's Logic, of the late Professor
Boole's Laws of Thought, and of Mr. De Mor-
gan's various publications on the same class of
subjects.

The following special objects have been aimed
at: —

1st. To, so far as possible, divest of their
mathematical dress the foundations of Professor
Boole's theory.

2nd. To independently and popularly expound
and interpret these foundations.

3rd. To include in this exposition some ac-
count of certain phrases and doctrines which
have been taken and adopted from the logic of
the past by common language and general
literature.

I. P. H.

THE LOGIC OF NAMES.

INTRODUCTION. — Man is a result of the opera-
tion of forces, some of which are known, and
some unknown ; the former subjects of know-
ledge, the latter subjects of belief. To the
unknown we give the name of Soul ; those that
are known we refer either to Mind or to Body.
By the distinction of Mind and Body is not
necessarily implied that between material and
immaterial. The immaterial we refer to the
unknown, to what is subject of belief ; but the mate-
rial each man divides for himself into that which
he cannot separate from his own individuality,
and that which he can so separate. Such a dis-
tinction is manifestly both ambiguous and fluctu-
ating. It is ambiguous, because it may be under-
stood in two senses. We may draw the dividing
line through different systems of points. It is
fluctuating, because, wherever placed in the first
instance, no subsequent tracing will repeat it. The
line may be drawn so as to separate all the matter
which composes the individual's body from other
matter. Such a line is uncertain to the kitten,
which runs after its own tail, and to the human

2 THE LOGIC OF NAMES.

being who, applying crossed fingers to the tip of
his nose, imagines for an infinitesimal portion of
time that he has two noses. A cultivated man
attempts to draw the line so as to include the
thinking part of his material frame only. Or,
rather, he assumes the line to be drawn, and calls
all on one side Mind, all on the other Bod}'.
When he sees a case of conscious insanity, a
madman who knows he is mad, his line fades
away from even his imagination.

The distinction between Mind and Body now
to be insisted on is this, — that the former is con-
nected with Soul, and so connected as not in our
thoughts to be either separable from it or coni-
binable with it, while in our knowledge it is both.
Mind is mutable and destructible by material
agencies, Soul is not. Mind is materially mani-
festible, Soul is not. "VVe ourselves are the two
together ; yet how can the material act with the
immaterial ?

But if Mind is that part of matter, or is in-
volved indissolubly with that part of matter which
a man in thought is forced to segregate into his
own individuality, — if it is that part of matter
which enters into the constitution of the man,
what is shown to us of it is a very small portion
either of Mind or Man. We can only see so
much of it as is revealed in the mirror of lan-
guage ; and that much, while not all its length
and breadth, is none of its depth. The province
of Logic, however, is, in all directions, determined
by the scope of language. Logic, accepting the

limitation so prescribed, is careful, in defining
the field of its speculations, not to pronounce any
opinion on what may lie outside the area thus set
apart.

I. LOGIC. — Logic is the name of the science, or
art, or instrument, in obedience to which, or by
means of which, we analyse verbal representations
of mental affections. As a science, logic pro-
fesses to give an account of the laws which words
necessarily obey when they are used in exhibiting
processes of thought. As an art or instrument, it
furnishes, or is used to furnish, rules by which
thinkers may be guided to the correction of in-
accuracies of thought or expression. A book
which gives an account of logic is called a
Logic.*

* Compare De Morgan's Syllabus of Logic, Section 1st.

Logic has also been defined " as the science of the conditions
on which correct thoughts depend, and the art of attaining to
correct, and avoiding incorrect, thoughts " ; and as " the art of
thinking, which means of correct thinking, and the science of the
conditions of correct thinking." Sir William Hamilton defines
logic as " the science of the laws of thought as thought." His
remarks on the terms of this definition may be summarised as
follows : — 1st. Logic is from the Greek adjective XoyiKjj, itself
from Xoyog, a substantive which meant, sometimes, "thought,"
sometimes, " the expression of thought." It was equivalent
both to the ratio and to the oratio of the Latins. 2nd. Logic is
a science, because it is a branch of knowledge. The distinction
between logic as a science, and logic as an art, at best only amounts
to saying that it can be viewed in more than one way ; that it is
a science when viewed absolutely, and not in relation to practice ;
an art when viewed as the application to practice of knowledge.
Even this distinction, however, which distinguishes nothing, is

4 THE LOGIC OF NAMES.

II. MIND. — "What we know in ourselves we have
received from without, from what we call Body ;
and that in us which receives we call Mind. The
medium of communication between body and
mind is furnished by the nerves. The nerves
discharge this function by successive acts which,
in their affection of the mind, are called sensa-
tions. The science of Mind is Psychology.*
Logic is the science of Mind, only in so far as it
regards mind when verbally manifested.

arrived at only by help of a wrong distinction of arts and
sciences. Art is a productive habit, poetic, or poietic as the Greeks
said, and is opposed to a habit merely of action, to a practical
habit, in the Greek sense of the word whence we derive practical.
Thus, ethics is a science with a practical side, but that does not
make it an art as well as a science. 3rd. Thought consists of the
acts of the faculty of comparison. In this sense, thought is a
recognition of similarity or difference between the objects which
are submitted to the faculty of comparison by its subsidiary
faculties. Logic, however, has only to do with the kind or
manner of this recognition ; that is to say, with this recognition
as recognition. Hence, by " thought as thought" is meant the kind
or manner of thought, in technical language the Forms of thought,
or Formal thought. Again, the form of thought, as the object
matter of a science, may be either contingent or necessary ; that
is to say, either such a form as may or may not appear, or such as
must appear. Logic has only to do with the form of thought
that must appear, that is, with necessary forms of thought. But
the necessary forms of thought must be those which are deter-
mined by the nature of the thinking subject itself, which there-
fore are not acquired but original, which therefore are universally
operative, and, consequently, are the laws or conditions of thought.
* Psychology has been described to be the Phenomenology of
Mind ; to treat of certain phenomena called mental, which are con-
ceived to establish the existence and describe the nature of an im-
material mind. It seems hard to distinguish it as a real science from
that portion of physiology which treats of man's nervous system.

THOUGHT — NERVOUS ACTION. 5

III. THOUGHT. — Mental affections* capable of
being expressed by words, or other signs, or
which are actually thus expressed to the conscious-
ness of the individual affected, are thought.f

IY. NERVOUS ACTION .J — It has been said that
what we know conies from without to the mind,
and that it comes to us by means of nervous action.
In its simplest form, the nervous action of animals
consists of an interchange of action between two
sorts of nerves ; to one of which sorts we may, so
far as our knowledge goes, refer every nerve. A
nerve is either afferent or efferent. An afferent
nerve, by transmission of an external force, is the
cause to an animal of an internal affection ; an
efferent nerve carries outward again to the ex-

* Note that bodily affections are also capable of being ex-
pressed by signs.

f The hypothesis of the text is not intended to contradict, and
does not contradict, the existence of volition. Nothing but ex-
periment can show that any particular phenomenon is an act of
volition : many phenomena, once thought to be acts of volition,
experiment has shown to be independent of volition : of very few
phenomena would it be possible to say that experiment had shown
them to be acts of pure volition, undetermined by aught else.

J In this and the following sections, no attempt is made to
introduce more of the results of physiology than is absolutely
necessary to give a meaning to the word sensation. Much is
nevertheless owing to Professor Huxley's "Elementary Phy-
siology," to Dalton's "Human Physiology," and especially to the
edition of Mr. Herbert Spencer's " Psychology," now publish-
ing. The student may be particularly recommended to Draper's
"Human Physiology," for some very suggestive and valuable
remarks on the compatibility of physiological results with those
of a non-materialistic philosophy.

6 THE LOGIC OF NAMES.

ternal world what of the force brought in is not
wanted to sustain the internal affection, and in
this way is capable of exhibiting the internal
affection. In some cases of very simple organi-
sation, the efference is almost immediately sequent
on, and almost exactly complementary to, the
afference. In those cases, nervous action might
be, not unfairly, diagrammatised by the capital
letter II, the downward stroke representing the
afferent nerve, the upward the efferent ; the af-
ference proceeding into efference without any
visible breach of continuity. The capital letter
Y may represent the case next in order of com-
plexity, where we find the afferent nerve merge
its continuity in a nervous vesicle, or a collection
of nervous vesicles, which we may call a nervous
centre ; and out of which again emerges the ef-
ferent nerve (or nerves). And a still more com-
plex case may be represented, still diagrammati-
cally, but more imperfectly, by the letter W,
where three nervous centres interpose between
the first afferent and the last efferent nerve, and
where we may distinguish the first upstroke from
the second, by saying that it stands for a centri-
petal nerve ; and the second downstroke from the
first, by saying that it stands for a centrifugal
nerve.* But this last diagram is very inadequate,
since the connection between any two nervous

* So far as is known, however, the number of the efferent
nerves which may be excited, is not regulated by the number of
the afferent nerves which excite them.

NERVOUS ACTION. 7

centres implies both centripetal and centrifugal
connections.

5. The idea, then, of nervous action, is simply
that of afference and efference, as the idea of a
railway system is that of trains bringing things
and people in, and taking things and people out.
But if we look at a map of England, we observe
that the railways have a many great centres of
junction, independent of and yet connected with
one another, at London, Birmingham, Manchester,
and other places, and that at any one of these
centres there are trains that stop, trains that start,
and trains that pass through ; with all manner of
other differences between the various trains and
companies. So, in considering the phenomenon
of nervous action, while we accept the words
afference and efference as expressive of its idea,
we shall in its details expect to meet with more
than all the complications of Bradshaw. Of these
details it is not necessary here to say else than
this, — that there are in the human body at least
three nervous centres, practically independent of
one another, yet connected, and in mutual relations
of superiority and inferiority.

6. The nervous centre which is most compre-
hensive and elaborate in its connections and
branches is that which is placed in what physio-
logists call the cerebral hemispheres. This is
that part of the body which man is wont to asso-
ciate with his individuality, and material injury
or benefit to which he calls injury or benefit to
his mind. And this is that part of the nervous

8 THE LOGIC OF NAMES.

system in which structural complexity and ob-
scurity is at its highest, and where nervous action
can only be imagined by aid of the analogies
afforded by less complex and less obscure nervous
systems.*

V. NAMING. — The result of efferent nervous
action which proceeds from excitements of the
simpler nerve centres is muscular action of va-
rious degree and kind.f In the case of the

* In the five-rayed star-fish, we have a separate nervous
centre, or ganglion, for each limb, and its nervous system might
be diagrammatised by five letters V, all with their angles in the
circumference of the same circle, but with their limbs outside the
circle. Each ray of the fish must be supposed to contain one
letter. This, we are told, is perhaps the simplest form of nervous
system extant as an independent existence.

f Here I must note some facts which may be contradictory of
the hypothesis of the text, and which I owe to Dr. Hughlings
Jackson, whose special writings on the subject are named in
another note. While all language is placed by the text on the
same level, it appears that disease of a particular part of the
brain may induce partial or complete defect of what is intelligibly
distinguished by Dr. Hughlings Jackson as intellectual language,
and not cause corresponding defect of emotional or interjectional lan-
guage. The typical patient in this disease misuses words, or cannot
use words at all, to express his thoughts ; nor can he express his
thoughts by writing, or by any signs sufficiently elaborate to
serve instead of vocal or written words ; nor can he read books
for himself. But he can smile, laugh, cry, sing, and employ
rudimentary signs of gesticulation. So far as these means of
communication serve, therefore, he is able to exhibit his feel-
ings to those around him. He can copy writing placed
before him, and, even without the aid of a copy, sign his
own name. He understands what is said to him, is capable of
being interested in books which are read to him, and remembers
incidents of tales. Sometimes he is able to utter a word or

cerebral hemispheres, the result seems to be
naming. When, from whatever cause, an afferent
nerve — either directly, by itself, or indirectly, by
means of more or fewer centripetal and centri-
fugal nerves — communicates its own excitement
to the organisation of the cerebral hemispheres,
the complementary efference throws a motor or-

words, which he cannot vary, and which he must utter if he
speak at all, no matter on what occasion. When excited, he can
swear, and even use elaborate formulae of swearing (as, for ex-
ample, "God bless my life,") which have come by use and wont
to be of only interjectional value. But he cannot repeat such
words and phrases at his own wish or the desire of others. And
as he is able to copy writing, so he can, when circumstances
dictate, as it were, to him, give utterance to phrases of more
special applicability. Thus, a child being in danger of falling,
one speechless patient, a woman, was surprised into exclaiming^
" Take care." But in this, as in every modern case, the patient
remains perfectly incompetent to repeat at pleasure the phrase he
has just used so appropriately and has so distinctly uttered.

It would seem that the part of the brain affected in such cases,
is that which is susceptible of education to language, and which
has been, after the birth of the patient, so educated. The effect of
the disease, in relation to speech, is to leave the patient as if he
had never been educated at all to language, and had been born
without the power of being so educated.

The disease in question is an affection of but one side, the left
side of the brain. This fact, coupled with the undoubted obser-
vation that speech is an acquired faculty, has led some physio-
logists to suppose that but one side of the brain is educated to
speech. The left side of the brain governs the right side of the
body, and hence it has been said that most people are born " left-
brained," just as most people are born "right-handed." Dr.
Hughlings Jackson, however, is of opinion that both sides of the
brain are educated to speech, and that, in the disease under remark,
the patient is speechless, but not wordless : his defect is an in-
ability to reproduce voluntarily the most special of the acquired
processes of speech.

10 THE LOGIC OF NAMES.

ganisation into activity, which results either in
language, or, if, from whatever cause, arrested
before it reaches the stage of language, in some-
thing which is so far an equivalent to language,
as to in turn become, like language itself, a cause
of afferent nervous action. This efferent motor
activity, either in its more incipient stage, which
is thought, or its complete phase, which is language*
we will call in its simplest act, naming. Naming,
therefore, is an indication or exhibition of a dis-
turbance or decomposition which has been excited
in the hemispherical nervous centre by the action,
more or less complicated, of afferent or centripetal
nerves.f

* The relation here hypothetised may be taken to explain the
generally admitted connection of thought with language, even
in cases where no voice, or writing, and little or no imagination
of words are present in sense or consciousness with thought.
And, taken in connection with what is said elsewhere in the text,
it may also explain how men can make and use a name long
before they can give a clear account of its meaning. Thus, in
Sir W. Hamilton, St. Augustine says, " If you ask of me what is
Time, I know not; if you do not ask me, I know." And thus,
Archbishop Thomson says, " The names we employ in speech
are not always symbols to another of what is explicitly under-
stood by us, but, quite as often, are symbols both to speaker and
hearer, the full and exact meaning of which neither of them stop
to unfold, any more than they regularly reflect that every
sovereign which passes through their bands is equivalent to
240 pence ! "

t One of the most recent observations of physicians is, that
disease of a particular region of the left cerebral hemisphere is
followed by a complete or partial loss of power in the naming
process, and by consequent inability to speak, even when all the
machinery of voice and articulation recognised in anatomy re-
mains untouched. On this subject the reader is referred to the

SENSATIONS. 11

8. The affection of the hemispherical nervous
centre which is signified by a name, we may call
a sensation. And as Mind, if not necessarily to
be identified with that nervous centre, at least is
in a connection with it, which is like that of a
body of railway proprietors to a railway, and is
only terminable by death (also, perhaps, by in-
sanity), we may conveniently describe a sensation
as a mental affection.

