The next thing which we observe is thatthe operation of comparing may be repeated on its own results; in other words, that we can think of the various resemblances and differences which we find and compare them with each other, making differences and resemblances of a higher order.The mind thus becomes aware of sets of similar differences, and forms series of terms with the same kind and amount of difference between them, terms which, as they succeed each other, maintain a constant direction of serial increase.This sense of constant direction in a series of operations we saw in Chapter XIII (p. 490) to be a cardinal mental fact. "A differs from B differs from C differs from D, etc.," makes aseriesonly when the differences are in the same direction. In any such difference-series all terms differ in just the same way from their predecessors. The numbers 1, 2, 3, 4, 5,... the notes of the chromatic scale in music, are familiar examples. As soon as the mind grasps such a series as a whole, it perceives thattwo terms taken far apart differ more than two terms taken near together, and that any one term differs more from a remote than from a near successor, and this no matter what the terms may be, or what the sort of difference may be, provided it is always the same sort.
Thisprinciple of mediate comparisonmight be briefly
(though obscurely) expressed by the formula "more than
the more is more than the less"—the wordsmoreandlessstanding simply for degrees of increase along a constant
direction of differences. Such a formula would cover all
possible cases, as, earlier than early is earlier than late,worse than bad is worse than good, east of east is east of
west; etc., etc.,ad libitum.[538]Symbolically, we might write
it asa The principle of mediate comparison is only one form
of a law which holds in many series of homogeneously
related terms, the law thatskipping intermediary terms
leaves relations the same. Thisaxiom of skipped intermediariesor oftransferred relationsoccurs, as we soon shall
see, in logic as the fundamental principle of inference, in
arithmetic as the fundamental property of the number-series,
in geometry as that of the straight line, the plane
and the parallel.It seems to be on the whole the broadest and
deepest law of man's thought. In certain lists of terms the result of comparison may
be to find no-difference, or equality in place of difference.
Here also intermediaries may be skipped, and mediate comparison
be carried on with the general result expressed by
theaxiom of mediate equality, "equals of equals are equal,"
which is the great principle of the mathematical sciences.
This too as a result of the mind's mere acuteness, and in
utter independence of the order in which experiences come
associated together. Symbolically, again:a = b = c = d...,with the same consequence as regards expunging terms
which we saw before. Thus we have a rather intricate system of necessary and
immutableideal truths of comparison, a system applicable to
termsexperiencedin any order of sequence or frequency, or
even to terms never experienced or to be experienced, such
as the mind's imaginary constructions would be. These
truths of comparison result inClassifications. It is, for some
unknown reason, a great æsthetic delight for the mind to
break the order of experience, and class its materials in serial
orders, proceeding from step to step of difference, and to
contemplate untiringly the crossings and inosculations of theseries among themselves. The first steps in most of the
sciences are purely classificatory. Where facts fall easily
into rich and intricate series (as plants and animals and
chemical compounds do), the mere sight of the series fills
the mind with a satisfactionsui generis; and a world whoserealmaterials naturally lend themselves to serial classification
ispro tantoa more rational world, a world with
which the mind will feel more intimate, than with a world
in which they do not. By the pre-evolutionary naturalists,
whose generation has hardly passed away, classifications
were supposed to be ultimate insights into God's mind,
filling us with adoration of his ways. The fact that
Nature lets us make them was a proof of the presence of
his Thought in her bosom. So far as the facts of experience
cannotbe serially classified, therefore, so far experience
fails to be rational inoneof the ways, at least,
which we crave. Closely akin to the function of comparison is that ofjudging, predicating, or subsuming. In fact, these elementary
intellectual functions run into each other so, that it
is often only a question of practical convenience whether
we shall call a given mental operation by the name of
one or of the other. Comparisons result in groups
of like things; and presently (through discrimination and
abstraction) in conceptions of therespectsin which the
likenesses obtain. The groups aregeneraorclasses, the
respects arecharactersorattributes. The attributes again
may be compared, forming genera of higher orders, and
their characters singled out; so that we have a new sort
of series,that of predication, or of kind including kind. Thus
horses are quadrupeds, quadrupeds animals, animals
machines, machines liable to wear out, etc. In such a
series as this the several couplings of terms may have
been made out originally at widely different times and
under different circumstances. But memory may bring
them together afterwards; and whenever it does so, our
faculty of apprehending serial increase makes us consciousof them as a single system of successive terms united by
the same relation.[539] Now whenever we become thus conscious, we may become
aware of an additional relation which is of the highest
intellectual importance, inasmuch as upon it the whole
structure of logic is reared.The principle of mediate predication
or subsumptionis only the axiom of skipped intermediaries
applied to a series of successive predications. It
expresses the fact that any earlier term in the series stands
to any later term in the same relation in which it stands
to any intermediate term; in other words, thatwhatever
has an attribute has all the attributes of that attribute;or more
briefly still, thatwhatever is of a kind is of that kind's kind.A little explanation of this statement will bring out all
that it involves. We learned in the chapter on Reasoning what our
great motive is for abstracting attributes and predicating
them. It is that our varying practical purposes require
us to lay hold of different angles of the reality at different
times. But for these we should be satisfied to 'see it
whole,' and always alike. The purpose, however, makes
one aspect essential; so, to avoid dispersion of the attention,
we treat the reality as if for the time being it were
nothing but that aspect, and we let its supernumerary determinations
go. In short, we substitute the aspect for
the whole real thing.For our purposethe aspectcanbe
substituted for the whole, and the two treated as the same;
and the wordis(which couples the whole with its aspect
or attribute in the categoric judgment) expresses (among
other things) the identifying operation performed. The
predication-seriesaisb, bisc, cisd,... closely resembles
for certain practical purposes the equation-seriesa = b,
b = c, c = d, etc. But what is our purpose in predicating? Ultimately,
it may be anything we please; but proximately and immediately,
it is always the gratification of a certain curiosityas to whether the object in hand is or is notof a kindconnected with that ultimate purpose. Usually the connection
is not obvious, and we only find that the object S
is of a kind connected with P, after first finding that it is
of a kind M, which itself is connected with P. Thus, to
fix our ideas by an example, we have a curiosity (our ultimate
purpose being conquest over nature) as to how Sirius
may move. It is not obvious whether Sirius is a kind of
thing which moves in the line of sight or not. When,
however, we find it to be a kind of thing in whose spectrum
the hydrogen-line is shifted, and when we reflect thatthatkind of thing is a kind of thing which moves in the line
of sight; we conclude that Sirius does so move. Whatever
Sirius's attribute is, Sirius is; its adjective's adjective can
supersede its own adjective in our thinking, and this with
no loss to our knowledge,so long as we stick to the definite
purpose in view. Now please note that this elimination of intermediary
kinds and transfer ofis's along the line, results from our
insight into the very meaning of the wordis, and into the
constitution of any series of terms connected by that relation.
It has naught to do with what any particular thing is
or is not; but,whateverany given thing may be, we see
that it also is whateverthatis, indefinitely. To grasp in
one view a succession ofis's is to apprehend this relation
between the terms which they connect; just as to grasp a
list of successive equals is to apprehend theirmutualequality
throughout. The principle of mediate subsumption
thus expresses relations of ideal objects as such. It can be
discovered by a mind left at leisure with any set of meanings
(however originally obtained), of which some are predicable
of others. The moment we string them in a serial
line, that moment we see that we can drop intermediaries,
treat remote terms just like near ones, and put a genus in
the place of a species. This shows thatthe principle of
mediate subsumption has nothing to do with the particular
order of our experiences, or with the outer coexistences and
sequences of terms.Were it a mere outgrowth of habit
and association, we should be forced to regard it as having
no universal validity; for every hour of the day we meetthings which we consider to be of this kind or of that, but
later learn that they have none of the kind's properties, that
theydo notbelong to the kind's kind. Instead, however, of
correcting the principle by these cases, we correct the cases
by the principle. We say that if the thing we named an M
has not M's properties, then we were either mistaken in calling
it an M, or mistaken about M's properties; or else that it
is no longer M, but has changed. But we never say that it
is an M without M's properties; for by conceiving a thing as
of the kind M I mean that itshallhave M's properties, be of
M's kind, even though I should never be able to find in the
real world anything which is an M. The principle emanates
from my perception of what a lot of successive is'smean.