VI. SENSATIONS.* — A sensation is a mental
state induced by the action, mediate or imme-
diate, of one or more afferent nerves, and signified
by the consequent reflex excitement of one or
more efferent nerves.f It is not necessarily a
momentary affection of mind. Its duration va-
ries, it would seem, according to the degree of
nervous force employed in its production. By
the duration of a sensation is meant the length of

footnote on the first sentence of this paragraph, to Dr. Hughlings
Jackson's "Physiology and Pathology of Language" (in the
press ; Churchill, London,) and to the same author's papers in
the "Medical Times and Gazette" for December 14, and De-
cember 21, 1867. I gladly take this opportunity of acknow-
ledging the assistance I have derived from the suggestions and
directions which Dr. Hughlings Jackson has given me in matters
of physiology.

* Sensation was denned by Dugald Stewart as the " change in
the state of mind which is produced by an impression upon an
organ of sense, of which change we can conceive the mind to be
conscious, without any knowledge of external objects."

f The text, it may be observed, does not assert that every
affection of every afferent nerve induces a particular mental

12 THE LOGIC OF NAMES.

time for which, in any individual case, it may
continue to form a part of the human organisa-
tion. Sensations may be repeated or re-excited.
A sensation may be repeated by a repetition of
its original cause. As a tuning-fork may be set
vibrating, if its own particular note, or one har-
monic with it, be sounded in its neighbourhood,
so a sensation may be re-excited by the repetition
or the re-excitement of the sensation next after
or next before it in order of time. In other
words, " if any two mental states be called up
together, or in succession, with due frequency
and vividness, the subsequent production of one
of them will suffice to call up the other, and that
whether we desire it or not."*

10. Of those sensations which are distinguished
by names, few are simple or elementary, though
many, if not all, appear on first impression to be
simple. To draw the finger along a tablet gives
a sensation which might appear to be simple, but
which is certainly to be resolved into the following
elements : —

i. A sensation of time,
ii. A sensation of contact.

in. A sensation of muscular action.

iv. Re- excitement of former related sensa-
tions, and of the relations of those sen-

* From Professor Huxley. "What are called phenomena of
memory, and, probably, those phenomena also which are termed
acts of judgment and imagination, seem to be wholly or partially
constituted by re-excitements of sensations.

f From Professor Huxley.

COMPOUND SENSATIONS. 13

sations, severally and collectively, to the
present sensation.

v. Re-excitement of sensations not formerly
related in knowledge, and of their rela-
tions with the present excited relation.

VII. COMPOUND SENSATIONS. — The same sen-
sations are so often repeated and re-excited in the
same mutual adjacencies of time, as commonly to
come to be regarded as forming, collectively,
separate and independent existencies, of which
the corporated integrity is generally the first fact
recognised by the mind, and is ever after regarded
as the principal fact. That is to say, the com-
pound sensation is at first taken for a simple sen-
sation, as the Cathedral of Glasgow was supposed
by the St. Kilda islander to be a rock hollowed out.
And even afterwards, when the compound nature
of the collective sensation is discovered, its indi-
vidual integrity is still strongly emphasised in
consciousness. Men call their consciousness of
its integral individuality a perception* and they

* " The word Perception expresses the knowledge we obtain,
by means of sensations, of the qualities of matter." DugaldSteivart
apud Dean Mansel. Other definitions of perception are that " it
is the apprehension through sense of external things," and that
it is " an apprehension of the relations of sensations to one
another," or "a discerning of the relation or relations between
states of consciousness." (See Herbert Spencer's " Psychology.")
The perception of an object has been called also an Intuition,
so far as it is an act of the mind. Its product, in the same
system of language, is a Presentation or Cognition or a Singular
Representation.

14 THE LOGIC OF NAMES.

suppose the several causes of its different com-
posing sensations to be qualities inherent in some
material existency which is independent of, but
analogous to, the human individuality, and which
is accordingly distinguished as a body or thing.
But when again, afterwards, on further repetition
of the compound sensation, they discover that it
encloses another compound sensation, its kernel
as it were, which is also the kernel of other
similarly inclusive compound sensations, they find
themselves unable to give this compound too an
objective reality of the same description with that
of the former. They cannot call it a body or
thing, because, although, on the one hand, it re-
mains still one and the same sensation, on the
other hand, they find it repeated in more than one
body or thing, and never find it isolated and un-
compounded with other sensations. Thus, Sir
William Hamilton says, " Let B, C and D repre-
sent a series of individual objects which all agree
in possessing the resembling attributes of y, y, y,
and severally diifer, in each respectively possessing
the non-resembling attributes i, o, u. * * * The
qualities expressed by y, y, y, determine in us
cognitive energies," cause in us such and such
sensations, " which we are unable to distinguish,
and which we therefore consider as the same." This
fact, however, does not make men reconsider
their hypothesis of the cause of the larger com-
pound sensation, of the B, or C, or D. They
refuse to say that they know the smaller sensa-
tion, the y, in the same way that they know the

COMPOUND SENSATIONS. 15

larger, the B, or 0, or D. Calling it a concept, a
notion, or an idea, they deny that it has any inde-
pendent and absolute existence as an object of
thought at all. " It is not cognizable in itself."
Its existence is only relative.* At the same time,
they describe this non-cognizable non-existent,
as a mental fact, internal, subjective to the man,
as opposed to the body or the thing which they
call a material fact, external and objective to the
man. But on the hypothesis of this book, things
and bodies, no less than concepts and ideas, are
called mental objects, seeing that they are all
alike groups of sensations, or compound sensa-
tions, of each of which the component parts are
mutually bound together by the one relation of
adjacency of time. In space these different
groups of sensations are, neither bodies nor con-
cepts, mutually independent and distinct, for they
all repeat, more or less identically, the same
elements. Their mode of composition is not
strictly analogous to that of their representatives
in language. For although names repeat more
or less the same letters and syllables, these letters

* Sir W. Hamilton thus negatively describes it — ""We cannot
figure in imagination any object adequate to the general notion
or term man ; for the man to be here imagined must be neither
tall nor short, neither fat nor lean, neither black nor white,
neither man nor woman, neither young nor old, but all and
yet none of these at once." With the exception of the italicised
words, this description is a faithful account of the facts con-
sidered in the text. The groups of sensations which are called by
Sir W. Hamilton " concepts" are like certain chemical elements —
they are never found but in combination.

16 THE LOGIC OF NAMES.

and syllables are not numerically the same. The
a in antelope is, numerically, one a ; the a in
apple, numerically, another a. Similarly, we
cannot strictly compare the grouping in com-
pound sensations to the elementary composition
of chemical molecules. The molecular formulae
(SO4) Zn and (SO4) M2 contain the same elements,
it is true, yet the atoms which are supposed to
constitute the SO4 of the one molecule do not
necessarily constitute the SO4 of the other. But
as an astronomer, in his fancy, could arrange the
stars of the sky into groups on different systems,
so that it might be possible for the same star,
keeping in the same place, to be at once the nose
of a bear, or the tail of a lion, or the mid-blade
of a sword : or, as the same astronomer may be a
working member of this society, an honorary
member of that, and secretary to a third; a
principal man in this social circle, a respectable
outsider in another ; a member of the Greek
church, but a subject of the British sovereign : so
one and the same sensation finds a place for itself
in innumerable different groups, in each of which
it occupies a different relative position, while in
all it remains unchanged and the same, relatively
to other sensations, in its absolute position.
In the words of Sir W. Hamilton : — " We are
conscious to ourselves that we can repeat our acts
of consciousness, — that we can think the same
thought over and over. This act, or this thought,
is always in reality the same, though manifested
at different times : for no one can imagine that in

COMPOUND SENSATIONS. 17

the repetition of the one and the same thought,
he has a plurality of thoughts ; for he is conscious
that it is one and the same thought which is re-
peated, so long as its contents remain identical."

12. All sensations that are really compound but
apparently simple, have, on repetition or re-
excitement, a tendency to resolve, to become more
distinct. Their individual elements, more or
fewer of them, begin to individually assert them-
selves ; and the sensation which, before, was in
knowledge integral, now becomes many — now be-
comes a group of sensations. By repetition it is that
a sensation is enabled to enter into more groups
than one, and that the intricate combinations ex-
hibited in language are made possible. But to the
mind, as a body of sensation, language is a gar-
ment which is some times scanty, and sometimes
voluminous. These sensations have more than
one name a-piece, those no name at all. Some-
times a sensation gets so identified with a particu-
lar relation, as to lose in repetition its own identity,
and its name in that relation loses all absolute
meaning ; in other relations it still retains an
independent existence to the consciousness, and
its name has again a separate meaning assigned
to it, or, perhaps, is duplicated by, or abandoned
for, another, possibly more significant, name.
There's an ocean round our words
That overflows and drowns them.
* * * *

Speech is hut broken light upon the depths of the unbroken. *

George Eliot's " Spanish Gipsy."
C

18 THE LOGIC OF NAMES.

13. The complications thus occasioned, though
considerable, would not by themselves be so intri-
cate as they become in result of another fact. All
sensations (there might be reason for adding, and
the names* of some sensations) become, for a
greater or less extent of time, a physical part of
the human organisation. This many of them
begin to be at such an early date in life, some
probably before actual birth, and continue to be
to such a late date, possibly are transmitted here-
ditarily to posterity, that the mind presents no
record of their first reception, and small sign of
its being possible for a mind to have them not.

Barest skill that Pablo half had caught
From an old, blind and wandering Catalan;
The other half was rather heritage
From treasure stored by generations past,
In winding chambers of receptive sense.

* * * *

Shall the mere curl of eye-lashes remain,
And God-enshrining symbols leave no trace
Of tremors reverent ? That maiden's blood
Is as unchristian as the leopard's.f

14. Such or some such mental affections are
those that have been put apart from others, and
called innate ideas. Nor is it wonderful, when
the seeming random and fortuitous way in
which sensations hit, as it were, the mind, is com-
pared with the ordered mode in which the same
sensations are exhibited in thought and language,

* That is, not as the causes, but as the products or accompani-
ments of sensations.

t George Eliot & " Spanish Gipsy."

COMPOUND SENSATIONS. 19

that people should be inclined to think of the
mind as an active agent, and to figure to themselves
that Mind deals with sensations as a builder deals
with building materials. A builder takes bricks,
and stones, and beams ; classifies and catalogues
them as convenience may dictate ; puts them in
store for use, and from, his store selects at any
time what he may want for due arrangement into
forms of building. • So Mind is thought to recog-
nise objects by means of perception ; by means of
comparison and differentiation, or, generally, of
abstraction, to shape out from its perceptions con-
cepts or notions ;* by means of language, to classify
and catalogue the things which it has thus found
and formed ; by means of memory to store them ;
by means of reason to arrange them into proposi-
tions and trains of argument.^ Of such imaginations
this book necessarily does 110 more than take note.
If all known of a kaleidoscope were this — that
from without came to it, at seeming random, bits
of many coloured and many shaped glass, and that
these were the same bits which, with the aid of
our optic organisation, we see projected in ordered,
various, and infinitely numerous arrangements on
the object glass, what room would not be left for

* In another terminology, General Notions or Representations.

f " The rude materials furnished by Sense, retained in Memory,
reproduced by Reminiscence and represented in Imagination, the
understanding elaborates into a higher knowledge, simply by
means of Comparison and Abstraction. The primary act of Com -
parison is exerted upon the individual objects of Perception and
Imagination alone." — Sir W. Hamilton.

20 THE LOGIC OF NAMES.

conjectures as to the nature and the action of the
kaleidoscope ! But the most ignorant of civilised
men has just enough knowledge to confine within
limits all such conjecture : there is nothing in the
kaleidoscope which he is accustomed to call life.
If the kaleidoscope had life, however, should we
then consider him justified in framing a Mela-
physic of kaleidoscope ? Perhaps we might. But
the explanation which the optician now gives of
the kaleidoscope would remain unmodified by any
admission, if any admission were made, that the
kaleidoscope was alive. And so whatever hypo-
thesis may be entertained of the agents which
produce what are called perceptions and concepts,
it remains that, so far as our knowledge goes, the
elementary constituents of both are alike, and are
bound up by a like relation. The same elements
enter by turns into the composition of a sensation,
of a perception, of a concept, and of a judgment
or proposition, and are in each case united by the
same mode of connection.

VIII. ABSTRACTION.* — Among those already

* Archbishop Thomson describes Abstraction as a process of five
acts : — " 1. Comparison is the act of putting together two or more
single objects, with a view to ascertain how far they resemble each
other. 2. Reflection is ascertainment of their points of resemblance
and their points of difference. 3. Abstraction is the separation
of the points of agreement from those of difference, that they
may constitute a new nature, different from, yet including, the
single objects. 4. Generalisation [without which, the Archbishop
elsewhere says, there can be no abstraction] is the recognition of
a class of things, each of which is found to possess the abstracted

ABSTRACTION. 21

mentioned, it is an important note of sensations
that the same simple or compound sensation has
the power of being a member of an indefinite
number of different groups of sensations. The
differences between compound sensations that, in
this way, contain a majority of common elements,
appear, in mind, only as results of the repetition
or re-excitement of the several compound sensa-
tions, and of their consequent resolution into
parts. A man, who is neither a huntsman nor
a shepherd, sees a flock of sheep or a pack of
hounds, and, if the animals are all of the same
size and shape, knows not, else than numerically,
one from the other. The shepherd or huntsman
probably distinguishes each individual animal in
the flock or pack from all the rest,* and possibly
has a distinct name for every one of them. The
reason is, that each animal of the flock or pack is
represented in the mind by a group of sensations

marks. 5. Denomination is the imposition of a name that shall
serve to recall equally the Genus, or Class, and the Common
Nature."

* " The Laplander by long practice knows and gives a name to
each rein-deer, though, as Linnaeus remarks, ' to distinguish one
from another among such multitudes was beyond my comprehen-
sion, for they were like ants on an ant-hill.' In Germany,
shepherds have won wagers by recognising each sheep in a flock
of a hundred, which they had never seen till the previous fort-
night. * * Verlot mentions a gardene'r who could distinguish
150 kinds of camellia, when not in flower; and it has been
positively asserted, that the famous old Dutch florist, Voorhelm,
who kept above 1,200 varieties of the hyacinth, was hardly ever
deceived in knowing each variety by the bulb alone." — Darwin's
"Animals and Plants under Domestication."