This perception can no more be confirmed by one set, or
weakened by another set, of outer facts, than the perception
that black is not white can be confirmed by the fact that
snow never blackens, or weakened by the fact that photographer's
paper blackens as soon as you lay it in the sun. The abstract scheme of successive predications, extended
indefinitely, with all the possibilities of substitution which
it involves, is thus an immutable system of truth which
flows from the very structure and form of our thinking.Ifany real terms ever do fit into such a scheme, they
will obey its laws;whetherthey do is a question as to
nature's facts, the answer to which can only be empirically
ascertained.Formal logicis the name of the Science
which traces in skeleton form all the remote relations
of terms connected by successiveis's with each other,
and enumerates their possibilities of mutual substitution.
To our principle of mediate subsumption she has given
various formulations, of which the best is perhaps this
broad expression, thatthe same can be substituted for the same
in any mental operation.[540] The ordinary logical series contains but threeterms—"Socrates, man, mortal." But we also have 'Sorites'—Socrates,
man, animal, machine, run down, mortal, etc.—and
it violates psychology to represent these as syllogisms
with terms suppressed. The ground of there being any
logic at all is our power to grasp any series as a whole,
and the more terms it holds the better. This synthetic
consciousness of an uniform direction of advance through
a multiplicity of terms is, apparently, what the brutes and
lower men cannot accomplish, and what gives to us our
extraordinary power of ratiocinative thought. The mind
which can grasp a string ofis's as a whole—the objects
linked by them may be ideal or real, physical, mental, or
symbolic, indifferently—can also apply to it the principle
of skipped intermediaries.The logic-list is thus in its origin
and essential nature just like those graded classificatory lists
which we erewhile described.The 'rational proposition' which
lies at the basis of all reasoning, thedictum de omni et nulloin all the various forms in which it may be expressed,
the fundamental law of thought, is thusonly the result of
the function of comparisonin a mind which has come by
some lucky variation to apprehend a series of more than
two terms at once.[541]So far, then,both Systematic Classification
and Logic are seen to be incidental results of the mere
capacity for discerning difference and likeness,which capacity
is a thing with which theorder of experience, properly so
styled, has absolutely nothing to do. But how comes it (it may next be asked) when systematic
classifications have so little ultimate theoretic importance—for
the conceiving of things according to their
mere degrees of resemblance always yields to other modes
of conceiving when these can be obtained—that the logical
relations among things should form such a mighty engine
for dealing with the facts of life? Chapter XXII already gave the reason (seep. 335,
above). This worldmightbe a world in which all things
differed, and in which what properties there were wereultimate and had no farther predicates. In such a world
there would be as many kinds as there were separate things.
We could never subsume a new thing under an old kind;
or if we could, no consequences would follow. Or, again,
this might be a world in which innumerable things were
of a kind, but in which no concrete thing remained of the
same kind long, but all objects were in a flux. Here again,
though we could subsume and infer, our logic would be of
no practical use to us, for the subjects of our propositions
would have changed whilst we were talking. In such worlds,
logical relations would obtain, and be known (doubtless) as
they are now, but they would form a merely theoretic
scheme and be of no use for the conduct of life. But our
world is no such world. It is a very peculiar world, and
plays right into logic's hands.Someof the things, at least,
which it contains are of the same kind as other things;someof them remain always of the kind of which they once were;
and some of the properties of them cohere indissolubly and
are always found together.Whichthings these latter things
are we learn by experience in the strict sense of the word,
and the results of the experience are embodied in 'empirical
propositions.' Whenever such a thing is met with by us
now, our sagacity notes it to be of a certain kind; our
learning immediately recalls that kind's kind, and thenthatkind's kind, and so on; so that a moment's thinking may
make us aware that the thing is of a kind so remote that
we could never have directly perceived the connection.
The flight to this last kindover the heads of the intermediariesis the essential feature of the intellectual operation here.
Evidently it is a pure outcome of our sense for apprehending
serial increase; and, unlike the several propositions
themselves which make up the series (and which may all
be empirical), it has nothing to do with the time- and space-order
in which the things have been experienced. So much for thea priorinecessities called systematic
classification and logical inference. The other couplings
of data which pass fora priorinecessities of thought are
themathematicaljudgments, and certain metaphysical propositions.These latter we shall consider farther on. As
regards the mathematical judgments, they are all 'rational
propositions' in the sense defined onp. 644, for they express
results of comparison and nothing more. The mathematical
sciences deal with similarities and equalities exclusively,
and not with coexistences and sequences. Hence they have,
in the first instance, no connection with the order of experience.
The comparisons of mathematics are between
numbers and extensive magnitudes, giving rise to arithmetic
and geometry respectively. Numberseems to signify primarily the strokes of our
attention in discriminating things. These strokes remain
in the memory in groups, large or small, and the groups can
be compared. The discrimination is, as we know, psychologically
facilitated by the mobility of the thing as a total
(p. 173). But within each thing we discriminate parts; so
that the number of things which any one given phenomenon
may be depends in the last instance on our way of
taking it. A globe is one, if undivided; two, if composed
of hemispheres. A sand-heap is one thing, or twenty
thousand things, as we may choose to count it. We amuse
ourselves by the counting ofmerestrokes, to form rhythms,
and these we compare and name. Little by little in our
minds the number-series is formed. This, like all lists of
terms in which there is a direction of serial increase, carries
with it the sense of those mediate relations between its
terms which we expressed by the axiom "the more than the
more is more than the less." That axiom seems, in fact,
only a way of stating that the terms do form an increasing
series. But, in addition to this, we are aware of certain
other relations among our strokes of counting. We may
interrupt them where we like, and go on again. All the
while we feel that the interruption does not alter the strokes
themselves. We may count 12 straight through; or count
7 and pause, and then count 5, but still the strokes will be
the same. We thus distinguish between our acts of counting
and those of interrupting or grouping, as between an
unchanged matter and an operation of mere shuffling performed
on it. The matter is the original units or strokes;which all modes of grouping or combining simply give
us back unchanged. In short,combinations of numbers
are combinations of their units, which is the fundamental
axiom of arithmetic,[542]leading to such consequences as that
7 + 5 = 8 + 4 because both = 12. The general axiom of
mediate equality, that equals of equals are equal, comes in
here.[543]The principle of constancy in our meanings, when
applied to strokes of counting, also gives rise to the axiom
that the same number, operated on (interrupted, grouped)
in the same way will always give the same result or be the
same. How shouldn't it? Nothing is supposed changed. Arithmetic and its fundamental principles are thus independent
of our experiences or of the order of the world.The matter of arithmetic ismental matter; its principles flow
from the fact that the matter forms a series, which can be cut
into by us wherever we like without the matter changing.
The empiricist school has strangely tried to interpret the
truths of number as results of coexistences among outward
things. John Mill calls number a physical property
of things. 'One,' according to Mill, means one sort of
passive sensation which we receive, 'two' another, 'three'
a third. The same things, however, can give us different
number-sensations. Three things arranged thus, ---, for
example, impress us differently from three things arranged
thus, -_-. But experience tells us that every real object-group
which can be arranged in one of these ways can always be
arranged in the other also, and that 2 + 1 and 3 are thus
modes of numbering things which 'coexist' invariably with
each other. The indefeasibility of our belief in their 'coexistence'
(which is Mill's word for their equivalence) is
due solely to the enormous amount of experience we have
of it. For all things, whatever other sensations they may
give us, give us at any rate number-sensations. Those
number-sensations which the same thing may be successively
made to arouse are the numbers which we deemequal to each other; those which the same thing refuses to
arouse are those which we deem unequal. This is as clear a restatement as I can make of Mill's
doctrine.[544]And its failure is written upon its front. Woe to
arithmetic, were such the only grounds for its validity!
The same real things are countable in numberless ways,
and pass from one numerical form, not only to its equivalent
(as Mill implies), but to its other, as the sport of
physical accidents or of our mode of attending may decide.
How could our notion that one and one are eternally
and necessarily two ever maintain itself in a world where
every time we add one drop of water to another we get not
two but one again? in a world where every time we add a
drop to a crumb of quicklime we get a dozen or more?—had
it no better warrant than such experiences? At most
we could then say that one and one areusuallytwo.
Our arithmetical propositions would never have the confident
tone which they now possess. That confident
tone is due to the fact that they deal with abstract and ideal
numbers exclusively.What we meanby one plus oneistwo; wemaketwo out of it; and it would mean two
still even in a world wherephysically(according to a
conceit of Mill's) a third thing was engendered every time
one thing came together with another. We are masters
of our meanings, and discriminate between the things
we mean and our ways of taking them, between our strokes
of numeration themselves, and our bundlings and separatings
thereof. Mill ought not only to have said, "All things are numbered."
He ought, in order to prove his point, to have
shown that they areunequivocallynumbered, which they notoriously
are not. Only the abstract numbers themselves are
unequivocal, only those which we create mentally and hold
fast to as ideal objects always the same. A concrete natural
thing can always be numbered in a great variety of ways.
"We need only conceive a thing divided into four equal
parts (and all things may be conceived as so divided)," asMill is himself compelled to say, to find the number four
in it, and so on. The relation of numbers to experience is just like that
of 'kinds' in logic. So long as an experience will keep its
kind we can handle it by logic. So long as it will keep its
number we can deal with it by arithmetic.Sensibly, however,
things are constantly changing their numbers, just as
they are changing their kinds. They are forever breaking
apart and fusing. Compounds and their elements are never
numerically identical, for the elements are sensibly many
and the compounds sensibly one. Unless our arithmetic
is to remain without application to life, we must somehowmakemore numerical continuity than we spontaneously find.
Accordingly Lavoisier discovers his weight-units which remain
the same in compounds and elements, though volume-units
and quality-units all have changed. A great discovery!
And modern science outdoes it by denying that compounds
exist at all. There is no such thing as 'water' for
'science;' that is only a handy name for H2and O when
they have got into the position H-O-H, and then affect
our senses in a novel way. The modern theories of atoms,
of heat, and of gases are, in fact, only intensely artificial
devices for gaining that constancy in the numbers of
things which sensible experience will not show. "Sensible
things are not the things for me," says Science, "because
in their changes they will not keep their numbers the same.
Sensible qualities are not the qualities for me, because they
can with difficulty be numbered at all. These hypothetic
atoms, however, are the things, these hypothetic masses
and velocities are the qualities for me; they will stay numbered
all the time." By such elaborate inventions, and at such a cost to the
imagination, do men succeed in making for themselves a
world in which real things shall be coercedper fas aut
nefasunder arithmetical law. The other branch of mathematics isgeometry. Its objects
are also ideal creations. Whether nature contain
circles or not, I can know what I mean by a circle and
can stick to my meaning; and when I mean two circles Imean two things of an identical kind. The axiom of constant
results (see above,p. 645) holds in geometry. The
same forms, treated in the same way (added, subtracted,
or compared), give the same results—how shouldn't they?
The axioms of mediate comparison (p. 645), of logic (p. 648),
and of number (p. 654) all apply to the forms which we
imagine in space, inasmuch as these resemble or differ
from each other, form kinds, and are numerable things.
But in addition to these general principles, which are true
of space-forms only as they are of other mental conceptions,
there are certain axioms relative to space-forms exclusively,
which we must briefly consider. Three of them give marks of identity among straight
lines, planes, and parallels. Straight lines which have two
points, planes which have three points, parallels to a given
line which have one point, in common, coalesce throughout.
Some say that the certainty of our belief in these axioms
is due to repeated experiences of their truth; others that
it is due to an intuitive acquaintance with the properties
of space. It is neither. We experience lines enough which
pass through two points only to separate again, only we
won't call them straight. Similarly of planes and parallels.
We have a definite idea of what we mean by each of these
words; and when something different is offered us, we see
the difference. Straight lines, planes, and parallels, as they
figure in geometry, are mere inventions of our faculty for
apprehending serial increase. The farther continuations
of these forms, we say,shallbear the same relation to their
last visible parts which these did to still earlier parts. It
thus follows (from that axiom of skipped intermediaries
which obtains in all regular series) that parts of these
figures separated by other parts must agree in direction,
just as contiguous parts do. This uniformity of direction
throughout is, in fact, all that makes us care for these
forms, gives them their beauty, and stamps them into fixed
conceptions in our mind. But obviously if two lines, or
two planes, with a common segment, were to part company
beyond the segment, it could only be because the direction
of at least one of them had changed. Parting company in
lines and planesmeanschanging direction, means assuminga new relation to the parts that pre-exist; and assuming a
new relation means ceasing to be straight or plane. If we
mean by a parallel a line that will never meet a second
line; and if we have one such line drawn through a point,
any new line drawn through that point which does not
coalesce with the first must be inclined to it, and if inclined
to it must approach the second, i.e., cease to be parallel
with it. No properties of outlying space need come in
here: only a definite conception of uniform direction, and
constancy in sticking to one's point. The other two axioms peculiar to geometry are that
figures can be moved in space without change, and that no
variation in the way of subdividing a given amount of space
alters its total quantity.[545]This last axiom is similar to
what we found to obtain in numbers. 'The whole is equal
to its parts' is an abridged way of expressing it. A man is
not the same biological whole if we cut him in two at the
neck as if we divide him at the ankles; but geometrically
he is the same whole, no matter in which place we cut him.
The axiom about figures being movable in space is rather
a postulate than an axiom.So far as they areso movable,
then certain fixed equalities and differences obtain between
forms,no matter where placed. But if translation through
space warped or magnified forms, then the relations of
equality, etc., would always have to be expressed with a
position-qualification added. A geometry as absolutely
certain as ours could be invented on the supposition of
such a space, if the laws of its warping and deformation
were fixed. It would, however, be much more complicated
than our geometry, which makes the simplest possible supposition;
and finds, luckily enough, that it is a supposition
with which the space of our experience seems to agree. By means of these principles, all playing into each
other's hands, the mutual equivalences of an immense number
of forms can be traced, even of such as at first sight
bear hardly any resemblance to each other. We move andturn them mentally, and find that parts of them will superpose.
We add imaginary lines which subdivide or enlarge
them, and find that the new figures resemble each other in
ways which show us that the old ones are equivalent too.
We thus end by expressing all sorts of forms in terms of
other forms, enlarging our knowledge of the kinds of things
which certain other kinds of things are, or to which they
are equivalent. The result is a new system of mental objects which can
be treated as identical for certain purposes, a new series ofis's almost indefinitely prolonged, just like the series of
equivalencies among numbers, part of which the multiplication-table
expresses. And all this is in the first instance
regardless of the coexistences and sequences of nature,
and regardless of whether the figures we speak of have ever
been outwardly experienced or not. Classification, logic, and mathematics all result, then,
from the mere play of the mind comparing its conceptions,
no matter whence the latter may have come. The essential
condition for the formation of all these sciences is that we
should have grown capable of apprehending series as such,
and of distinguishing them as homogeneous or heterogeneous,
and as possessing definite directions of what I have
called 'increase.' This consciousness of series is a human
perfection which has been gradually evolved, and which
varies greatly from man to man. There is no accounting
for it as a result of habitual associations among outward
impressions, so we must simply ascribe it to the factors,
whatever they be, of inward cerebral growth. Once this
consciousness attained to, however,mediatethought becomes
possible; with our very awareness of a series may
go an awareness that dropping terms out of it will leave
identical relations between the terms that remain; and
thus arises a perception of relations between things so
naturally separate that we should otherwise never have
compared them together at all. The axiom of skipped intermediaries applies, however,
only to certain particular series, and among them to thosewhich we have considered, in which the recurring relation
is either of difference, of likeness, of kind, of numerical addition,
or of prolongation in the same linear or plane direction.