22 THE LOGIC OF NAMES.

which, while it contains very many elements that
are common to the groups which represent its
fellows, also includes comparatively a few elements
that are proper to itself: the group representing
the individual animal constituting in common
language a perception, and that which comprises
only the elements common to all the individuals
forming a concept. The constituent elements,
however, whether of the perception or concept,
do not appear but in result of many repetitions.
The shepherd or huntsman has had the advantage
of such repetitions, the stranger not.

16. It generally follows, therefore, that, in the
case of all compound sensations which possess
many common elements, the first result of repeti-
tion or re-excitement is the appearance of the
resemblances between the compound sensations re-
peated or re-excited. The appearance of the
differences between them will be a second result.
In other words, men begin by seeing resemblances.
Afterwards, they distinguish differences. Simi-
larly, when we say that one thing or group of
sensations is equal to another, we shall mean that
more or fewer of the elements composing the one
group also enter into the composition of the other
group, and are, in our particular point of view,
the characteristic element or elements of both
groups. To 'say "this is like that" implies a
lesser but a still remarkable elementary com-
munity. But to say "this is identical with that "
can obviously only mean that this name is the
name for which that is a name. A sensation re-

ABSTRACTION. 23

mains the same sensation, no matter how often it
be repeated or re-excited. It is unaltered by
being added to itself, or by being multiplied into
itself. And whatever is done with it, it will still
remain as it was, and where it was, and distinct
from every other sensation.

17. Let us now suppose a man to have seen but
one large quadruped, say a dog, and to have given
it the name, Bog. This name will be to the man
the name of a sensation, which he may know to
be compound, but which he will certainly have
very imperfectly analysed. For, show him a
sheep, and he will call that a dog too. The word
Dog, from a proper name, as grammarians would
say, proper to one thing, will have become a
common name, common to more things than one.
If, now, an antelope and a goat are successively
introduced, they will be " dogs " also ; but, almost
simultaneously, differences between "dogs" will
also have been noticed. Every time the sensation
of dog number one, dog number two, dog number
three, or dog number four is repeated, it resolves
into more elements than it seemed to contain
before. While some of these elements are re-
peated in the remaining compounds, others of
them are not, and seek for names of their own.
Thus, one animal may get the name of "the
barking dog " ; another that of " the woolly
dog " ; the third may be styled " the horned
dog " ; the fourth, " the horned dog with a
beard." The original word, dog, will remain as
the constant element or elements repeated in

24 THE LOGIC OF NAMES.

all.* It is called a class name, or an abstract name,
the name of a concept, a notion, or idea, of a crea-
tion of the mind. The other names, so long as they
remain singular — remain the names of individual
animals — are called, in opposition, names of per-
ceptions ; of, that is to say, things external to us,
but perceived by our minds to exist, and to have
qualities- which we may separately name. But the
analysis we have been making in this paragraph
does not suggest any such distinction. It suggests,
on the contrary, that the supposition of the ab-
solute existence even of this dog, or of that dog,
is only a way of numerically stating the groups
into which our sensations resolve themselves.
This same inference is, at the same time, decisively
negatived by the fact that we have no power to
give any such objective reality to the contained
group of elements which is common to all the
dogs, although we have just as much reason for
giving it to this group as we have for giving it to
the group which represents any one dog.

18. The mental affections we have just been
tracing involve what is called, in the literature of
logic, Abstraction.^ This name supposes that in

* Brown quotes from Captain Cook's account of a visit to one
of the South Sea Islands:— " The inhabitants were afraid to
come near our cows and horses, nor did they form the least con-
ception of their nature. But the sheep and goats did not surpass
the limits of their ideas, for they gave us to understand that they
knew them to be birds." These same people, it appears, were
already acquainted with hogs and dogs.

f Professor 3 fax 3IiilZe>-'s summation of the philological his-
tory of abstraction is, that all names may be derived or identified

ABSTRACTION. 25

the process which has just been described the
mind is really an active agent. Comparing the
four dogs together, the mind finds them to agree
in certain respects, and to differ in others. It
throws the different qualities out of account, takes
them away, abstracts them, in order to concentrate
its attention on those that agree. These it brings,
in thought, together, forming a concept, or a general,
or an abstract idea.

19. Another view * of the same mental process
is more coincident with that which it is here
attempted to unfold. A vast number of objects
are constantly presenting themselves to our senses ;

with roots which invariably signify a general, not an indi-
vidual idea, originally expressing " one out of the many attributes
of a thing ; and that attribute, whether it be a quality or an
action, is necessarily a general idea " (" Lectures on Language,"
Fifth Edition, 1866). That is, in the language of the text, the
first names were names of simple sensations ; a compound sen-
sation was designated by the name of the principal or the
primarily recognised simple sensation among those which formed
its parts. Thus Professor Max Mailer's views may be quoted in
support of the hypothesis of the logic of names. He goes on to
say — " The word thus formed was intended for one object only,
though, of course, it was almost immediately extended to the
whole class to which this object seemed to belong."

This position, and the hypothesis of the text, are copiously illus-
trated by Professor Max Miiller. He tells us that " moon " means
to measure ; " sun," to beget ; " earth," to plough ; pasu, orpecus,
to feed. "Rhine" means to run; Gangd, to go ;'' Indus,"
to irrigate ; "name," to know. Compare also Sir W. Hamilton's
dictum, " Our knowledge commences with the confused and
complex, which, as regarded in one point of view or in another,
may easily be mistaken for the individual, or for the general."

* From Morell, who gives it as a view of "several of the
modern German psychologists."

26 THE LOGIC OF NAMES.

the perception of these objects leaves mental im-
pressions which continue to exist, though apart
from consciousness, and which may at any time be
re-awakened. "These latent impressions insen-
sibly blend together by the law of similarity ;
and when a result is obtained, in which all refer-
ence to time and place is lost, and all memory of
the actual objects of perception from which the
generalisation takes place, we term this result a
concept. Thus the concept, rose, it would be said,
is obtained by the insensible blending of all our
experiences of this flower, so soon as the varieties
are all lost sight of, and the common similarity
becomes absolutely predominant."

IX. CONSCIOUSNESS. — A sensation, it is said, is
not necessarily present to the mind. The mind
must be conscious of it, advert to it, attend to it,
perceive it, before it can become a mental fact,
before it can have a name. Sensation may, in
some cases, be almost amounting to a pain when
the mind is only beginning to take cognisance of
it. And of the relation which so connects a
number of different sensations that they form one
compound sensation, or so connects a number of
compound sensations that they in turn constitute
as constituent elements one great compound sen-
sation, still more complex than themselves, — of
that relation it may be said that it is no sensation
at all.

21. In regard to these interpretations of mental
phenomena, the present hypothesis is this — that

CONSCIOUSNESS. 27

the intellectual mind may be viewed as a sensitive
surface, the excitement of which at any one mo-
ment can only take place at one point ; that this
excitement may be called consciousness ; that any
one particular excitement may be spoken of as a
fact of consciousness (facts of consciousness thus
being equivalent to what in preceding sections
have been called sensations) ; that the human
organisation allows facts of consciousness to be
registered internally at the moment of their
origin, and for a greater or lesser portion of time,
remaining meanwhile latent, and not actually
facts of consciousness, but still on certain con-
ditions reproducible to consciousness ; and, in
conclusion, that the human organisation makes
possible, by signs addressed to the ear or the eye,
the external registration and exhibition of facts
of consciousness. The following conditions or
laws of thought may be deduced from, or recon-
ciled with, these hypotheses. A fact of con-
sciousness must be itself, it cannot be not itself.
The sign A, therefore, must be A ; it cannot be a
sign which is not A. The first of these affirma-
tions asserts what is called the Principle of
Identity ; the second that of Contradiction, or
Difference.* Again, in respect of any fact of

* Differently expressed thus:— 1. It is impossible that the
same quality should hoth belong and not belong to the same
thing. 2. "What is contradictory is unthinkable. 3. It is im-
possible that the same thing can at once be and not be. 4. The
attribute cannot be contradictory of the subject.

This law of Contradiction only differs from that of Identity by
a negative expression. The law of Identity has been thus ex-

28 THE LOGIC OF NAMES.

consciousness, A is or is not its sign. Between
these two alternatives there is no mean ; and the
principle which declares this fact is known as the
Law of Excluded Middle.*

X. GRAMMAR. — While the necessary instru-
ment of thought is language, and language con-
sists of words and their combinations, there
happen to be many languages — that is to say,
many co-ordinate and more or less equivalent
systems of verbal combinations. A treatise which
professes to give an account of one or more such
systems will be properly called a grammar. To
trace the elements of a language or languages to
their historical origins, and to describe the par-
ticular forms which they take, and the particular
arrangements which they are susceptible of, in
time and in use, is Grammar.

XL WORDS, which for Grammar are many
things, are for Logic only one thing, J^ames.f

pressed: — 1. Everything is equal to itself. 2. In the predicate
the whole is contained explicitly which in the subject is contained
implicitly. 3. Xota notae est nota rei ipsius. 4. Conceptions
which agree can be affirmed of the same subject at the same
time.

* This law has been thus expressed : — 1. Either a given pro-
position or its contradictory must be true. 2. Of contradictory
attributions we can only affirm one of a thing ; and if one be
explicitly affirmed, the other is implicitly denied.

f The distinction of parts of speech in Grammar arises from
an intrusion of grammarians into) the territory of logicians, so
far. that is to say, as such a distinction in speech is supposed to
involve corresponding distinctions in thought. The necessary

WORDS. 29

24. "When it is uttered, a name, from a result of
sensation, becomes a cause, and the mind is

existence of any such distinction in thought is denied by
the theory of this book. Both logicians and grammarians
have fetched their raw materials directly or indirectly from one
and the same language, namely, Greek. From that language all
the commonly — that is, the unscientifically — recognised laws of
speech and thought have been virtually deduced. If any lan-
guage has furnished exceptions to the laws thus made out, so
much the worse for the language. It has been either dragooned
into submission, or stigmatised as indulging in eccentricities beyond
the pale of reason. Of this tyranny the most signal victim, per-
haps, is the vernacular of England and America, where Lindley
Murray and his crew of followers have been exalted into supreme
authorities over the language of Shakespeare and Milton. The
student will find that, within the bounds of English and Greek
almost all the parts of speech are interchangeable in actual use.
And within the four seas of Great Britain there is a spoken and
written language which hardly recognises the distinction of case,
and which places, or did place, the article, disguised to gram-
marians as an expletive, before prepositions and verbs. Professor
Max Miiller takes us further afield in the same sort of illustration.
In his " Lecture on Language," (5th Edition, 1866), we are told
that the Chinese language has, according to common report, " no
grammar at all — that is to say, it has no inflections, no declension
and conjugation in our sense of these words — it makes no formal
distinction of the various parts of speech, noun, verb, adjective,
etc. Yet there is no shade of thought which cannot be rendered
in Chinese." No analysis of any kind seems to be required for
the discovery of the component parts of a Chinese sentence. Thus,
" the Chinese sound ta means, without any change of form, great,
greatness, and to be great." That is, it is equivalent to all three
English words. " If ta stands before a substantive, it has the
meaning of an adjective. Thus, tajin means a great man. If ta
stands after a substantive, it is a predicate. * * 1hns,jin ta
(oi-jin ta ye] would mean the man is great."

Again, " when we say in Latin baculo, with a stick, we say in
Chinese y*c~dng. * * * This y~ is a root; it is the same word
which, used as a verb, would mean " to employ." Therefore, in

30 THE LOGIC OF NAMES.

affected by it as it would be by any other cause of
sensation. Names thus become creatures of the
voice and the hand. They have attached to them
histories and prerogatives, which open themselves
to the grammarian and the philologist. They
serve as elementary symbols of number, and so
once expressed all that men knew of mathematics.
Lastly, they are symbols of sensations, and as
such demand the attention of logicians.

25. Words as symbols of number have not
always been distinguished from words as names.
The science of number is the evolution of the con-
sequences imposed upon thought by the condition
of time. The most elementary of these conse-
quences, being exhibitable by modifications of
names, have come to be regarded as inseparable
from the import of names ; and, as a necessary
part, therefore, of Logic. It is a manifest con-
venience of common and unscientific life to use
the same word to express both a name and a
number. It is as convenient to do so in elemen-
tary logic as in elementary arithmetic. But as
scientific arithmetic confines itself to words which
are numbers only, so logic, if it also is to be
scientific, must use words that are names only.
In logic, therefore, " man " and " men " are, sub-
ject to the exception elsewhere noted, two names
for the same thing — two collective symbols for
one and the same highly complex and imperfectly

Chinese y <?dng means literally employ stick." Of course it may
said, that a change of position is equivalent with a change of
form.

WORDS. 31

analysed group of sensations.* Viewed logically,
the forms " a man," " some men," " the men,"
" all f men" are to "man" or "men" as com-
pound names to simple names. The added word
is in each case the name of another sensation
which, for the time, enters into the group that, by
itself, would be simply nominated " man." As x
in Algebra stands for an unknown number, so ar,
some,^. or the, stands for the unstated sensations

* Of course " men" may also be a logical name for the human
population of the earth. Xumbers may also have logical names.
Twenty-five is the name in logic of a certain number. " Five
men " is a name in logic of a body of human beings distinguished
from other bodies by the name " five." In " He dealt the cards
by fives," "fives" is also a logical name.

All numerical symbols are logical names, but all logical names
are not numerical symbols. When a name is used as a name, it
forms part of the subject matter of Logic ; when as a numerical
symbol, of the subject matter of Number.

f The student has his attention called elsewhere to the am-
biguity of all, -which generally means "each and every," but
sometimes means " all taken together."

J "Some," Archbishop Thomson writes, may mean either
" Some, we know not how many," or " A certain number which
we have in our thoughts." The former meaning is the logical
meaning of the name ; the latter meaning it is susceptible of, as a
pronominal word. Archbishop Thomson's example is the proposi-
tion, " Some democratic governments have ended in a tyranny,"
which he supposes to occur as a consequence of historical reading
on the part of the enunciator. But the question would seem to
be, not what reasons may have led the enunciator to enounce his
proposition, but what he means to declare by it to the reader or
hearer. As he does not mention a definite or " certain " number,
he certainly does not mean to convey it by his proposition.

It seems to be a purposeless analysis in Logic of a proposi-
tion, which sets out as its object the foundations of the assertion,
as distinct from the mva.ting of the assertion.

32 THE LOGIC OF NAMES.

that must be added to those making up man, if an
individual man is to be denoted ; for those that
must be added to express a perfectly indefinite
number of individuals (one or more than one) ;
or for those that must be added when a particular
body of men is signified, as in " the men who lap
with their mouths.'7 Thus, " a man," " some
men," are compounded names. Each element of
each of these compounded names stands for a
separate sensation, or a separate group of sensa-
tions, and both of these elementary constituents
combine to form a third compound sensation,
which is conveniently denominated by the name
of these its parts. As these names, so com-
pounded, are mostly written together, as mathe-
matical symbols which numerically multiply one
another are written together by mathematicians,
we may conveniently say that they are logically
multiplied together ; and generally we may treat as
logical factors any names, however connected,
which are intended to be taken together as being
severally part-names of the same logical whole.

26. English names may appear as logical
factors in the following forms : —

I. Noun with article or pronoun : A man, my
horse, that house.

IT. Noun with adjective or adverb : A bright
noon, the then king.

in. Two nouns with or without a third name in
the shape of a preposition, conjunction, or inflec-
tion : A man of war, a pen maker) yesterday 's dinner,
brandy and water.

WORDS. 33

IY. More or fewer of the foregoing combina-
tions put together : Thomas Smith, a heavy fat
man, crier of the court.

v. Verbal forms with or without other parts of
speech : To rain, a swearing drunken brute, Amanda
trying on a new bonnet, a nascent virtue.

vi. Foregoing combinations joined to sentences :
A straight line which touches a circle.

vn. Combinations of words which have lost
their separate significations: Wood-cock, black-
bird.

27. To the last class might be added such com-
pounds as " presence of mind." In all much-
used compound names the words which constitute
their parts have a tendency to lose their own
separate significations. A sign of this tendency
may be recognisable in the omission of the article,
which is only prefixed so long as the separate
words retain in composition their original mean-
ings.

28. Logic not only combines, but dissects words
into names. Signs of the possessive case, of the
plural number, of present and past time, priva-
tive and strengthening prefixes, modifying affixes
and terminations, are all, in Logic, names, equally
with their several stem words. In this sense,
Logic makes one word into more than one name.
In another sense it does the same thing, by what
are called equivocal words, as, " light," which may
mean lux or leois ; as " dear/' which may be
beloved or high-priced. With synonymous words,
again, Logic enforces the reverse process; "heavy,"

D

34 THE LOGIC OF NAMES.

it says, is identical with " weighty," " continuous
transition " it declares to be the same as " transi-
tion with continuity." * Similarly, it sees no
difference between,

i. If two sides of a trianyle be equal, the angles at
their bases are equal ; and,

ii. In any triangle the angles at the bases of two
equal sides are themselves equal :

Or, between,

i. If a triangle is equilateral, it is also equiangular,
and,

ii. Equilateral triangles are equiangular.

Or, between,
( For \

i. < As > All triangles contain two right angles ;

( Since )

and, because this is a triangle, this also contains two
right angles ; and

ii. All triangles contain two right angles ; but this
s a triangle ; therefore this contains two right
angles.

29. In the same spirit, Logic demands general
exactness from language. Meeting with such a
proposition as —

All right angled parallelograms are squares or
rectangles, it obliges the meaning to be made

* A unwocal name is a name which has only one meaning. An
equivocal name has more than one absolute and independent mean-
ing. A metaphorical name is that which has more than one
meaning, hut of its meanings more or fewer are temporary and
provisional, in other words pronominal. Thus, a particular part of
an animal is always named foot ; the lower part of a tree, or of a
mountain, is sometimes named foot.

WORDS. 35

independent of the matter by a more explicit
statement, as —

All right angled parallelograms are squares, or, if
not squares, rectangles.

30. And, similarly, it paraphrases,

i. All non acute angles are right or obtuse ; as,
All non acute angles are right and not obtuse, or

obtuse and not right.

11. The ground is wet because it has rained ; as,
The cause of the ground being wet is that it has

rained. And

in. It has rained because the ground is wet ; as,
The cause of our knowledge that it has rained is

our knowledge that the ground is wet.

31. An interrogative pronoun is, in logic, simply
a note of interrogation ; i.e., a name of that about
which a question is asked.* The English language
puts the character which marks an interrogation
at the end of the sentence, but the word which
marks it generally at the beginning. In Spanish,
the character is put first, as well as last; in
Greek, the word is often put last.t These differ-
ences are only noticeable so far as they show the
independence of idiomatic language, which is a
characteristic of logic.

32. A proposition becomes a question by a change
in the order of its words, or by a change in the
incidence of its accent. Then the change of order
or of accent is a logical name.

* Latham.

f And often in English as well. This is what ? is as idiomatic
as What is this ? The first, however, illustrates better the force
of an interrogative name, This is the thing about which I ask.

36 THE LOGIC OF NAMES.

33. A negative word, or affix, again, is the sign
of a subtracting operation which is not performed
but only indicated. In " it is not so," the sensa-
tions defined by "so" are exhibited by "not" in
process of subtraction from all sensations. " Not "
is the name of a subtraction, which may be
imaginary, and need not take place, in fact.
Suppose it to have taken place, and then the form
"not so" may stand for the name of the re-
mainder. When it is the name, and is not
standing for the name, it is no longer negative,
but positive. In names like inhuman, immortal,
for instance, the negative has lost its force, the
subtraction by degrees having come to be regarded
as having been effected, and its name as a sign
'for the remainder.

34. A pronominal word is a word which stands
by convenience for another word. The list of
such words in Grammar might well be extended
so as to take in such words as " thus," "so," and
" do," in many of their uses. In Logic, however,
they are all names with provisional and temporary
meanings defined by the context of the moment.
If we said " swans are white," we should mean
that among those elements which make up the
compound sensation, "swan," is that element
which we name " whiteness." It is a usage of
language which imposes in certain circumstances
a change of whiteness into white.* And the

* Compare the word Concrete, which is a term relatively ap-
plied to any one of a number of groups of sensations which contain,
as a common element, another group of sensations. This common

WORDS. 37

cause of this usage is another usage, — the am-
biguous use of the substantive verb. "Is" or
"are" may express either nominal identity or
logical relation between the names it joins. In
order to meet this ambiguity, language makes a
change, not in that which joins, but in that
which is joined. Between these two sen-
tences—

i. A particular compound of elementary rays is
whiteness; and

n. A particular compound of elementary rays is
ivhite.

the real difference of meaning* lies in a word
that is the same in each, " is " ; which, in the
first case, expresses a relation of nominal identity ;
in the second, the relation which one element in
a group of sensations bears to another element or
elements in the same group, by virtue of their
being in that one and the same group. This
relation we distinguish as the logical relation.
In Logic, " is " is used only in this signification.

element may be abstracted from any of those -which contain it.
They are concrete, therefore, and it is abstract. In this broad
sense the name of any concept or notion is abstract ; that of any
object, thing, or numerical individual is concrete. In a narrower
but analogous sense, an abstract name may be denned as that of a
quality considered apart from that which possesses it, as whiteness ;
while a concrete name is that of a quality considered as being
possessed by something else, as white. But this distinction is
merely a paraphrase, with something like logical language, of
a grammatical distinction, which answers to no difference in
thought.

* Supposing " white " not to be used for " whitish."

38 THE LOGIC OF NAMES.

When Logic finds it to be used by common
language in another signification, it can only
interpret it by a paraphrase, as, for example,
" James is," by " James exists."

35. If the distinction between a substantive and
an adjective disappears in Logic, so does that also
between a substantive and an adverb, a prepo-
sition, or a conjunction. In

The danger is very great,

the meaning of " very " is strictly provisional to
the temperament of the speaker and the cir-
cumstances of the case. It means that the pro-
bability of the event, or result, to which the
apprehension of danger attaches, is as much
nearer to 1 than to 0 as the speaker (and the
hearer in assumed sympathy with him) is accus-
tomed to mark, or supposes himself to mark, by
the word " very." In

The risk is comparatively high,
" comparatively " has also a provisional meaning.
Although it explicitly implies the process of com-
parison, it also supposes a provisional standard of
comparison. But in

The bill introduced by him was avowedly directed
against the neutral powers,

" avowedly " has a positive signification, namely,
" with an avowal that."

36. Prepositions and conjunctions in Grammar,
like "is" and "do," are pronominal. Thus,
"of" may stand for "belonging to," as, "the
martyrs of the fight " ; for the Latin de, as in " I
could not sing of love"; for "from," as in

NAMES. 39

" orient hues unborrowed of the sun " ; for " by,"
as in " Ye shall be hated of men." *

XII. NAMES. — A name f is the sign, token or

* From Howard's " Grammar of the English Tongue" (pub-
lished at the Education Society's press, Bombay). The imper-
fections of language, so far as they are liable to affect the validity
of logical forms, constitute Fallacies. A few of the instances
commonly given may be noted here.

" To speak of stones is possible ; to speak of stones is speech of
the speechless ; therefore speech of the speechless is possible ; "
•where there is an ambiguity in "of."

" 7 and 2 are odd and even ; 9 is 7 and 2 ; therefore 9 is odd
and even" ; where there is an ambiguity in " and. "

" What he was beaten with was what you saw him beaten
with ; what you saw him beaten with was your eyes ; therefore he
was beaten with your eyes" ; where there is a confusion in the
applications of "with."

" The people suffer from famine ; you are one of the people ;
therefore you suffer from famine" ; where "one of the people"
is confounded with "people."

" All these trees make' a thick shade ; this is one of them ;
therefore it makes a thick shade" ; where the fallacy is similar
to that in the preceding instance.

" Projectors are unfit to be trusted ; this man has formed a pro-
ject, therefore he is unfit to be trusted " ; where the conventional
meaning of "projector" is taken for its etymological meaning.

" What is bought in the market is eaten ; raw meat is bought
in the market ; therefore raw meat is eaten " ; where the first
assertion is imperfect, and might be repaired by reading, "is
bought to be eaten."

All such mistakes are to be guarded against, by making lan-
guage state exactly that which thought presents.

•(• The idea of a name, as conceived in this Logic, may be illus-
trated by saying that it answers to Leibnitz's symbolical cognition,
as that is defined by Archbishop Thomson, who uses the follow-
ing words : — " A name, then, employed in thought, is called a
symbolical cognition."

40 THE LOGIC OF NAMES.

symbol of a mental idea, concept or notion ; or of
a sensation, or a feeling or perception ; of some
impression or impressions that have been so made
on our sense, as to be felt or perceived by the
mind to form one whole."* "When this sensation
is simple, indivisible to the mind, its name, if it
have one, is necessarily a simple name. When it
is compound, is in fact not one sensation, but
many, so that the mind may verbally exhibit
more or fewer of these sensations ; the name may
be a simple or a compound name, may, either, by
a simple form, collectively designate the various
simple sensations which make up the compound
sensation, or by a complex form designate in
detail the same compound sensation; the complex
form consisting of more or fewer of the names
themselves of the constituent sensations. In the
former case the name may be called a simple
name, in the latter a compound name ; but in
each the name, as a name, is what it is in the
other case. Many compound sensations have two
names — one a simple name and the other a com-
pound name. Ofttimes a compound sensation has
no simple name, but can only be denominated,
imperfectly denominated, by a name composed of
the names of its parts.

* Or a name may be defined as standing for a " thing," and a
"thing" as " a simple or compound fact of consciousness." In
what follows of the text, the words idea, concept, notion, feeling,
perception, or any one of them, may be substituted, at pleasure,
1'or sensation.

4.1

These gems have life in them : their colours speak,
Say what words fail of. So do many things,
The scent of jasmine, and the fountain's plash,
The moving shadows on the far-off hills,
The slanting moonlight, and our clasping hands.*

38. Sometimes the name of one of the parts of a
compound sensation stands for the whole. Some-
times the parts are not distinguished, or have no
name. There is, of course, no difference between
simple and compound names viewed as names. f
The elements of a compound name may be com-
pound names themselves, and any number of
words together may form but one name.J

* George Eliot's " Spanish Gipsy."

t " "When a language is transmitted from one generation to
another, not merely the words, but their mode of connection, as
sentences, is also transmitted and appropriated by unconscious
imitation, and thus becomes fixed. The latter point is not suffi-
ciently appreciated, though it is quite clear that we do not think
in words but in whole sentences ; hence we may assert, that a
living language consists of sentences, not of words. But a sentence
is formed not of single independent words, but of words which
refer to each other in a particular manner, like the corresponding
thought which does not consist of single independent ideas but of
such as, connected, form a whole, and which determine each other
mutually."— Waitz, translated by Collingivood.

% This seems to be the place for noticing the fact that logicians
sometimes take the trouble of dividing into classes those things
which it appears to them are capable of being named. Thus, Mr.
Mill discusses at length the following division of things : —
I. Feelings or states of consciousness.

1st. Sensations.

2nd. Thoughts.

3rd. Emotions.

4th. Volitions.

42 THE LOGIC OF NAMES.

XIII. MEANING. — The " meaning " of a name
is the thing or things for which it stands. Any
word which has a meaning, therefore, when it
stands by itself, and any " sign " whatever, is, for
the purposes of this book, a name.

"Even your loved words
Float in the larger meaning of your voice
As something dimmer."*

40. All words, then, are names ; for they may all
appear in the pages of a dictionary with one or more
meanings attached to them. Particles as — yes, no,
to, for, by — are, accordingly, names; and we might
describe a name as a sign, mark, or symbol which
represents to the senses what may not be, cannot
be, or is not, of itself apprehended, at the time,

II. Substances.

1st. Body, or that which may he assumed to he the ex-
ternal cause of sensation.

2nd. Mind, or that which may he assumed to he the in-
ternal cause of sensation.

III. Attributes.

1st. Qualities.
2nd. Quantity.
3rd. Eelations.

a. Likeness, unlikeness.

b. Nearness, distance.

c. Succession, concurrence, precession.

d. Being greater than, equal to, less than,

e. Cause, effect.
/. Etc., etc.

Such classes of things are known in logical literature as cate-
gories, a word which literally signifies accusations, and which has
been transferred to logic in the sense of predications. The
doctrine of categories has always been considered extra logical.

* George Eliot's " Spanish Gipsy."

MEANING. 43

by the sense.* Names may thus stand for sensa-
tions which are not in effect repeated or re-
excited at the moment of utterance, or which
have already become parts of the human organi-
sation.

41. It is possible for some compounded sensations
to have become so integrated, as it were, with the
physical system as to lose in consciousness their
compound character. In such a case the separate
names of the compounded sensations will also
have lost their force as symbols of distinct things.
But here to the aid of the logician comes the
philologist. The history of language shows that
before the integrating process had set in, or before
it had reached its present stage, these very same
words were in use, with very definite meanings
attached.

42. When the meaning of a name consists of
many parts, more or fewer of which have their
own names, as in the case of the simple name of
a compound sensation, the names of the sensations
so compounded, or the compounded sensations
themselves, are called by logicians attributes.
These attributes may be thought of as the marks
of the group of things which is signified under
that simple name of which, collectively, their

* " Jump," says the shepherd to his dog, and the dog knows
that this vocal articulation orders him to make a given muscular
effort. The man has spoken to the dog. During the night some
one opens the gate of the farmyard, and the watchdog barks ; he
thus tells his master that something unusual is happening." —
Pouchet, translated by Beavan.

44 THE LOGIC OF NAMES.

particular names express the meaning. And col-
lectively, also, these particular names constitute
to logicians the connotation, the comprehension, or
the intension of that simple name.