It is therefore not a purely formal law of thinking,
but flows from the nature of the matters thought about. It
will not do to say universally that in all series of homogeneously
related terms the remote members are related to
each other as the near ones are; for that will often be
untrue. The series A is not B is not C is not D.... does
not permit the relation to be traced between remote terms.
From two negations no inference can be drawn. Nor, to
become more concrete, does the lover of a woman generally
love her beloved, or the contradictor of a contradictor contradict
whomever he contradicts. The slayer of a slayer
does not slay the latter's victim; the acquaintances or enemies
of a man need not be each other's acquaintances or
enemies; nor are two things which are on top of a third
thing necessarily on top of each other. All skipping of intermediaries and transfer of relations
occurs within homogeneous series. But not all homogeneous
series allow of intermediaries being skipped and relations
transferred. It depends on which series they are,
on what relations they contain.[546]Let it not be said that it
is a mere matter of verbal association, due to the fact that
language sometimes permits us to transfer thenameof a
relation over skipped intermediaries, and sometimes does
not; as where we call men 'progenitors' of their remote as
well as of their immediate posterity, but refuse to call them
'fathers' thereof. There are relations which areintrinsicallytransferable, whilst others are not. The relation ofcondition, e.g., is intrinsically transferable. What conditions
a condition conditions what it conditions—"cause of cause
is cause of effect." The relations of negation andfrustration,on the other hand, are not transferable: what frustrates a
frustration does not frustrate what it frustrates. No
changes of terminology would annul the intimate difference
between these two cases. Nothing but the clear sight of the ideas themselves
shows whether the axiom of skipped intermediaries applies
to them or not. Their connections, immediate and remote,
flow from their inward natures. We try to consider them
in certain ways, to bring them into certain relations, and
we find that sometimes we can and sometimes we cannotThe question whether there are or are not inward and essential
connections between conceived objects as such, really is the same
thing as the question whether we can get any new perception
from mentally coupling them together, or pass from one to
another by a mental operation which gives a result.In the
case of some ideas and operations we get a result; but no
result in the case of others. Where a result comes, it is
due exclusively to thenatureof the ideas and of the operation.
Take blueness and yellowness, for example. We can
operate on them in some ways, but not in other ways. We
can compare them; but we cannot add one to or subtract
it from the other. We can refer them to a common kind,
color; but we cannot make one a kind of the other, or infer
one from the other. This has nothing to do with experience.
For wecanadd bluepigmentto yellowpigment, and subtract
it again, and get a result both times. Only we know
perfectly that this is no addition or subtraction of the blue
and yellow qualities or natures themselves.[547] There is thus no denying the fact thatthe mind is filled
with necessary and eternal relations which it finds between certain
of its ideal conceptions, and which form a determinate
system, independent of the order of frequency in which experience
may have associated the conception's originals in time and space. Shall we continue to call these sciences 'intuitive,' innate,'
or 'a priori' bodies of truth, or not?[548]PersonallyI should like to do so. But I hesitate to use the terms,
on account of the odium which controversial history has
made the whole of their connotation for many worthy persons.
The most politic way not to alienate these readers
is to flourish the name of the immortal Locke. For in truth
I have done nothing more in the previous pages than to
make a little more explicit the teachings of Locke's fourth
book: "The immutability of the same relations between the same immutable
things is now the idea that shows him that if the three angles of
a triangle were once equal to two right angles, they will always be
equal to two right ones. And hence he comes to be certain that what
was once true in the case is always true; what ideas once agreed will
always agree.... Upon this ground it is that particular demonstrations
in mathematics afford general knowledge. If, then, the perception
that the same ideas will eternally have the same habitudes and relations
be not a sufficient ground of knowledge, there could be no knowledge
of general propositions in mathematics.... All general knowledge
lies only in our own thoughts, and consists barely in the contemplation of
our abstract ideas. Wherever we perceive any agreement or disagreement
amongst them, there we have general knowledge; and by putting
the names of those ideas together accordingly in propositions, can with
certainty pronounce general truths.... What is once known of such
ideas will be perpetually and forever true. So that, as to all general
knowledge, we must search and find it only in our own minds and it is
only the examining of our own ideas that furnisheth us with that.
Truths belonging to essences of things (that is, to abstract ideas) areeternal, and are to be found out only by the contemplation of those
essences.... Knowledge is the consequence of the ideas (be they what
they will) that are in our minds, producing there certain general propositions....
Such propositions are therefore called 'eternal truths,'...
because, being once made about abstract ideas so as to be true, they
will, whenever they can be supposed to be made again, at any time past
or to come, by a mind having those ideas, always actually be true. For
names being supposed to stand perpetually for the same ideas, and the
same ideas having immutably the same habitudes one to another, propositions
concerning any abstract ideas that are once true must needs
be eternal verities." "The immutability of the same relations between the same immutable
things is now the idea that shows him that if the three angles of
a triangle were once equal to two right angles, they will always be
equal to two right ones. And hence he comes to be certain that what
was once true in the case is always true; what ideas once agreed will
always agree.... Upon this ground it is that particular demonstrations
in mathematics afford general knowledge. If, then, the perception
that the same ideas will eternally have the same habitudes and relations
be not a sufficient ground of knowledge, there could be no knowledge
of general propositions in mathematics.... All general knowledge
lies only in our own thoughts, and consists barely in the contemplation of
our abstract ideas. Wherever we perceive any agreement or disagreement
amongst them, there we have general knowledge; and by putting
the names of those ideas together accordingly in propositions, can with
certainty pronounce general truths.... What is once known of such
ideas will be perpetually and forever true. So that, as to all general
knowledge, we must search and find it only in our own minds and it is
only the examining of our own ideas that furnisheth us with that.
Truths belonging to essences of things (that is, to abstract ideas) areeternal, and are to be found out only by the contemplation of those
essences.... Knowledge is the consequence of the ideas (be they what
they will) that are in our minds, producing there certain general propositions....
Such propositions are therefore called 'eternal truths,'...