43. To set forth the meaning of a name in terms,
is to define it. When thus set forth, the meaning
is called a definition* As sensations in repetition
or re-excitement tend to resolve themselves, the
meanings of their original names are, in the
course of time and discovery, liable to be ex-
tended, and their definitions, therefore, being
expressed in words, to become, in a sense, incom-
plete. But as long as the definition is sufficient,
in view of the purpose in hand, for marking off
what the name defined stands for from other
things, it ought to be held to be a competent
definition. Thus, "Man is a rational animal,"
will remain a valid definition until it can be
shown that some other animal is rational also.

44. When a definition is necessarily very tem-
porary or provisional in its nature, it is commonly
and usefully distinguished as a description.

45. Tn language and the practice of logic, it is
allowable, for the employment of a word in any

* Sir William Hamilton puts definition under the wider term,
Declaration, and says that a declaration is called an explication
when it indeterminately involves only some of the names which
constitute the meaning. It is called an exposition, when it con-
tains several explications. It is called a description, when it
consists of names which wholly or partially suggest only, but do
not express, the meaning. Finally, in cases set forth in the text,
under the head of classification, he calls it a definition proper.

RELATION. 45

particular chain of reasoning, to limit or even
vary its meaning. Thus, for the purposes of
science, it is possible to have names the meanings
of which are exhaustively and exactly statable.

XI Y. RELATION.* — Since no sensation can be
repeated without a revival or re-excitement of the
sensation or sensations proximate to it in order of
time, no two sensations become facts of conscious-
ness without a consciousness of their number ;
that is, of their sequence, of a fresh sensation — a
sensation of relation between them. This being
the one universal relation (we are accustomed to
speak also of relations of equivalents, likeness,
etc.^, it has been taken as a sort of necessary
factor to the connection of sensations, and as that
which renders any two or more simple sensations
capable of being related to the same group, and
of being named under the same compound name.

47. As the distinction between the elements of
a compound sensation thus appears to be succes-
sion, that between compound sensations themselves
may be taken to be an interval or break of suc-
cession. This distinction is, however, a distinction
of manner, not of kind, the relation between one
compound sensation and its successor being in-

* This seems to be the place for noticing what have been
called Relative Conceptions. A relative conception cannot be
thought of alone, but only in conjunction -with its necessary
complement, or correlative. Such are father and son, pronominal
names, respectively used for all groups of sensations which have
certain common elements.

46 THE LOGIC OF NAMES.

trinsically the same as that between a simple
sensation and its successor ; and the foundation
of the relation is evidently without the mind.
Sensations come to it in a certain order ; and this
order is invariably maintained in all their repe-
titions and re- excitements, and constitutes what
we call its knowledge.*

XV. PROPOsrxiONS.t — The name of the logical
relation, if expressed, has therefore the office of a
copula or nexus between the names of the con-
stituent elements. It asserts that the names it is

* Professor Max Mutter, in his " Lectures on Language " (5th
Edition, 1866), says, " How do we know things ? "We perceive
things by our senses, but our senses convey to us information
about single things only. But to know, is more than to feel, than
to perceive — more than to remember, more than to compare.
* * * We know a thing if we are able to bring it, and any
part of it, under more general ideas. "We then say, not that we
have a perception, but a conception, or that we have a general
idea of a thing. The facts of nature are perceived by our
senses ; the thought of nature, to borrow an expression of
Oersted, can be conceived by our reason only." Excepting,
perhaps, the expression of Oersted's, nothing in this passage seems
to amount to more than a statement of the facts discussed in the
text.

f A proposition which must he taken for granted as self-
evident is an Axiom. If not only to be taken as a fact self-
evident for belief, but as a rule to be acted on, or instrument to
be employed, .it is called a Postulate. If it is not self-evidently
true, but only to be shown true by means of other propositions,
it is called a Theorem. "When it is of a complex order and gives
certain premises (data) as the conditions of action (solution),
which must result in a certain conclusion (qucEstio), it is a Problem.
When it is an immediate inference from another proposition, it is
called a Corollary from that proposition. A proposition borrowed

THE COPULA. 47

interposed between may together form one com-
pound name, or be together replaced by one
simple name. Such an assertion, taken along
with its subject matter, is what is called a propo-
sition. In accordance with this view, a proposi-
tion may be described as the exhibition of a
compound name in analysis or synthesis.* The
enunciator wishes, by stating a fact, to ascertain
it for himself, or to demonstratef it for another.
In the one case he may be said to construct a
compound name, in the other to dissect it.

XYI. THE COPULA. — In a proposition the name
of the connecting relation is distinguished as the
copula. In language the copula is sometimes
understood, but most often is expressed by what
is called a verbal inflection, or by the verb " to
be " in some one of its forms, or, where the copula
has to join compound names which themselves
are in the form of propositions, by such a word

from one science as an auxiliary to propositions in another science,
is called a Lemma. "When it serves as an illustration only to
propositions of its own science, and is not a necessary link in a
main chain of reasoning, it is a Scholion. A. proposition which is
proposed for discussion or proof, is termed a Thesis. "When, to
explain certain facts, it is provisionally adopted as a demonstrable
Theorem, it becomes a Hypothesis.

* Compare Sir William Hamilton. "A concept is a judgment
* not explicitly developed in thought, and not formally
expressed in terms ;" "concept" answering to the "compound
name," and "judgment" to the "proposition," of the text.

t A demonstration is the verbal exhibition of a mental affec-
tion.

48 THE LOGIC OF NAMES.

as "therefore." The word "to be," however,
forms the general sign of the copula ; and, as a
copula, has somewhat arbitrarily ascribed to it
various significations.* It can always be substi-
tuted for the other signs of the copula.f

XYII. TERMS.J — In a proposition, the names of
the sensations between which the asserted rela-
tion is supposed to exist, are distinguished as the
terms. These, in the typical form of propositions,
must be two in number. For, as has been already
intimated, more than one sensation cannot be ex-
hibited by the mind without the exhibition of a
logical relation. The mind can exhibit a plurality
of sensations only in the form of a succession of
names coming in pairs ; the latter member of each
pair being the name of the logical relation, and
also the first member of the succeeding pair.
The name of the logical relation, consequently,
virtually becomes, in each case, a copula between
the two extremes of a dipodium ; as thus —
a c, c b \ b c, c d \ dc, c e \ etc.§ Such a succession

* Namely, identity, accompaniment, sequence, cause, or re-
semblance.

t For " John runs," may be substituted "John is running."
In the case of " therefore," the subslitxition would be less idiom-
atic sometimes, but equally intelligible.

J Terms are so called because they are considered to be the
bounds or extremes of a proposition.

§ The dual nature of the proposition may perhaps receive a
kind of illustration from the following newspaper cutting : —
" He never could learn the whole lesson. In this instance he
was unable to remember the third component part of gunpowder.

LOGICAL WHOLES. 49

as the above is, in language, speedily transformed
in to a succession of triads; thus, acb \ bed \ dee \
etc., in which each triad is a type of the ordinary
proposition of language, with its two terms united
by a copula.*

XVIII. LOGICAL WHOLES.J — Sensations which

Whichever two he remembered, the third was always forgotten.
His captain, attributing this failing to obstinacy, reported the
matter to the colonel, who examined the man himself. ' What
is gunpowder made of ? ' — ' Charcoal, saltpetre, and — ' ' Sulphur,'
said the colonel. ' Now rsmember that, my friend— sulphur.
Now tell ma what is gunpowder made of ? ' — ' Sulphur, charcoal,
and—' ' Saltpetre,' added the colonel. ' Now, my friend, don't
be nervous ; forget that I am your colonel ; think of me only as
your comrade, who, slapping you on the back, asks, Tell me, old
fellow, what is gunpowder made of? What would you say ?' —
' I would say,' growled out the soldier, ' that as you know it
better than I do you are a damned fool to ask me.' "

* The theory involved in the text may be exemplified by
stating that in the proposition " Man is mortal," it considers two
judgments to be involved, having one common term, " is." "With
respect to the ordinary logical distinctions between terms, as, for
instance, into singular, common, collective, abstract, and attribu-
tive, they are generally accounted for in subsequent paragraphs
of the text. A collective noun is that which is otherwise called
a noun of multitude, and is the noun of a logical whole which
has been formed by a process of numerical addition. It is some-
times opposed to a Distributive name which is the name of a
logical whole formed by abstraction. An abstract term is the
name of a quality, considered independently of that which
possesses it ; as, " goodness ": an attributive term is the name of a
quality considered as inherent in that which possesses it ; as. " it is
good" This distinction is grammatical, like that between univo-
cal, equivocal and metaphorical terms.

f " Wholes may be first divided into two genera, — into a Whole
by itself (Mum per se), and a Whole by accident (totum per
aceidens). A Whole per se is that which the parts of their proper

50 THE LOGIC OF ^AMES.

by force of a mutual relation form one group, so
as to be capable of designation under one name,
and which can be expressed in this connection by
a compound name, by a proposition, or by a series
of propositions of which their names constitute
the terms, are said to form a logical whole. If,
then, simple sensations in logic are taken as
analogous to atoms in Chemistry, a logical whole,
in its simplest form, will be analogous to a chemi-
cal molecule. One definition of a name might

nature necessarily constitute ; thus, body and soul constitute the
man. A Whole per accidens is that which the parts make up
contingently; as, when man is considered as made up of the
poor and the rich. A Whole per se may, again, he subdivided
into five kinds, — into a Logical, a Metaphysical, a Physical, a
Mathematical, and a Collective. 1. A Logical, styled also a
Universal ; a Subject or Subjective ; a Potential Whole, is a genus
containing under it species, or a species containing under it indi-
viduals ; and 2. A Metaphysical, styled also a Formal or an
Actual Whole, is an individual as containing in it species or a
species as containing in it genera. 3. A Physical, or, as it is
likewise called, an Essential Whole, is that which consists of
matter and of form, in other words, of substance and of acci-
dent, as its essential parts. 4. A Mathematical, called likewise
a Quantitative, an Integial, more properly an Integrate, Whole
(totwn integratuni), is that which is composed of integral, or,
more properly, of integrant, parts (paries integrantes*). In this
Whole every part lies out of every other part ; whereas, in a
physical whole, the matter and form, the substance and accident,
permeate and modify each other. Thus, in the integrate Whole
of a human body, the head, body, and limbs, its integrant
parts, are not contained in, but each lies out of, each other.
6. A Collective, styled also a whole of Aggregation, is that
which has its material parts separate and accidentally thrown
together ; as an army, a heap of stones, a pile of wheat, etc."—
From Sir JT. Hamilton.

LOGICAL WHOLES. 51

make it the sign or symbol of a logical whole,
and anything to which one can give a name
might be called a logical whole.

52. The different ways in which names may be
used in expressing logical wholes are usefully dis-
tinguished by the employment of mathematical
terms. The following compound name, for ex-
ample, " The-tent-royal-of-their-Emperor," ex-
hibits three names, (two being compound them-
selves), which are written together so as to form
one name as one whole. The expression consists of
a single term, of which the component parts are
combined without any connecting sign, as if by
the algebraic process of multiplication. The
actual process may, therefore, be conveniently
styled the logical process of multiplication. A
further analogy between this logical process and
its algebraic parallel appears in the fact, that, in
both cases, the relative position of any particular
symbol makes no difference to its value as a factor.
The entire expression would remain unchanged in
import if the fancy of the writer or the idiom of
the language had placed that first which now goes
third, or that second which now goes first.
Another language might make "the" come after
"tent," or "royal" before either, and so on.
Thus Mr. Morris in his " Earthly Paradise" writes
lines such as this : —

" Like the gold people of antiquity ;"
the equivalent form to which in prose English

52 THE LOGIC OF XAMES.

would have " gold " before " antiquity," in Ice-
landic " the," if used at all, after " people," and
in Latin " of" after " antiquity."

53. Again in the following sentence : —
The angles which one straight line makeswith another
falling on one side of it are two right angles, or (if) not-
two-right- angles (are together equal to} two-right-
angles. Considered as one proposition and relieved
of the surplusage of mere language, there are
four terms and a copula. Of the four terms, one
comes before the copula. Of the remaining three
terms, one is separated from the other two by the
intervention of "or." And the two terms left
are united by the word " if," which, being only a
sign of multiplication, has been treated as surplus-
age. But " or" is different from " if." The latter,
according to the account we have given of logical
multiplication, only stands for a dead copula,
represents a relation supposed to be already de-
monstrated, which is sufficiently evidenced with-
out it. " If," at most, is like the sign x in
algebraic multiplication when it is written out,
and not understood. But "or," like +, is not
left to be understood. It expresses an alternative,
and the terms which it separates or brings to-
gether are in a very different relation from that
of logical multiplication. This relation may be
conveniently distinguished as that of logical addi-
tion. Very frequently it may be represented by
" and " ; as in

Merchants are wholesale dealers and retail dealers,
[which we know to mean,

LOGICAL EQUALITY. 53

Merchants are wholesale dealers, or if not whole-
sale dealers (then) retail dealers.^
And as in

English Celts and Saxons,

[where Celts and Saxons are logically added to-
gether by the sign " and," the name " English "
being logically multiplied into each of them.]

54. Logical addition should not be confounded
with the addition of number and magnitude.
Such addition is frequently expressed by " and,"
as in " two and two are four," " water is oxygen
and hydrogen," or " it is brandy and water."
This ambiguity of the word " and " in part arises
from that general parallelism of the sciences of
names and numbers which, we shall see further on,
has occasioned confusion between Classification and
Logic.

XIX. LOGICAL EQUALITY. — Of the various re-
lations that in language may be represented by
the sign of the copula, the logic of names only
takes cognisance of the universal relation which
has been already defined, and which may be
conveniently named logical equality. This word
" equality " is in logic a different thing, but not
an opposed thing, to the equality of the sciences
of Number and Magnitude. In logic, one thing
is equal to another,* or, rather, one name is equal
to another, if it may be taken in thought with

* Of course, one sensation can only be equal to another so far
as they are both sensations.

54 THE LOGIC OF NAMES.

that name to form, as integral parts, the same
logical whole. The terms of every proposi-
tion, therefore, are equal to one another, the
copula is a sign of logical equality, and a propo-
sition is a logical equation.

56. In the case of synonyms, it should be noted
that the expression of logical equality becomes an
expression of nominal identity. When we say
that plumbago is black lead, we mean to say that
plumbago and black lead are two names for the
same thing.

XX. NUMERICAL VALUES. — In English gram-
mar a distinction is often made between so-called
common and proper names which might be ex-
tended to all names. Every name in a language
may be said to fall in one or other of these two
classes, — the class where every name in one sense
is proper to one thing, and the class where every
name in one sense is common to more than one
thing. The names in the latter of these classes
may reasonably be called common names ; those in
the former, proper names; and that number of
things which a name may happen to stand for we
will nominate its numerical value.