because, being once made about abstract ideas so as to be true, they
will, whenever they can be supposed to be made again, at any time past
or to come, by a mind having those ideas, always actually be true. For
names being supposed to stand perpetually for the same ideas, and the
same ideas having immutably the same habitudes one to another, propositions
concerning any abstract ideas that are once true must needs
be eternal verities." But what are these eternal verities, these 'agreements,'
which the mind discovers by barely considering its own
fixed meanings, except what I have said?—relations of likeness
and difference, immediate or mediate, between the
terms of certain series. Classification is serial comparison,
logic mediate subsumption, arithmetic mediate equality of
different bundles of attention-strokes, geometry mediate
equality of different ways of carving space. None of these
eternal verities has anything to say about facts, about what
is or is not in the world. Logic does not say whether Socrates,
men, mortals or immortalsexist; arithmetic does
not tell us where her 7's, 5's, and 12's are to befound; geometry
affirms not that circles and rectangles arereal. All
that these sciences make us sure of is, thatifthese things
are anywhere to be found, the eternal verities will obtain
of them. Locke accordingly never tires of telling us that the "universal propositions of whose truth or falsehood we can have certain
knowledge, concern not existence.... These universal and self-evident
principles, being only our constant, clear, and distinct knowledge
of our own ideas more general or comprehensive, can assure us of
nothing that passes without the mind; their certainty is founded only
upon the knowledge of each idea by itself, and of its distinction from
others; about which we cannot be mistaken whilst they are in our
minds.... The mathematician considers the truth and properties
belonging to a rectangle or circle only as they are in idea in his own
mind. For it is possible he never found either of them existing mathematically,
i.e., precisely true, in his life. But yet the knowledge he
has of any truths or properties belonging to a circle, or any other mathematical
figure, are nevertheless true and certain even of real things
existing; because real things are no farther concerned nor intended to
be meant by any such propositions, than as things really agree to those
archetypes in his mind. Is it true of the idea of a triangle, that itsthree angles are equal to two right ones? It is true also of a triangle
wherever it really exists. Whatever other figure exists that is not exactly
answerable to that idea in his mind is not at all concerned in that
proposition. And therefore he is certain all his knowledge concerning
such ideas is real knowledge: because, intending things no farther than
they agree with those his ideas, he is sure what he knows concerning
those figures when they have barely an ideal existence in his mind will
hold true of them also when they have a real existence in matter." But
"that any or what bodies do exist, that we are left to our senses to
discover to us as far as they can."[549] "universal propositions of whose truth or falsehood we can have certain
knowledge, concern not existence.... These universal and self-evident
principles, being only our constant, clear, and distinct knowledge
of our own ideas more general or comprehensive, can assure us of
nothing that passes without the mind; their certainty is founded only
upon the knowledge of each idea by itself, and of its distinction from
others; about which we cannot be mistaken whilst they are in our
minds.... The mathematician considers the truth and properties
belonging to a rectangle or circle only as they are in idea in his own
mind. For it is possible he never found either of them existing mathematically,
i.e., precisely true, in his life. But yet the knowledge he
has of any truths or properties belonging to a circle, or any other mathematical
figure, are nevertheless true and certain even of real things
existing; because real things are no farther concerned nor intended to
be meant by any such propositions, than as things really agree to those
archetypes in his mind. Is it true of the idea of a triangle, that itsthree angles are equal to two right ones? It is true also of a triangle
wherever it really exists. Whatever other figure exists that is not exactly
answerable to that idea in his mind is not at all concerned in that
proposition. And therefore he is certain all his knowledge concerning
such ideas is real knowledge: because, intending things no farther than
they agree with those his ideas, he is sure what he knows concerning
those figures when they have barely an ideal existence in his mind will
hold true of them also when they have a real existence in matter." But
"that any or what bodies do exist, that we are left to our senses to
discover to us as far as they can."[549] Locke accordingly distinguishes between 'mental truth'
and 'real truth.'[550]The former is intuitively certain; the
latter dependent on experience. Onlyhypotheticallycan we
affirm intuitive truths of real things—bysupposing, namely,
that real things exist which correspond exactly with the
ideal subjects of the intuitive propositions. If our senses corroborate the supposition all goes well.
But note the strange descent in Locke's hands of the dignity
ofa prioripropositions. By the ancients they were
considered, without farther question, to reveal the constitution
of Reality. Archetypal things existed, it was assumed,
in the relations in which we had to think them. The mind's
necessities were a warrant for those of Being; and it was not
till Descartes' time that scepticism had so advanced (in 'dogmatic'
circles) that the warrant must itself be warranted,
and the veracity of the Deity invoked as a reason for holding
fast to our natural beliefs. But the intuitive propositions of Locke leave us as regards
outer reality none the better for their possession.
We still have to "go to our senses" to find what the
reality is. The vindication of the intuitionist position
is thus a barren victory. The eternal verities which
the very structure of our mind lays hold of do not necessarily
themselves lay hold on extra-mental being, nor have
they, as Kant pretended later,[551]a legislating character evenfor all possible experience. They are primarily interesting
only as subjective facts. They stand waiting in the mind,
forming a beautiful ideal network; and the most we can
say is that wehopeto discover outer realities over which the
network may be flung so that ideal and real may coincide. And this brings us back to 'science' from which we diverted
our attention so long ago (seep. 640). Science thinks
that she has discovered the outer realities in question.
Atoms and ether, with no properties but masses and velocities
expressible by numbers, and paths expressible by analytic
formulas, these at last are things over which the
mathematico-logical network may be flung, and by supposing
which instead of sensible phenomena science becomes
yearly more able to manufacture for herself a world about
which rational propositions may be framed. Sensible phenomena
are pure delusions for the mechanical philosophy.
The 'things' and qualities we instinctively believe in do
not exist. The only realities are swarming solids in everlasting
motion, undulatory or continued, whose expressionless
and meaningless changes of position form the history
of the world, and are deducible from initial collocations
and habits of movement hypothetically assumed. Thousands
of years ago men started to cast the chaos of nature's
sequences and juxtapositions into a form that might seem
intelligible. Many were their ideal prototypes of rational
order: teleological and æsthetic ties between things, causal
and substantial bonds, as well as logical and mathematical
relations. The most promising of these ideal systems at first
were of course the richer ones, the sentimental ones. The
baldest and least promising were the mathematical ones; but
the history of the latter's application is a history of steadily
advancing successes, whilst that of the sentimentally richersystems is one of relative sterility and failure.[552]Take those
aspects of phenomena which interest you as a human being
most, and class the phenomena as perfect and imperfect, as
ends and means to ends, as high and low, beautiful and ugly,
positive and negative, harmonious and discordant, fit and
unfit, natural and unnatural, etc., and barren are all your
results. In the ideal world the kind 'precious' has characteristic
properties. What is precious should be preserved;
unworthy things should be sacrificed for its sake;
exceptions made on its account; its preciousness is a reason
for other things' actions, and the like. But none of
these things need happen to your 'precious' object in the
real world. Call the things of nature as much as you like
by sentimental, moral, and æsthetic names, no natural
consequences follow from the naming. They may be of
the kinds you allege, but they are not of 'the kind's kind':
and the last great system-maker of this sort, Hegel, was
obliged explicitly to repudiate logic in order to make any
inferences at all from the names he called things by. But when you give things mathematical and mechanical
names and call them just so many solids in just such positions,
describing just such paths with just such velocities,
all is changed. Your sagacity finds its reward in the verification
by nature of all the deductions which you may next
proceed to make. Your 'things' realize all theconsequencesof the names by which you classed them. The modern
mechanico-physical philosophy of which we are all so
proud, because it includes the nebular cosmogony, the
conservation of energy, the kinetic theory of heat andgases, etc., etc., begins by saying that theonlyfacts are
collocations and motions of primordial solids, and the only
laws the changes of motion which changes in collocation
bring. The ideal which this philosophy strives after is a
mathematical world-formula, by which, if all the collocations
and motions at a given moment were known, it would
be possible to reckon those of any wished-for future moment,
by simply considering the necessary geometrical,
arithmetical, and logical implications. Once we have the
world in this bare shape, we can fling our net ofa priorirelations over all its terms, and pass from one of its phases
to another by inward thought-necessity. Of course it is a
world with a very minimum of rationalstuff. The sentimental
facts and relations are butchered at a blow. But
the rationality yielded is so superbly complete informthat
to many minds this atones for the loss, and reconciles the
thinker to the notion of a purposeless universe, in which
all the things and qualities men love,dulcissima mundi
nomina, are but illusions of our fancy attached to accidental
clouds of dust which will be dissipated by the eternal