58. Names which have different senses are
capable of being in some senses common names,
in other senses proper names. This is an affair
of usage. Thus man in one sense is proper ; it
is the name of mankind. In another sense it is
common, being indifferently applicable to every
individual man. Viewed as being originally a

NUMERICAL VALUES. 55

common name, the idiom of the English language
provides two ways of using it, in derived senses,
as equivalent to a proper name. " The " being
placed before man, viewed as a common name,
that name is made proper to some individual man ;
as, " I will kill the Man who breaks this law." *
In the plural number, as Men, it again, viewed as
a common name, is made equivalent to a proper
name, as in " Men are mortal." And both methods
may be combined, as in " I will kill the Men who
break this law." It appears, therefore, that a
common name may be used as equivalent to a
proper name, or for a proper name, — first, by
having affixed the definite article, which may be
called a sign of the proper sense ; second, by
being inflected in the plural number. " Horse,"
for another example, is never, except in the sense
of " horseflesh," used as a proper name. "We do
not say, " Horse is a noble animal." But "horse"
can be made equivalent to a proper name. "We may
say, " The horse is a noble animal," or " Horses

* Other examples :— The Punjauh, The Doab, The Deccan,
The Peninsula, in the English of to-day ; The Bath, The Massa-
chusetts, in last century English. As a general rule, when an
English name of place or person is preceded by the definite
article, we may assume that the name does or did connote some-
thing or other in addition to what it at present denotes. At the
present day Englishmen and Americans, while they usually speak
of " Hamlet " and " King Lear," as generally say, " The Medea,"
" The (Edipus Rex." Civilians talk and write of men-of-war as
" The Arethusa," " The Bellerophon," etc. In naval writing
the article is frequently omitted. The causes or explanations of
these variations in usage are easily suggested by what is said in
the text.

56 THE LOGIC OF NAMES.

are noble animals," or " The Horses of Arabia are
noble animals." When a common name is much
used in a particular proper sense, the force of
usage and the course of time will often render
unnecessary the indication of the article. Thus,
we invariably say now " Massachusetts." In last
century they often said, " The Massachusetts.'1
Then " Massachusetts " was at least traditionally
a common name, having meant "Blue Moun-
tains " ; and it was used in a proper sense, as
proper to a certain province. Hence the affixed
article. Now usage has turned the common
name into a proper name, and the article is
unnecessary.

59. A word may be used in any one proposition
according to its numerical value as limited by the
context, either for all the individuals it is nor-
mally common to, or for some of them. In the
former case it is said to be distributed ; in the latter
undistributed. In "Men are animals/' "men" is
said to be distributed ; in " Some men are ani-
mals," 4'men" is said to be undistributed. In
both propositions " animals " is said to be undis-
tributed, it obviously not standing for all the
individuals it is normally common to. But, in
the method of this book, " some men " is regarded
as a pronominal name ; that is, as a compound
name with'a provisional meaning, proper in sense
and distributed in logic. No numerical value
has been changed. Two terms have been mul-
tiplied together, and the result is a new term.
The same holds of all names which stand in

NUMERICAL VALUES. 57

the relation to one another of logical factors.
Similarly, the alteration of numerical value in
the case of " animals " is to be regarded as a
change of sense. In the one proposition, it stands
for one thing, that is one numerical value ; in the
other proposition, for another numerical value ; in
each case its numerical value being determined
by the other term. But the other term, scien-
tifically considered, is in each case a proper name,
though with a provisional meaning ; and its nu-
merical value must, by the definition of a proper
name, be either 1 or 0 : — 1, if the name of a thing
supposed really to exist, or of a proposition sup-
posed to be true ; — 0, if the name of a thing which
is supposed not to exist, or of a proposition which
is supposed not to be true. As this reasoning
holds of all names, for they may all be terms of
propositions, it generally follows that the only
numerical values assignable by the logic of names
to names are 1 and 0 ; that all names are proper,
and all distributed ; and that there is no logical
distinction between names as singular and plural.*
Manifestly the same conclusions follow from the

* Except that to a singular name a plural name stands as a
compound name to a siinp'e, or as the name of an included com-
pound sensation to that of its larger and including compound
sensation. Thus, from Professor Max Midler, we learn that
"man" in Chinese is'yin, and that "the whole," or "totality,"
is Mai. The two, added together, give *gin-kiai, the Chinese for
"men." And again, pe'i in Chinese means "a class," i means
"a stranger," and l-pei means "strangers." The English lan-
guage gives analogous illustrations in \vords like "mankind,"
" Christendom."

58 THE LOGIC OF NAMES.

definition of a name as the distinctive mark of
one sensation, or one group of sensations.

60. It may be remarked that Q admits indif-
ferently of the values 1 and 0. Therefore it
would be admissible as the expression of the
numerical value of a logical name, and would
imply that that name was of indefinite numerical
value. Such a name is "animal," in "All men
are animals," for its numerical value is determined
by that of the other term, and may, therefore, be
either 1 or 0. Relatively to its original numerical
value, absolute 1. it may now be any fraction of 1 ;
yet whatever fraction it may be relatively and in
form, that fraction must be absolutely equal to
either 1 or 0 ; a condition satisfied by the fraction
g. g in this use finds an expression in the name
" some," and " men are some animals " is accord-
ingly a correct paraphrase of " men are animals."

XXI. CLASSIFICATION. — Coleridge asked his son
why he was called Hartley. " Which Hartley? "
said the boy. " Why, is there more than one
Hartley ? " " Yes, there is a deal of Hartleys ;
there is picture Hartley" (Hazlitt had painted a
picture of him), " and Shadow Hartley, and
there 's Echo Hartley, and there 's Catch-me-fast
Hartley," "seizing his own arm very eagerly.
Hartley perhaps thought that for every separate
word used as a name there must exist in nature a
separate thing, and that the same thing has no
business to have more than one name. We may

CLASSIFICATION. 59

suppose him to have gone on from this beginning
to discover that there were more " picture people "
in the world than himself, and that in the various
simple names he had been putting together to form
names of himself, all but the one word Hartley
were common names. This discovery would have
introduced him to the science of Classification.

62. Picture, Shadow, Echo and Catch-me-fast,
are all names which, in the sense given them by
Hartley, are each respectively common to more
than one person or thing, and they in conse-
quence require the addition of the word "Hartley "
to make them proper names. By themselves, in
Hartley's use of them, and as numerical symbols,
they each have a numerical value greater than 1,
the numerical value of the name Hartley is neither
more nor less than 1.

63. We may also conceive Hartley to have ex-
tended his list, and to have consequently found
words of a sort such that, while they are common
to respectively different numbers of things, they
are all, for a certain number, common to the same
things. A series of this kind would be, for one —
pictures, artificial-representations, works of man,
productions generally ; for another — echo, sound,
vibration, motion ; for a third — philosopher, man,
animal. Philosopher and man are, up to a certain
number, common to the same things ; but, assum-
ing that philosophy is confined to man, the
numerical value of man is greater than that of
philosopher ; it is a common name to more things
than philosopher is common to ; there are some

60 THE LOGIC OF NAMES.

men who are not philosophers, though all philoso-
phers are men. In the same manner, and on the
same supposition, the numerical value of animals
is in such a way greater than those of men and of
philosophers, that all philosophers are men, all
men are animals, while some animals are neither
men nor philosophers ; others are men but not
philosophers ; others, again, all the rest in fact,
are both men and philosophers. Hartley, philoso-
pher, man, animal, then, form a series in which
every subsequent includes, numerically and identi-
cally, its antecessor ; the numerical value increasing
at every remove from the initial name, which,
its numerical value being 1, we may call the unit
term. The end of such a series, (and every
possible name can be placed in such a series),
may be nothing but the boundary, in that direc-
tion, of language itself.* After animal might
come living-body, with a still greater numerical
value than animal, but yet inclusive of it. In
the same way, after living-body might come
body. In the language of common logic the
denotation, or extension, of the names in the series

* " Thus proceeding, and at each step ejecting from the com-
prehension those chanicters which are found the proximate im-
pediments to the amplification of the extension of the concept,
we at each step diminish the former quantity precisely as we in-
crease the latter ; till, at last, we arrive at that concept which is
the necessary constituent of every other, — as that concept which
all comprehension and all extension must equally contain, hut in
which comprehension is at its minimum, extension at its maxi-
mum,— I mean the concept of Being or Existence." — Sir W.
Hamilton.

CLASSIFICATION. 61

regularly increases as we proceed from the unit
term.

64. Again, another fact to be noticed about the
series in question is, that philosopher is not
really the name of all Hartley, but only of what
in Hartley is common to him and other philoso-
phers. Man, similarly, is not the name of all
philosopher, but only of what is common to
philosopher with man who is not philosopher, of
the human body with its living, sentient and
reasoning forces. And so on, as we proceed in
the series, we have to drop one part of the mean-
ing of the initial name, Hartley, after another
part, until we have nothing but body left, out of
Hartley, as that for which the last member of the
series is the actual name. To revert to the dis-
tinction of a previous paragraph, the last name of
the series is that of the simplest thing, the first of
the most complex ; the last stands for the minimum
number of grouped sensations, the first for the
maximum number; and exactly in accordance
with their respective places in their series, will the
intervening names differ in the same relation.
The meaning of each term in a series is thus less
than and included in the term that precedes,
greater than and inclusive of the term that
follows. It is with special reference to this re-
lation, the opposite relation to that of extension
or denotation, that logicians call the meaning of a
term its intension, comprehension or connotation.

65. To form such a series as the one we have
been considering is differently called abstraction

62 THE LOGIC OF NAMES.

or determination. It is called abstraction when,
to make it, we proceed from the initial or unit term
by taking away from the meaning of each name
successively in order to get at the next name.
When we proceed in the contrary direction, that
is to say from the term of maximum numerical
value, we return to each preceding name by
cutting off so much of the numerical value of its
successor, and the process is called determination.
66. The things to which any one name is
common, form by that fact a class.* The series
we have been considering may therefore be
called a scheme of classification. In such
schemes, the unit term — that is, the term which
has unity for its numerical value — may be dis-
tinguished as the name of the individual.^ The
other names are class names ; and of the class
names, that which comes next after the individual
is the name of the infima species, so called, because,
according to the scheme, it contains individuals
only and not classes. All the other species de-
noted by the other class names, do contain classes.
The species named next after the infima species,
in the present case, obviously contains two classes
or species, namely, the infima species or philoso-

* The technical terms of logic, such as genus, species, etc., are
called in the literature of logic, names of the second intention.
The name of anything viewed as a mere existence, such as desk,
table, etc., is a name of the first intention.

f So called because its numerical value 1 is not divisible in
logic ; logical division being the resolution into its parts of the
extension of a name.

CLASSIFICATION. 63

pher, and the class which we may nominate non-
philosopher. Relatively to these two contained
species, it itself is styled a genus ; but relatively
to its succeeding term, " animal," it is a species ;
and " animal " to it is a genus. The class
" animal," again, contains at least two species,
man and not-man. To them it is a genus, and in
turn is itself a species to the succeeding term.
This double character will be found to attach to
every term in succession between the name of the
infima species and the last term. As the series
stands, Body, obviously can be a genus alone, and
not a species. It is, therefore, distinguished as
the summum genus ; the other genera being called
subalterna genera.

67. The series which has just been analysed is
a typical series. Nearly every name, simple or
compound, may be made the unit term of an
indefinite number of such series. Every com-
pound name may, in like manner, be made the
summum genus of more or fewer such series,
converging to it as to a common centre. Thus, a
compound name may be the meeting point for an
indefinite number of other series, each starting
from an independent unit term. For example,

Hartley. Boxer.

Philosopher. Mastiff. Oaks. Palms.

I III

Man. Dog. Exogens. Endcgens.

Animals. Plants.

-^,

Living Bodies.

64 THE LOGIC OF NAMES.

68. Here "man" and "dog" are both species,
co-ordinate specie*, of the including genus next
after them, their proximate genus,* as it is called,
namely, animals; "animal" and "plant," again,
are co-ordinate to each other, and their proximate
genus is " living body." That which distinguishes
a species from its co-ordinates is called its dif-
ferentia.

69. Classification, though a very important part
of most works on logic, is not a part of logic. It
is a separate branch of knowledge, a distinct
science. The distinction, however, has not been
recognised, and classification is so conveniently
treated with logic, that the meaning of the name
logic is most frequently wrested into an inclusion
of classification as a part of logic. But classifi-
cation plainly has to do with the matter of thought,
as opposed to the form. Those, consequently, who
limit logic to being a science of the forms of
thought, ought to exclude classification^ Classi-

* The genus next above any given species is called proximate.

f The following description of classification occurs in Arch-
bishop Thomson's " Applied Logic," and is interesting, not only in
itself, but as illustrating the extra logical character of classifica-
tion:— "A class cannot always be defined in words, so as to de-
scribe every species in it. From the lowest of its subdivisions to
the highest, we pass through so many shades of difference, that
we have a difficulty in perceiving and expressing the likeness
between the extremes ; and properties which were prominent at
the bottom of the scale, are in the higher steps forgotten, as
nobler ones come into view. To distinguish the polyp, the lowest
species in the animal series, from a plant, it imist be defined as
' having a digestive cavity' ; whereas, the definition usually given
for higher animals, and for the conception animal in general, con-

CLASSIFICATION. 65

fication, again, implies that a name can have
numerical values other than 1 or 0. It, there-
fore, stands outside the method of this logic,
where no name, as a name, can have any other
numerical value than 1 or 0. Classification, ac-
cordingly, is a separate science, as the science of
names considered both as names and as symbols

veys that they are ' heings endowed with life and sensation.' Still
•we group them together by our perception of likeness ; which,
though not so obviously applicable to the ends of the series
viewed together, and apart from the intermediate links, become
so when we pass regularly along the chain. We might not be
able to prove that the polyp had sensation at all, if there were
not creatures a little higher in the scale of being, resembling
the polyp in other particulars, and exhibiting more plainly the
sense of feeling. "We presume that it exists in the lower, be-
cause we see it in the higher, and though it decreases as we de-
scend, we cannot show that it has ceased. The definition of a
genus is the adequate definition of its lowest species only, since
one which included any higher properties than the lowest ex-
hibits, would of course exclude it. But in classification, the
definition is not so much used as the type, by likeness or un-
likeness to which we arrange the others, and assign them a
higher or lower degree.

" Though the species in any great class rise by the steps of a
regular arrangement, the same series must not be continued
from the highest of one kingdom to the lowest of the next above
it. The highest plant is often considered next below the lowest
animal, whereas it is much more like, though infinitely inferior
to, the highest animal. The animal, vegetable, and mineral king-
doms rather resemble ladders of equal height resting upon three
different steps of a house, than ladders raised one upon the other.
The lowest animal, the lowest plant, and the lowest mineral
answer to each other ; and the complex animal organism, the
tall and beautiful tree, and the regular group of crystals, corre-
spond in some measure at the top of the respective scales." —
ARCHBISHOP Thomson, pp. 264, 5.
F

66 THE LOGIC OF NAMES.

of number. In this view, classification is an im-
portant though not an extensive branch of know-
ledge. And it is necessary, as a part of education
which the logician may naturally take within his
charge, generally to understand the nomenclature
which classification has introduced into litera-
ture.

70. The leading fact in the science of classifi-
cation, is the distinction of names into connotative
and denotative. By the connotative import of a
name we signify its meaning, the attributes it
implies or connotes ; by its denotative import we
signify the individuals, or classes of individuals,
which possess those connoted attributes. If we
consider the schemes of classification into which
the names of our sensations arrange themselves,
we shall perceive that in many the connotation or
meaning of class names is indefinite. A sensation
on each new repetition, resolves itself into new
elements, and human experience, in many cases,
has not yet completed this process of resolution.
Thus it happens that, with our means, it is as yet
impossible to exhaust the meanings or connotations
of such names as man, sheep, etc. At the same
time, the meaning or connotation of quadrangle,
or triangle, is very definite. This distinction
between definite and indefinite meanings is recog-
nised in the science of classification. That part
of the meaning or connotation of a class-name
which constitutes its proximate genus, and serves
to distinguish it as a species from its co-ordinate
species, is called its essence. If, for example, animal

CLASSIFICATION. 67

is a proximate genus to the species man, if the
possession of reason distinguishes the species man
from the other constituents of animal, then " ra-
tional animal " expresses the essence of man. The
essence of a class name, therefore, consists of two
parts : that which expresses its proximate genus,
and is called the genus, in the case just cited,
"animal" ; and that which distinguishes it from
its co-classes, from its co-ordinate species, and is
called its differentia. What of the connotation
or meaning of a class name is not included in its
essence, constitutes its propria. A proprium may
be defined as one of those attributes of a name or
thing which do not enter into its essence. The
name proprium simply means, proper to, and
should, therefore, signify all those simple sensa-
tions which the resolution of a compound sensa-
tion into its elements may be made constantly to
exhibit. As a consequence, those names which
mark the genus and differentia are also propria,
and propria may be divided into

1st. Those which express the genus of the name
into the meaning of which they enter.

2nd. Those which distinguish the species.

3rd. Those which, constituting neither the
genus nor the differentia, still always appear in
the analysis of the meaning.

71. The analysis of a compound sensation will,
however, generally yield elements which, or the
names of which, cannot be considered propria,
inasmuch as they are not found to be present in
all analyses. In a number of successive repe-

68 THE LOGIC OF NAMES.

titions of the sensation "horse," for instance, we
may observe sometimes that the element "black"
appears among the rest, at other times "white,"
sometimes both, and so on. Black, white, etc.,
are, therefore, not proper but possible 'elements
in the exhibitions of the compound sensation
Horse. Classification calls them accidents.*

72. The immediate application of the theory of
classification is to Definition, or the resolution into
its parts of the comprehension of a name, and to
Division, or the like resolution of the extension of
a name.

73. Division is part of Determination, in that it
descends from genus to species ; but its peculiar
office is to divide the proximate genera of a com-
pound series of class names into their constituent
species. This process of division is partly arbi-
trary, and partly fixed. It is arbitrary, because
the same name may appear as proximate genus to
more than one system of constituent species. For
instance, Star may be a star which revolves only
round its own centre, i.e., a star fixed ; or a star

* A distinction is sometimes made between separable accidents
and inseparable; tbose accidents which, experience tells us are
practically universal of the name, although no part, and in no
visible relation to any part, of its meaning, being called in-
separable. . Black is thus an inseparable accident of crow, though
we may conceive a white crow ; and although if we saw a bird
in all respects like a crow, but white, and not black in colour, we
should call it a crow.

In the language of Archbishop Thomson, " accident is a quality
which belongs indeed to a subject, but can be taken away from it
without destroying its nature or essence."

CLASSIFICATION. 69

which revolves round a fixed star ; or a star which
revolves round a star that itself moves round
another star ; or a star which revolves round a
point in space external to it. Or again, Star
may be a star with rings and moons ; with rings
but not moons ; with moons but not rings ; or with
neither rings nor moons.

74. In division, then, the selection of the prin-
ciple of division, the fundamentum relationis, as it
is called, is more or less arbitrary. We have seen
that, in dividing " Star," the principle of division
may be either Position relative to a centre of
revolution, or Concomitancy of certain adjuncts.
And it would have been possible to select other
relations as principles of division, for many others
would be suggested by observation. It is in
applying the arbitrarily selected principle that
division becomes fixed. The principle, once
chosen, must be adhered to throughout the
process. It would not be a just division to divide
stars into stars fixed, stars revolving round other
stars, and stars with satellites ; for, to speak of
nothing else, in such a division more than one
Jundamentum relationis would have been made
use of.

75. Another condition of division is, that the
numerical value of the constituent species must
be together equal to that of the proximate genus.
Practically, this rule is applied by asking whether
there is in the genus any individual to be found
which is not to be found in any one of the con-
stituent species ; and by applying a third rule,

70 THE LOGIC OF NAMES.

which lays down that no one individual must be
found in more than one species of the same
division. A fourth rule, the completing condition
of a just division, is, that every individual in the
species must also belong to the genus. For that
process of division, however, which is regarded
as most purely logical, the first only of these rules
is required as a guide, the others are only useful
as tests. This process is known as Dichotomy,
which means division into pairs of opposites. By
"opposites" we signify the opposition between
the members of a pair, like Policemen, and not-
policemen. The second member of this pair may
be again divided into a similar pair, as People
imprisoned, and people not-imprisoned. It is
evident that such a process might be carried on
to an indefinite extent.

76. As division is a particular operation in de-
termination, so definition is included in abstraction.
The rules for performing it having been already
sufficiently illustrated, it is enough here to simply
state them. The definition of a name should give
the essence of the name ; nothing beyond the
essence, and nothing short of the essence. The
definition of philosopher, for example, should
show that a philosopher must be a man ; it
should contain enough to distinguish philosopher
from all non-philosophers, but it should not con-
tain more than this.

77. It is obvious that a logic, which limits
numerical values to 1 or 0, recognises definitions,
but not divisions.

LOGICAL ADDITION. 71

XXII. LOGICAL ADDITION. — The schemes of
classification treated of in the preceding section,
though they come within the plan of this book,
diverge from its method, which, as said before,
knows no numerical value of a name save 1 or 0,
and, consequently, takes no account of what is
called in grammar, plurality ; in logic, extension
or denotation. It considers a proximate genus as
a physical whole — a group of sensations, and its
division into the constituent species, therefore, as
an act of what, as division, is technically styled
partition.* In other words, it reduces logical
division to definition. Nevertheless, it finds an
expression for the relation of co-ordinate species
to one another ; thus —

A. mastiff is an animal.

A man is an animal.

A mastiff and a man are animals.
79. These three propositions are all indepen-
dently intelligible and demonstrable, while the
third can be made out from the first and second
by the process of logical addition, of which "and,"

* Partition in logic is generally defined to be the division of
the individual — of the unit term, in a scheme of classification.
According to the logical theory which calls the unit term indi-
vidual, this is impossible, and partition, therefore, is reckoned
extra-logical. Logical division, by the same reasoning, and also
because it is confined to the analysis of extension, is only appli-
cable to class names. The division of an arrow into the point,
the shaft, and the feather is intended for an act of partition ; but
the division of missiles into those which are propelled by me-
chanical forces, and those which are propelled by chemical forces,
is intended for an act of logical partition.

72 THE LOGIC OF NAMES.

and the plural sign are symbols. " And," it may
be remarked, which here is a sign of logical
addition, sometimes betokens logical multiplica-
tion ; as in " Ammonia has-a-pungent-smell, and
exercises-a- powerful-corrosive- action - on - animal-
tissues."

80. Logical addition may be defined as the ex-
pression of a partition of a logical whole.

XXIII. LOGICAL SUBTRACTION.— As one group
of sensations may be contained in another group,
the expression of its withdrawal from the con-
taining group would be a name for the sensations
left after its withdrawal, and would be the ex-
pression of an operation which may be conve-
niently styled logical subtraction. The operation
so indicated may be impossible in fact, or may be
only indicated and not performed. Indeed, the
logic of names can in no case have to do with the
performance.

82. As an example of the expression in lan-
guage of logical subtraction, we may instance
non-philosopher. This is, in effect, the expression
of the subtraction of "philosopher" from some
group of sensations which includes philosopher,
and is, therefore, a name for the remainder which
such an operation, if performed, would leave.
The including class is generally taken for the
proximate genus which, in the case of philo-
sopher, is man.

83. All negative names may be subjected to
the same analysis as non-philosopher. Any group

LOGICAL SUBTRACTION. 73

of sensations, in fact, may be imagined to be
subtracted from an including group of sensations,
even though all we know about such an: including
group is, that if it existed and had a name, the
numerical value of that name would certainly
be 1. Thus it has been possible for common lan-
guage to contain such a word as nothing. Tiling
is a name of that universal logical relation which
binds up all our sensations into one logical whole.
It stands for the whole of our knowledge, and its
subtraction from something greater than itself is,
therefore, both a numerical and logical impossi-
bility. Not/ting, consequently, is an uninter-
pretable symbol, and is used in logic much as
-s/ — 1 is used in Trigonometry. The same mode of
interpretation will explain Infinite.

84. It follows, unity being the most general
representative we can have of the name of the
including group of sensations, from which we are
supposed to take the group signified by the given
positive name, that, if any positive name be
given, the corresponding negative name may be
signified by the expression of the logical subtrac-
tion of the positive name from unity. Such an
expression, be it noted, is not in itself a name,
but used for a name — for the name which the
remainder has, may have, or might have. A
negative name is, therefore, a true pronoun.

85. Finally, it should be clearly understood that
the operation of logical subtraction, as indicated
in a negative name, is only indicated but not
performed. To actually take one name from

74 THE LOGIC OF NAMES.

another name is impossible ; to actually take the
numerical value of one name from that of
another, both names being assumed to be names
of realities, will leave nothing as a remainder.

86. It is perhaps, therefore, incorrect to say
that a negative, (or privative) name is the opposite
of its positive. In the first place, we have seen
that it is not absolutely but only provisionally a
name ; it is an expression for a name. In the
second place, looking at the components of the
expression, a negative name, if a name, is a name
which is not a name ; and a privative name in the
same way is a name, if a name, which is deprived
of all meaning. The negative names in language
may be divided into two classes : first, those which
indicate the operation of logical subtraction, such
as those we have been considering ; second, those
that are in reality positive names, as "unmer-
ciful," which practically means " cruel." To this
latter class Archbishop Thomson's instance of a
privative conception, unkindness, would seem to
belong.

XXIY. PREDICATION.— In any proposition, that
term which determines for common language the
numerical value of the other term, is called the
subject * of that proposition. In

Men are animals,

Some men are animals,

* Subject, in the logical sense of the word, is by Hobbes made
equivalent 1o supposition, or hypnkeimeuon. But it more natu-
rally may be derived from its philosophical antithesis to object.

PREDICATIOX. 75

"Men" and "Some men" are the subjects of
their respective propositions. In each proposition
" animals " has a particular numerical value, de-
rived from its place in that proposition, and
different from what it would have if itself were
the subject of a proposition. The term which
thus has its numerical value determined for it is
called the predicate of the proposition.*

Object may mean, first, that which absolutely is, whether known
to exist or not ; or, second, that which is only supposed to exist,
and exists relatively only, that is, exists relatively to the knower.
John Smith has an absolute existence as an individual man ; as a
father he has a relative existence, he exists relatively to John
Smith, his son. Taking any object, that which is in it is sub-
jective with regard to that object ; that which is external to it is
objective. Taking the mind as an object, an act of imagination is
subjective to the mind ; an image of imagination is objective.
Taking a horse as an object, the horse, as existing, is subjective ;
as known to a man, the horse is objective. Thus, everything is
capable both of an objective and subjective relation. And thus,
as everything knows or is known, everything subjectively knows
or is objectively known. Taking any individual man, to him his
conscious mind, or ego, knows, and all other things are known.
That, therefore, which resides in, belongs to, or is dependent on
the knowing mind in general, may be generally called subject, or
subjective; everything not falling under this head, which does
not reside in, belong to, or depend upon the knowing mind, will
be object, or objective. And by an obvious analogy, on the one
hand, men have given the name subject to that term of a propo-
sition which determines numerical value for the other term,
finally ending by construing subject into a synonym of object ;
on the other hand, they have made object a synonym of motive
end, final cause. — From SIR William Hamilton, in his edition of
Reid,

* With respect to such a proposition as " No men are perfect,"
in this connection, the reader is referred to the section headed
" Negative Propositions."

76 THE LOGIC OF NAMES.

88. Generally speaking, a name may be said to
be a predicate of any name into the meaning of
which, it enters, or with which it enters, by mul-
tiplication, into the meaning of another name.
In its relation to any one or more of its pre-
dicates, again, any name may be called a subject.
In a proposition, however, viewed as a logical
equation, there can be admitted no such difference
between the terms as is implied by the distinction
of subject and predicate. But when a proposition
is viewed as a sentence, the distinction becomes
useful to the grammarian.*

89. We may avail ourselves of the distinction
in propositions between subject and predicate, and
of the distinction in terms between distributed
and undistributed, to shortly state the common
logical division of propositions into universal and
particular. Those propositions are universal
which have the subject distributed; those are
particular which have the subject undistributed.
Thus, " Men are animals," is a universal propo-
sition ; " Some men are animals," is a particular
proposition.

* Of the relations between -words which are named by gram-
marians, that designated by the word " predication " seems the
only one which can be called a relation of thought. It is a per-
fectly universal relation. Thus, an article or a preposition is the
pronominal name of a relation as predicated of a noun ; an ad-
jective or adverb is the name of a quality as predicated of a noun
or verb; a conjunction, when used to connect sentences, is the
name of a proposition as predicated of another proposition. And
if the logical copula is taken to be anything more than a sign of
predication, it must be taken as predicated of the subject, and the
following noun or adjective as predicated of the copula.

PREDICABLES. 77

XXY. PREDICABLES. — Any two names which
may form the two terms of the same proposition
are predicable one of the other. An adjective,
consequently, ought to be predicable of its sub-
stantive.

91. It is a consequence of the numerical
equality which is a property of logical equality
that the terms of a proposition are mutually pre-
dicable. But as common language exclusively
determines the numerical value of the predicate
by that of the subject, not by a distinct expres-
sion, the terms of a proposition of common lan-
guage, taken literally, cannot always be said to
be mutually predicable, the subject cannot be in
its turn always literally predicable of the predi-
cate. In technical phrase, a proposition of
common language is not always simply convertible,
in fact, is never convertible, except when the
terms are both distributed or both undistributed.

92. The same defect of common language pre-
vents an adjective and its substantive from being
mutually predicable. In common language, an
adjective, as a numerical symbol, stands for more
things than its substantive stands for. Its exten-
sion is greater. But the numerical value or ex-
tension of the predicate must be equal to, or
greater than, that of the subject.

93. In the literature of logic, a predicable is a
word that can be used as a predicate. There are
five classes or two classes of such words. The
five classes are an inference from the typical
scheme of classification. "With respect to any

78 THE LOGIC OF NAMES.

two names which occur in a scheme of classifica-
tion, and which are taken as the subject and pre-
dicate, respectively, of a proposition, the predi-
cate must express either the genus, the difference,
or the species ; a property or an accident. Ac-
cording to the more reasonable division into two
classes, a predicate may express either the whole
meaning of a name, or part only of the meaning.
In the former case it is a definition, in the latter
an attribute.