cosmic weather as carelessly as they were formed. The popular notion that 'Science' is forced on the mindab extra, and that our interests have nothing to do with its
constructions, is utterly absurd. The craving to believe
that the things of the world belong to kinds which are related
by inward rationality together, is the parent of Science
as well as of sentimental philosophy; and the original investigator
always preserves a healthy sense of how plastic
the materials are in his hands. "Once for all," says Helmholtz in beginning that little work of his
which laid the foundations of the 'conservation of energy,' "it is the
task of the physical sciences to seek for laws by which particular processes
in nature may be referred to general rules, and deduced from
such again. Such rules (for example the laws of reflection or refraction
of light, or that of Mariotte and Gay-Lussac for gas-volumes) are
evidently nothing but generic-concepts for embracing whole classes of
phenomena. The search for them is the business of the experimental
division of our Science. Its theoretic division, on the other hand,
tries to discover the unknown causes of processes from their visible
effects; tries to understand them by the law of causality.... The
ultimate goal of theoretic physics is to find the lastunchangingcausesof the processes in Nature. Whether all processes be really ascribable
to such causes, whether, in other words,nature be completely intelligible,or whether there be changes which would elude the law of a necessary
causality, and fall into a realm of spontaneity or freedom, is not here
the place to determine; but at any rate it is clear that the Science
whose aim it is to make nature appear intelligible [die Natur zu
begreifen] must start with theassumptionof her intelligibility, and
draw consequences in conformity with this assumption, until irrefutable
facts show the limitations of this method.... The postulate that
natural phenomena must be reduced to changeless ultimate causes next
shapes itself so thatforces unchanged by timemust be found to be
these causes. Now in Science we have already found portions of matter
with changeless forces (indestructible qualities), and called them
(chemical) elements. If, then, we imagine the world composed of elements
with inalterable qualities, the only changes that can remain
possible in such a world are spatial changes, i.e. movements, and the
only outer relations which can modify the action of the forces are
spatial too, or, in other words, the forces are motor forces dependent
for their effect only on spatial relations. More exactly still: The phenomena
of nature must be reduced to [zurückgeführt, conceived as,
classed as] motions of material points with inalterable motor forces
acting according to space-relations alone.... But points have no
mutual space-relations except their distance,... and a motor force
which they exert upon each other can cause nothing but a change of
distance—i.e. be an attractive or a repulsive force.... And its intensity
can only depend on distance. So that at last the task of Physics
resolves itself into this, to refer phenomena to inalterable attractive
and repulsive forces whose intensity varies with distance. The solution
of this task would at the same time be the condition of Nature's
complete intelligibility."[553] "Once for all," says Helmholtz in beginning that little work of his
which laid the foundations of the 'conservation of energy,' "it is the
task of the physical sciences to seek for laws by which particular processes
in nature may be referred to general rules, and deduced from
such again. Such rules (for example the laws of reflection or refraction
of light, or that of Mariotte and Gay-Lussac for gas-volumes) are
evidently nothing but generic-concepts for embracing whole classes of
phenomena. The search for them is the business of the experimental
division of our Science. Its theoretic division, on the other hand,
tries to discover the unknown causes of processes from their visible
effects; tries to understand them by the law of causality.... The
ultimate goal of theoretic physics is to find the lastunchangingcausesof the processes in Nature. Whether all processes be really ascribable
to such causes, whether, in other words,nature be completely intelligible,or whether there be changes which would elude the law of a necessary
causality, and fall into a realm of spontaneity or freedom, is not here
the place to determine; but at any rate it is clear that the Science
whose aim it is to make nature appear intelligible [die Natur zu
begreifen] must start with theassumptionof her intelligibility, and
draw consequences in conformity with this assumption, until irrefutable
facts show the limitations of this method.... The postulate that
natural phenomena must be reduced to changeless ultimate causes next
shapes itself so thatforces unchanged by timemust be found to be
these causes. Now in Science we have already found portions of matter
with changeless forces (indestructible qualities), and called them
(chemical) elements. If, then, we imagine the world composed of elements
with inalterable qualities, the only changes that can remain
possible in such a world are spatial changes, i.e. movements, and the
only outer relations which can modify the action of the forces are
spatial too, or, in other words, the forces are motor forces dependent
for their effect only on spatial relations. More exactly still: The phenomena
of nature must be reduced to [zurückgeführt, conceived as,
classed as] motions of material points with inalterable motor forces
acting according to space-relations alone.... But points have no
mutual space-relations except their distance,... and a motor force
which they exert upon each other can cause nothing but a change of
distance—i.e. be an attractive or a repulsive force.... And its intensity
can only depend on distance. So that at last the task of Physics
resolves itself into this, to refer phenomena to inalterable attractive
and repulsive forces whose intensity varies with distance. The solution
of this task would at the same time be the condition of Nature's
complete intelligibility."[553] The subjective interest leading to the assumption could
not be more candidly expressed. What makes the assumption
'scientific' and not merely poetic, what makes a Helmholtz
and his kindiscoverers, is that the things of Nature
turn out to act as if theywereof the kind assumed. They
behave as such mere drawing and driving atoms would behave;
and so far as they have been distinctly enough translated
into molecular terms to test the point, so far a certain
fantastically ideal object, namely, the mathematical sum
containing their mutual distances and velocities, is found to
be constant throughout all their movements. This sum is
called the total energy of the molecules considered. Its constancyor 'conservation' gives the name to the hypothesis
of molecules and central forces from which it was logically
deduced. Take any other mathematico-mechanical theory and it
is the same. They are all translations of sensible experiences
into other forms, substitutions of items between which
ideal relations of kind, number, form, equality, etc., obtain,
for items between which no such relations obtain; coupled
with declarations that the experienced form is false and the
ideal form true, declarations which are justified by the appearance
of new sensible experiences at just those times
and places at which we logically infer that their ideal correlates
ought to be. Wave-hypotheses thus make us predict
rings of darkness and color, distortions, dispersions,
changes of pitch in sonorous bodies moving from us,
etc.; molecule-hypotheses lead to predictions of vapor-density,
freezing point, etc.,—all which predictions fall true. Thus the world grows more orderly and rational to the
mind, which passes from one feature of it to another by deductive
necessity, as soon as it conceives it as made up of
so few and so simple phenomena as bodies with no properties
but number and movement to and fro. But alongside of these ideal relations between terms
which the world verifies, there are other ideal relations not
as yet so verified. I refer to those propositions (no longer
expressing mere results of comparison) which are formulated
in such metaphysical and æsthetic axioms as "The
Principle of things is one;" "The quantity of existence is
unchanged;" "Nature is simple and invariable;" "Nature
acts by the shortest ways;" "Ex nihilo nihil fit;" "Nothing
can be evolved which was not involved;" "Whatever
is in the effect must be in the cause;" "A thing can only
work where it is;" "A thing can only affect another of its
own kind;" "Cessante causa, cessat et effectus;" "Nature
makes no leaps;" "Things belong to discrete and permanent
kinds;" "Nothing is or happens without a reason;"
"The world is throughout rationally intelligible;" etc.,etc., etc. Such principles as these, which might be multiplied
to satiety,[554]are properly to be calledpostulates of
rationality, not propositions of fact. If naturedidobey
them, shewouldbepro tantomore intelligible; and we seek
meanwhile so to conceive her phenomena as to show that
she does obey them. To a certain extent we succeed. For
example, instead of the 'quantity of existence' so vaguely
postulated as unchanged, Nature allows us to suppose that
curious sum of distances and velocities which for want of
a better term we call 'energy.' For the effect being 'contained
in the cause,' nature lets us substitute 'the effectisthe cause,' so soon as she lets us conceive both effect and
cause as the same molecules, in two successive positions.—But
all around these incipient successes (as all around the
molecular world, so soon as we add to it as its 'effects' those
illusory 'things' of common-sense which we had to butcher
for its sake), there still spreads a vast field of irrationalized
fact whose items simplyaretogether, and from one to
another of which we can pass by no ideally 'rational' way. It is not that these more metaphysical postulates of
rationality are absolutely barren—though barren enough
they were when used, as the scholastics used them, as
immediate propositions of fact.[555]They have a fertility asideals, and keep us uneasy and striving always to recast
the world of sense until its lines become more congruent
with theirs. Take for example the principle that 'nothing
can happen without a cause.' We have no definite idea of
what we mean by cause, or of what causality consists in. But
the principle expresses a demand forsomedeeper sort of
inward connection between phenomena than their merely
habitual time-sequence seems to us to be. The word 'cause'
is, in short, an altar to an unknown god; an empty pedestal
still marking the place of a hoped-for statue.Anyreally inward belonging-together of the sequent terms, if
discovered, would be accepted as what the word cause was
meant to stand for. So we seek, and seek; and in the
molecular systems we find a sort of inward belonging in
the notion of identity of matter with change of collocation.
Perhaps by still seeking we may find other sorts of inward
belonging, even between the molecules and those 'secondary
qualities,' etc., which they produce upon our minds. It cannot be too often repeated that the triumphant
application of any one of our ideal systems of rational relations
to the real world justifies our hope that other systems
may be found also applicable. Metaphysics should
take heart from the example of physics, simply confessing
that hers is the longer task. Naturemaybe remodelled,
nay, certainly will be remodelled, far beyond the point at
present reached. Just how far?—is a question which only
the whole future history of Science and Philosophy can
answer.[556]Our task being Psychology, we cannot even
cross the threshold of that larger problem. Besides the mental structure which results in suchmetaphysical principles as those just considered, there is
a mental structure which expresses itself in The æsthetic principles are at bottom such axioms as
that a note sounds good with its third and fifth, or that
potatoes need salt. We are once for all so made that when
certain impressions come before our mind, one of them will
seem to call for or repel the others as its companions. To
a certain extent the principle of habit will explain these
æsthetic connections. When a conjunction is repeatedly
experienced, the cohesion of its terms grows grateful, or at
least their disruption grows unpleasant. But to explainallæsthetic judgments in this way would be absurd; for it is
notorious how seldom natural experiences come up to our
æsthetic demands. Many of the so-called metaphysical
principles are at bottom only expressions of æsthetic feeling.
Nature is simple and invariable; makes no leaps, or
makes nothing but leaps; is rationally intelligible; neither
increases nor diminishes in quantity; flows from one principle,
etc., etc.,—what do all such principles express save
our sense of how pleasantly our intellect would feel if it
had a Nature of that sort to deal with? The subjectivity
of which feeling is of course quite compatible with Nature
also turning out objectively to be of that sort, later on. Themoralprinciples which our mental structure engenders
are quite as little explicablein totoby habitual
experiences having bred inner cohesions. Rightness is notmereusualness, wrongness notmereoddity, however numerous
the facts which might be invoked to prove such identity.
Nor are the moral judgments those most invariably and
emphatically impressed on us by public opinion. The
most characteristically and peculiarly moral judgments
that a man is ever called on to make are in unprecedented
cases and lonely emergencies, where no popular
rhetorical maxims can avail, and the hidden oracle alone
can speak; and it speaks often in favor of conduct
quite unusual, and suicidal as far as gaining popular
approbation goes. The forces which conspire to this
resultant are subtle harmonies and discords between theelementary ideas which form the data of the case. Some of
these harmonies, no doubt, have to do with habit; but
in respect to most of them our sensibility must assuredly
be a phenomenon of supernumerary order, correlated with
a brain-function quite as secondary as that which takes
cognizance of the diverse excellence of elaborate musical
compositions. No more than the higher musical sensibility
can the higher moral sensibility be accounted for by the
frequency with which outer relations have cohered.[557]Take
judgments of justice or equity, for example. Instinctively,
one judges everything differently, according as it pertains
to one's self or to some one else. Empirically one notices
that everybody else does the same. But little by little
there dawns in one the judgment "nothing can be right for
me which would not be right for another similarly placed;"
or "the fulfilment of my desires is intrinsically no more imperative
than that of anyone else's;" or "what it is reasonable
that another should do for me, it is also reasonable
that I should do for him;"[558]and forthwith the whole mass
of the habitual gets overturned. It getsseriouslyoverturned
only in a few fanatical heads. But its overturning
is due to a back-door and not to a front-door process.
Some minds are preternaturally sensitive to logical consistency
and inconsistency. When they have ranked a
thing under a kind, theymusttreat it as of that kind's
kind, or feel all out of tune. In many respects we do class
ourselves with other men, and call them and ourselves by
a common name. They agree with us in having the same
Heavenly Father, in not being consulted about their birth,in not being themselves to thank or blame for their natural
gifts, in having the same desires and pains and pleasures,
in short in a host of fundamental relations. Hence,if these
things be our essence,we should be substitutable for other
men, and they for us, in any proposition in which either
of us is involved. The more fundamental and common
the essence chosen, and the more simple the reasoning,[559]the more wildly radical and unconditional will the justice
be which is aspired to. Life is one long struggle between
conclusions based on abstract ways of conceiving cases, and
opposite conclusions prompted by our instinctive perception
of them as individual facts. The logical stickler
for justice always seems pedantic and mechanical to
the man who goes by tact and the particular instance,
and who usually makes a poor show at argument. Sometimes
the abstract conceiver's way is better, sometimes that
of the man of instinct. But just as in our study of reasoning
we found it impossible to lay down any mark whereby
to distinguishrightconception of a concrete case fromconfusion(seepp. 336,350), so here we can give no general
rule for deciding when it is morally useful to treat a concrete
case assui generis, and when to lump it with others
in an abstract class.[560] An adequate treatment of the way in which we come by
our æsthetic and moral judgments would require a separate
chapter, which I cannot conveniently include in this book.
Suffice it that these judgments express inner harmonies
and discords between objects of thought; and that whilst
outer cohesions frequently repeated will often seem harmonious,
all harmonies are not thus engendered, but our
feeling of many of them is a secondary and incidental function
of the mind. Where harmonies are asserted of the
real world, they are obviously mere postulates of rationality,
so far as they transcend experience. Such postulates
are exemplified by the ethical propositions that the individual
and universal good are one, and that happiness and
goodness are bound to coalesce in the same subject. I will now sum up our progress so far by a short summary
of the most important conclusions which we have
reached. The mind has a native structure in this sense, that certain
of its objects, if considered together in certain ways,
give definite results; and that no other ways of considering,
and no other results, are possible if the same objects
be taken. The results are 'relations' which are all expressed by
judgments of subsumption and of comparison. The judgments of subsumption are themselves subsumed
under thelaws of logic. Those of comparison are expressed inclassifications, and
in thesciences of arithmetic and geometry. Mr. Spencer's opinion that our consciousness of classificatory,
logical, and mathematical relations between ideas is
due to the frequency with which the corresponding 'outer
relations' have impressed our minds, is unintelligible. Our consciousness of these relations, no doubt, has a
natural genesis. But it is to be sought rather in the inner
forces which have made the brain grow, than in any mere
paths of 'frequent' association which outer stimuli may
have ploughed in that organ. But let our sense for these relations have arisen as it
may, the relations themselves form a fixed system of lines
of cleavage, so to speak, in the mind, by which we naturally
pass from one object to another; and the objects connected
by these lines of cleavage are often not connected by any
regular time- and space-associations. We distinguish,
therefore, between the empirical order of things, and this
their rational order of comparison; and, so far as possible,
we seek to translate the former into the latter, as being the
more congenial of the two to our intellect. Any classification of things into kinds (especially if the
kinds form series, or if they successively involve each
other) is a more rational way of conceiving the things than
is that mere juxtaposition or separation of them as individuals
in time and space which is the order of their crude
perception. Any assimilation of things to terms between
which such classificatory relations, with their remote and
mediate transactions, obtain, is a way of bringing the things
into a more rational scheme. Solids in motion are such terms; and the mechanicalphilosophy is only a way of conceiving nature so as to
arrange its items along some of the more natural lines of
cleavage of our mental structure. Other natural lines are the moral and æsthetic relations.