XXYI. LOGICAL MULTIPLICATION. — It has been
already provided that the mutual predication of
names that are written together, so as to repre-
sent the compound name of one logical whole,
may be distinguished as logical multiplication,
The verbal exhibitions of logical multiplication
and some consequences which come from it may
be here conveniently illustrated.

95. In "this hat is black," this and hat are
logically multiplied together. In " this is a black
hat "black and hat are logically multiplied together.
Generally, therefore, the names which form any
compound name, and which, consequently, are all
compredicable of the same thing, are to be con-
sidered as logically multiplied together. When
now a compound name is the name of a non-
existent— 'that is, when the names composing it are
the names of sensations that cannot come together,
are non-compredicable names — the numerical
value of that compound must be, as we have seen
in a preceding paragraph, equal to 0. That is to

LOGICAL MULTIPLICATION. 79

say, the result of the multiplication together of
the factors composing that compound name is 0,
and the predication or predications which it im-
plies are false.

96. The following examples, of which the third
is, by logical multiplication, a deduction from the
others, may now be intelligible* : —

i. Man is mortal.
II. Man is immortal,
in. Man man is mortal immortal.

97. The subjects of i. and 11. multiplied to-
gether are unchanged. A name multiplied by
itself equals itself. The square of a name equals
the name.f The subject of in. might be as well
expressed by " man " as by " man man." And
this is reasonable. For names stand for sensa-
tions. But a sensation repeated is the same sensa-
tion still.

98. Again, supposing mortal to be the pure
negative of immortal, the two words multiplied
together must equal nothing. For, together,

* It may be rendered more intelligible by the following ex-
ample : —

i. Honesty is deserving reward,
ii. A negro is a fellow-creature.

in. An honest negro is a fellow-creature deserving reward.
The two logical equations, I. and II., logically multiplied to-
gether, produce III. The example is taken from Archbishop
Thomson, who brings it forward as an instance of " Immediate
Inference by added Determinants."

t In mathematical language, if x stand for the name of any
logical whole, then, x*=x. The same follows, also, from the
numerical value of a name as the sign of a logical whole. Either
i, o, or ?, multiplied into itself, equals itself.

80 THE LOGIC OF NAMES.

they form the compound name of a plain non-
existent ; one of them is a false predication.
Again, taken separately, both being predicated of
the same subject in i. and u. ; one must of
necessity be a true predication, and the other a
false one. Then the numerical value of the one,
will be 1, of the other, 0. But these numbers
multiplied together as numbers equal 0 ; just as
we have seen that the corresponding names when
multiplied together are equal to 0. Hence we
may take as a rule, that a name logically multi-
plied into its negative must give 0 as the numerical
value of the resulting compound name.*

XXVII. NEGATIVE PROPOSITIONS.— The inter-
pretation given above of negative names applies
equally to negative propositions. A proposition
is but a name in analysis or synthesis, and a nega-
tive attached to it which is to be referred not to
the subject nor to the predicate, but to the whole
proposition, merely indicates that the compound
sensation signified by the proposition is to be
considered as subtracted from a larger and in-
cluding sensation. The operation itself, it may
be remarked, is signified by the negative sign
only, which in effect declares that the name or
proposition to which it is attached, is the subject
of the operation. In a negative name, then, the

* Numerically, this rule is deducible from the law xI=x, an
equation which may be written thus, x — 0^=0, whence x(i — x)=0.
It is obvious that the rule, whether stated in words or in symbols,
is only an expression of the principle of contradiction.

NEGATIVE PROPOSITIONS. 81

negative sign plays the part of an adjective, in
a negative proposition, of a predicate. A nega-
tive proposition is not a simple but a compound
proposition. It is a proposition which for a subject
has another proposition.

100. This analysis of negative propositions is
to some extent verified by the forms of language.
In English, the universal negative proposition is
idiomatically expressed thus —

JVo men are good,

where the negative is placed before the proposi-
tion as an adjective before its substantive, and,
accordantly with the genius of the language, can
be referred neither to subject, copula, nor pre-
dicate.*

101. In view of this interpretation f of-a nega-
tive proposition, it becomes useless to dispute
whether the negative proposition should be
attached to the predicate or the copula. If to
enunciate a negative proposition is to affirm a
negative of an affirmative proposition taken as a
subject, the negative proposition is only a com-
plex form of the affirmative proposition.

102. In ordinary logic, the recognition of the

* So, in the common example, " All that glitters is not gold,"
what is meant is, "it is not true that all that glitters is
gold." Those who virtually take " not " as part of the predicate
are obliged to apply a collective in place of a distributive sense
to " all."

t Countenanced, I observe, by the high authority of Mr.
Latham, who " doubts whether it be in accordance with the phe-
nomena of language to make the negative element of propositions
a part of either predicate or copula." — Logic, p. 26.

82 THE LOGIC OF NAMES.

negative form of proposition doubles the number
of types. As there is an affirmative universal, so
there must be a negative universal ; and with the
affirmative particular also must stand the negative
particular.* All negative propositions distribute
the predicate. If we say " no men are innocent,"
we assert of all innocent things that none of
them are men. If we say " some triangles are
not scalene," we assert of all scalene triangles that
they number none of those particular triangles
that we define by the word " some."

103. Affirmative propositions, on the contrary,
do not distribute the predicate. When we say
" All men are animals," or " Some men are
animals," we do not speak of all animals.

104. Finally, as the subject of every universal
proposition is distributed (see the section headed
Predication), and the subject of every particular
proposition undistributed, it follows that the uni-
versal affirmative has the subject alone distributed,
the universal negative both subject and predicate,
the particular negative only the predicate, the
particular affirmative neither subject nor predi-
cate.

XXVIII. THE CALCULUS OF LOGIC. — "We have
seen that the logic of names provides for the ex-
pression of operations on names and of the uni-

* The attribution to a proposition of affirmation or negation
constitutes its quality; of universality or particularity, its
quantity.

THE CALCULUS OF LOGIC. 83

versal logical relation between names, of logical
multiplication, addition, subtraction, and of logical
equality : that we may indicate operations on
names that neither are nor can be performed ;
and that in all operations and equalities the names
employed must each have for its numerical value
either 1 or 0. These facts constitute the basis of
Professor Boole's " Calculus of Logic," which may
be denned to consist of the laws, the axioms, and
the processes of an Algebra, in which the symbols
x, y, .?, etc., admit indifferently of the values 0 and
1, and of these values alone.

APPENDIX.

Mr. Stanley Jevons has published a work entitled "Pure
Logic," which he, himself, characterises as being little more than
an attempt to translate Professor Boole's forms into processes of
self-evident meaning and force. The mention of this fact may
introduce certain observations that have been suggested by
Mr. Jevons' s critical remarks on Professor Boole's system, — re-
marks which the present writer is the more induced to notice,
because they constitute the only detailed criticism of Professor
Boole's system which he has been yet fortunate enough to meet
with.

Mr. Jevons1 s remarks are chiefly grouped under separate " ob-
jections." His first objection is that " Boole's symbols are essen-
tially different from the names or symbols of common discourse, —
his logic is not the logic of common thought." Mr. Jevons, in
enforcing this objection, remarks that Professor Boole's symbols,
in expressing this proposition, " A peer is either a duke, or a
marquis, or an earl, or a viscount, or a baron," would necessarily
imply that a peer can not be at once a duke and marquis, or
marquis and earl. The answer is, that while common discourse
can, but does not, express the compredicability of these various
titles, it is a cardinal point with Professor Boole, equally with Sir
William Hamilton, that everything implied in thought should be
expressed by Logic. He would, therefore, before symbolising the
given sentence, enquire whether the terms " duke," " marquis,"
etc., were meant to be mutually exclusive or not : it is therefore
not strictly correct to say that his symbols, if expressing the
given sentence, would necessarily imply that a duke could not be a
marquis. Mr. Jevons, indeed, seems to think that such a preliminary
enquiry is " consulting the matter," and therefore extra-logical.
But until it is known what meaning he attaches, in this connection,
to the phrase "consulting the matter," it is only necessary to
say, that Professor Boole's logic is scientific ; common discourse is
unscientific, and leaves things to be understood which science
expresses. But as the logic only pretends to interpret the dis-
course, this difference between them seems hardly to constitute
an essential difference. At any rate, Mr. Jevons's objection is

APPENDIX. 85

equally valid against Professor Boole's symbol for A, y=vx,
against Sir William Hamilton's "all x is some y" and against,
perhaps, the majority of logicians, who, if they do not name the
some in A, direct the student to think it.

Mr. Jevons again takes the form #= y + z, and then calls x
" Caesar"; y, " Conqueror of the Gauls" ; z, " First Emperor of
Home"; from these assignments, interpreting the form to mean
" Caesar is the conqueror of the Gauls or the first emperor of
Eome." Next he proceeds to subtract z from both sides, getting
x—z=y, and thus, with some triumph, interprets the result,
"Caesar, providing he is not the first emperor of Rome, is the
conqueror of the Gauls ! "

It is perhaps sufficient to say here that Mr. Jevons treats Pro-
fessor Boole's symbols as he would not treat those of common
algebra. It would be easy, by assigning arbitrary values to the
separate symbols involved in a given equation, to deduce all
manner of absurd consequences from their connection as fixed by
the equation. "Were the sentence " Caesar is the conqueror of the
Gauls or the first emperor of Rome," submitted in good faith to
Professor Boole's system, the first question would be what " or "
meant. Is it disjunctive, as in " saint or sinner," and in "saint
or latter-day saint," or is it expressive of a synonym, as in
" sleep or slumber"? If the former, the symbolical expression
of the sentence " Caesar is the conqueror of the Gauls or the first
emperor of Rome " might be something like the form given by
Mr. Jevons, as x=y (1 — z)+(l — y] z; or x=y -f (1 — y) z; if the
latter, x=yz.

In common discourse the same questions would have to be
somehow answered before the meaning of the proposition could
be considered to be settled. In this case again we find common
discourse to be ambiguous, so far unscientific, and so far
necessarily different from what logic necessarily must be, so long
as logic pretends to be a science.

The second objection, which is that there are no such opera-
tions in pure logic as addition and subtraction, may be taken with
the third, which is that Professor Boole's system is "inconsistent
with the self-evident law of thought" in Mr. Stanley Jevons' s
system, a law which he expresses thus, (A +A=A).

It is perplexing to find Mr. Jevons first stating that there is no
such thing in his logic as addition, and then, in almost the
next page, using the sign of addition in enunciating his own

86 APPENDIX.

" self-evident law of thought." It can only he conjectured that
one of two things is the case, — either that Mr. Jevons uses the sign
of addition where Professor Boole uses that of multiplication, or
that he has omitted to take into account the import of the first
proposition in Professor Boole's chapter of "Abbreviations." It
may be admitted, however, that Professor Boole's phraseology
does not always recognise the distinction between the logics of
extension and intension.

The fourth and last objection taken against Professor Boole's

system, is taken d-propos of the symbols I, 9, ", -. Shortly

stated, it is that the calculus made use of by Professor Boole is
a system which only points out truths that, by another system of
reasoning, we have to learn are certainly true. This objection, if
subjected to certain modifications, has a justification. It need only
be added here now, that whatever agreements or disagreements
may exist between their views on matters of detail, the present
writer cordially concurs with Mr. Jevons where the latter says of
logic as it now is, since the appearance of Professor Boole's
"Laws of Thought," that it "is to logic before that work as
mathematics with equations of any degree are to mathematics
with equations of only one degree."

INDEX.

*#* The Figures refer to paragraphs.

A, 25.

Abstraction, 14, 15, 18, 34, 65,

76.

Accidents, 71.

Affirmative propositions, 103.
Attributes, 42, 93.
Axiom, 48.

Categories, 38.
Class, 66.

Classification, 54, 61.
Cognition (symbolical), 37.
Class-name, 17, 66.
Common names, 57.
Comparison, 14, 15.
Comprehension, 42, 64.
Concept, 11, 14, 15, 17, 48.
Conception (relative), 46.
Concrete, 34.
Connotation, 42, 64.
Connotative, 70.
Consciousness, 20, 21.
Contradiction, 21, 98.
Convertible, 91.
Co-ordinate species, 68.
Copula, 49.
Corollary, 48.

Data, 48.
Declaration, 43.
Definition, 43, 72, 76, 93.
Denomination, 15.
Demonstration, 48.
Denotation, 63, 64.
Denotative, 70.
Description, 43, 44.
Determination, 63.
Dichotomy, 75.
Difference, 21.
Differentia, 68, 70.
Distribution, 59, 102.
Division, 73.

Equal, 16.

Equivocal, 28.
Essence, 70.
Explication, 43.
Exposition, 43..
Extension, 63, 64.

Fallacies, 36.

Generalization, 15.
Genus, 66.
Grammar, 22.

Hypothesis, 48.

Idea, 11, 17.

Idea, innate, 14.

Identical, 16.

Identity, 16.

Identity, the principle of, 21.

Interrogative, 31.

Individual, 66.

Infima species, 66.

Intension, 42, 64.

Intention (first and second), 66.

Judgment, 48.
Knowledge, 47-

Language, 7, 22.

Lemma, 48.

Like, 16.

Logic, 1, 2.

Logical addition, 53, 78, 80.

Logical equality, 55.

Logical multiplication, 25, 52,

79, 94.

Logical subtraction, 81.
Logical whole, 25, 51, 80.

Meaning, 39.
Memory, 14.
Metaphorical, 28.
Metaphysics, 14.

INDEX.

Middle, law of excluded, 21.
Mind, 2.

Names, 24, 37, 40, 51.
Naming, 7, 8.

Negative propositions, 99, 102.
Negative words, 33, 83, 98, 99.
Nervous action, 4.
Nothing, 83.
Notion, 11, 14, 17.
Number, 25.
Numerical value, 57.

Particular, 89.
Partition, 78.
Parts of speech, 25.
Perception, 11, 14, 15, 17.
Postulate, 48.
Predicables, 90.
Predicate, 87.
Predication, 87.
Privative names, 86.
Problem, 48.

Pronominal words, 28, 34, 36.
Proper names, 57.
Propositions, 14, 48, 50.
Proprium, 70.
Proximate genus, 68.
Psychology, 2.

Quaestio, 48.

Quality, 102.
Quantity, 102.

Reflection, 15.
Eelation, 34, 46, 50, 55.
Relative conceptions, 46.
Representations, 14.
Resemblance, 16.

Scholion, 48.
Sensations, 8, 9.
Sensations, compound, 11.
Solution, 48.
Some, 25.
Species, 66.
Subaltema genera, 66.
Subject, 87.
Summum genus, 66.
Symbolical cognition, 37.

Terms, 50.
The, 25.

Thesis, 48.
Thought, 3.

Universal, 89.
Univocal, 28.

Words, 23.

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