Philosophy is still seeking to conceive things so that these
relations also may seem to obtain between them. As long as things have not successfully been so conceived,
the moral and æsthetic relations obtain only betweenentia rationis, terms in the mind; and the moral and æsthetic
principles remain but postulates, not propositions, with
regard to the real world outside. There is thus a large body ofa priorior intuitively
necessary truths. As a rule, these are truths ofcomparisononly, and in the first instance they express relations between
merely mental terms. Nature, however, acts as if
some of her realities were identical with these mental
terms. So far as she does this, we can makea prioripropositions
concerning natural fact. The aim of both science
and philosophy is to make the identifiable terms more
numerous. So far it has proved easier to identify nature's
things with mental terms of the mechanical than with mental
terms of the sentimental order. The widest postulate of rationality is that the worldisrationally intelligible throughout, after the pattern ofsomeideal system. The whole war of the philosophies is over
that point of faith. Some say they can see their way
already to the rationality; others that it is hopeless in any
other but the mechanical way. To some the very fact that
there is a world at all seems irrational. Nonentity would be
a more natural thing than existence, for these minds. One
philosopher at least says that the relatedness of things to
each other is irrational anyhow, and that a world of relations
can never be made intelligible.[561] With this I may be assumed to have completed the
programme which I announced at the beginning of the chapter,
so far as thetheoreticpart of our organic mental structuregoes. It can be due neither to our own nor to our ancestors'
experience. I now pass to those practical parts of
our organic mental structure. Things are a little different
here; and our conclusion, though it lies in the same direction,
can be by no means as confidently expressed. To be as short and simple as possible, I will take the
case of instincts, and, supposing the reader to be familiar
withChapter XXIV, I will plungein medias res. Instincts must have been either 1) Each specially created in complete form, or 2) Gradually evolved. As the first alternative is nowadays obsolete, I proceed
directly to the second. The two most prominent suggestions
as to the way in which instincts may have been evolved
are associated with the names of Lamarck and Darwin. Lamarck's statement is that animals havewants, and
contract, to satisfy them,habitswhich transform themselves
gradually into so many propensities which they can neither
resist nor change. Thesepropensities, once acquired, propagate
themselves by way of transmission to the young, so
that they come to exist in new individuals, anteriorly to all
exercise. Thus are the same emotions, the same habits,
the sameinstincts, perpetuated without variation from one
generation to another, so long as the outward conditions
of existence remain the same.[562]Mr. Lewes calls this the
theory of 'lapsed intelligence.' Mr. Spencer's words are
clearer than Lamarck's, so that I will quote from him:[563] "Setting out with the unquestionable assumption, that every new
form of emotion making its appearance in the individual or the race is
a modification of some pre-existing emotion, or a compounding of
several pre-existing emotions, we should be greatly aided by knowing
what always are the pre-existing emotions. When, for example, we
find that very few, if any, of the lower animals show any love of accumulation,
and that this feeling is absent in infancy; when we see that
an infant in arms exhibits anger, fear, wonder, while yet it manifests
no desire of permanent possession; and that a brute which has no acquisitive
emotion can nevertheless feel attachment, jealousy, love of approbation,—we
may suspect that the feeling which property satisfies is
compounded out of simpler and deeper feelings. We may conclude
that as when a dog hides a bone there must exist in him a prospective
gratification of hunger, so there must similarly, at first, in all cases
where anything is secured or taken possession of, exist an ideal excitement
of the feeling which that thing will gratify. We may further conclude
that when the intelligence is such that a variety of objects come to
be utilized for different purposes; when, as among savages, divers wants
are satisfied through the articles appropriated for weapons, shelter,
clothing, ornament,—the act of appropriating comes to be one constantly
involving agreeable associations, and one which is therefore
pleasurable, irrespective of the end subserved. And when, as in civilized
life, the property acquired is of a kind not conducing to one order
of gratifications, but is capable of ministering to all gratifications, the
pleasure of acquiring property grows more distinct from each of the
various pleasures subserved—is more completely differentiated into a
separate emotion.[564]It is well known that on newly-discovered islands
not inhabited by man, birds are so devoid of fear as to allow themselves
to be knocked over with sticks, but that in the course of generationsthey acquire such a dread of man as to fly on his approach, and
that this dread is manifested by young as well as old. Now unless this
change be ascribed to the killing off of the least fearful, and the preservation
and multiplication of the more fearful, which, considering the
small number killed by man, is an inadequate cause, it must be ascribed
to accumulated experiences, and each experience must be held to have
a share in producing it. We must conclude that in each bird that escapes
with injuries inflicted by man, or is alarmed by the outcries of
other members of the flock,... there is established an association of
ideas between the human aspect and the pains, direct and indirect, suffered
from human agency. And we must further conclude that the
state of consciousness which impels the bird to take flight is at first
nothing more than an ideal reproduction of those painful impressions
which before followed man's approach; that such ideal reproduction
becomes more vivid and more massive as the painful experiences, direct
or sympathetic, increase; and that thus the emotion, in its incipient
state, is nothing else than an aggregation of the revived pains before
experienced. As, in the course of generations, the young birds of this
race begin to display a fear of man before they have been injured by
him, it is an unavoidable inference that the nervous system of the race
has been organically modified by these experiences; we have no choice
but to conclude that when a young bird is thus led to fly, it is because
the impression produced on its senses by the approaching man entails,
through an incipiently reflex action, a partial excitement of all those
nerves which, in its ancestors, had been excited under the like conditions;
that this partial excitement has its accompanying painful consciousness;
and that the vague painful consciousness thus arising constitutes
emotion proper—emotion undecomposable into specific experiences,
and therefore seemingly homogeneous. If such be the explanation
of the fact in this case, then it is in all cases. If the emotion
is so generated here, then it is so generated throughout.If so, we must
perforce conclude that the emotional modifications displayed by different
nations, and those higher emotions by which civilized are distinguished
from savage, are to be accounted for on the same principle.
And, concluding this, we are led strongly to suspect that the emotions
in general have severally thus originated."[565] "Setting out with the unquestionable assumption, that every new
form of emotion making its appearance in the individual or the race is
a modification of some pre-existing emotion, or a compounding of
several pre-existing emotions, we should be greatly aided by knowing
what always are the pre-existing emotions. When, for example, we
find that very few, if any, of the lower animals show any love of accumulation,
and that this feeling is absent in infancy; when we see that
an infant in arms exhibits anger, fear, wonder, while yet it manifests
no desire of permanent possession; and that a brute which has no acquisitive
emotion can nevertheless feel attachment, jealousy, love of approbation,—we
may suspect that the feeling which property satisfies is
compounded out of simpler and deeper feelings. We may conclude
that as when a dog hides a bone there must exist in him a prospective
gratification of hunger, so there must similarly, at first, in all cases
where anything is secured or taken possession of, exist an ideal excitement
of the feeling which that thing will gratify. We may further conclude
that when the intelligence is such that a variety of objects come to
be utilized for different purposes; when, as among savages, divers wants
are satisfied through the articles appropriated for weapons, shelter,
clothing, ornament,—the act of appropriating comes to be one constantly
involving agreeable associations, and one which is therefore
pleasurable, irrespective of the end subserved. And when, as in civilized
life, the property acquired is of a kind not conducing to one order
of gratifications, but is capable of ministering to all gratifications, the
pleasure of acquiring property grows more distinct from each of the
various pleasures subserved—is more completely differentiated into a
separate emotion.[564]It is well known that on newly-discovered islands
not inhabited by man, birds are so devoid of fear as to allow themselves
to be knocked over with sticks, but that in the course of generationsthey acquire such a dread of man as to fly on his approach, and
that this dread is manifested by young as well as old. Now unless this
change be ascribed to the killing off of the least fearful, and the preservation
and multiplication of the more fearful, which, considering the
small number killed by man, is an inadequate cause, it must be ascribed
to accumulated experiences, and each experience must be held to have
a share in producing it. We must conclude that in each bird that escapes
with injuries inflicted by man, or is alarmed by the outcries of
other members of the flock,... there is established an association of
ideas between the human aspect and the pains, direct and indirect, suffered
from human agency. And we must further conclude that the
state of consciousness which impels the bird to take flight is at first
nothing more than an ideal reproduction of those painful impressions
which before followed man's approach; that such ideal reproduction
becomes more vivid and more massive as the painful experiences, direct
or sympathetic, increase; and that thus the emotion, in its incipient
state, is nothing else than an aggregation of the revived pains before
experienced. As, in the course of generations, the young birds of this
race begin to display a fear of man before they have been injured by
him, it is an unavoidable inference that the nervous system of the race
has been organically modified by these experiences; we have no choice
but to conclude that when a young bird is thus led to fly, it is because
the impression produced on its senses by the approaching man entails,
through an incipiently reflex action, a partial excitement of all those
nerves which, in its ancestors, had been excited under the like conditions;
that this partial excitement has its accompanying painful consciousness;
and that the vague painful consciousness thus arising constitutes
emotion proper—emotion undecomposable into specific experiences,
and therefore seemingly homogeneous. If such be the explanation
of the fact in this case, then it is in all cases. If the emotion
is so generated here, then it is so generated throughout.If so, we must
perforce conclude that the emotional modifications displayed by different
nations, and those higher emotions by which civilized are distinguished
from savage, are to be accounted for on the same principle.
And, concluding this, we are led strongly to suspect that the emotions
in general have severally thus originated."[565]
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