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possibility (although not for all cases the only ground)
of reproduction.

12. When a concept becomes not entirely, but only
in part, transformed into an effort, we must guard
against considering this part as a severed portion of
the whole concept. It has certainly a definite magni-
tude (upon the knowledge of which much depends)*
but this magnitude indicates only a degree of the ob-
scuration of the whole concept. If the question be
in regard to several parts of one and the same concept,
these parts must not be regarded as different, severed
portions, but the smaller divisions may be regarded
as being contained in the larger. The same is true of
the remainders after the collisions — i. e., of those parts
of a concept which remain unobscured, for those parts
are also degrees of the real concept.



CHAPTER II.

EQUILIBRIUM AND MOVEMENT OF CONCEPTS.

13. When a sufficiency of opposition exists be-
tween concepts, the latter are in equilibrium. They
come only gradually to this point. The continuous
change of their degree of obscuration may be called
their movement.

The statics and mechanics of the mind have to do
with the calculation of the equilibrium and movement
of the concepts.

14. All investigations into the statics of the mind



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12 FUNDAMENTAL PRINCIPLES.

begin with two different quantitative factors, viz.,
the sum (or the aggregate amount) of the resistances
and the ratio of their limitation. The former is the
quantity which rises from their encounter, to be divided
between the opposing concepts. If one knows how to
state it, and knows also the ratio in which the different
concepts yield in the encounter, then, by a simple cal-
culation in proportion, the statical point of each con-
cept — i. e., the degree of its obscuration in equilibrium
— may be found.

15. The sum as well as the ratio of the mutual
limitation depends upon the strength of each indi-
vidual concept which is affected in inverse ratio to its
strength, and upon the degree of opposition between
the two concepts. For their influence upon each other
stands in direct ratio to the strength of each.

The principle determining the sum of the mutual
limitation is, that it shall be considered as small as
possible, because all concepts strive against suppres-
sion, and certainly submit to no more of it than is
absolutely necessary.

16. By actual calculation, the remarkable result is
obtained that, in the case of the two concepts, the one
never entirely obscures the other, but, in the case of
three or more, one is very easily obscured, and can be
made as ineffective — notwithstanding its continuous
struggle — as if it were not present at all. Indeed, this
obscuration may happen to a large number of con-
cepts as well as to one, and may be effected through
the agency of two, and even through the combined in-
fluence of concepts less strong than those which are
suppressed.

Here the expression " threshold of consciousness "



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EQUILIBRIUM AND MOVEMENT OP CONCEPTS. 13

must be explained, as we shall have occasion to use it.
A concept is in consciousness in so far as it is not
suppressed, but is an actual representation. When it
rises out of a condition of complete suppression, it
enters into consciousness. Here, then, it is on the
threshold of consciousness. It is very important to
determine by calculation the degree of strength which
a concept must attain in order to be able to stand beside
two or more stronger ones exactly on the threshold of
consciousness, so that, at the slightest yielding of the
hindrance, it would begin to rise into consciousness.

Note. — ^The expression " A concept is in consciousness " must
be distinguished from t&at, ** I am conscious of my concept."
To the latter belongs inner perception ; to the former not. In
psychology, we need a word that will indicate the totality of all
simultaneous actual presentations. No word except conscious-
ness can be found for this purpose.

Here we are obliged to be content with a circumlocution — and
this all the more, because the inner perception which is usually
attributed to consciousness has no fixed limit where it begins or
ceases, and, moreover, the act of perceiving is not itself per-
ceived ; so that, since we are not conscious of it in ourselves, wo
must exclude it from consciousness, although it is an active
knowing, and in no way a restricted or suppressed concept.

17. Among the many, and, for the most part, very
complicated laws underlying the movement of con-
cepts, the following is the simplest :

While the arrested portion {Hemmungssumme) of
the concept sinks, the sinking part is at every mo-
ment proportional to the part unsuppressed.

By this it is possible to calculate the whole course
of the sinking even to the statical point

Note. — Mathematically, the above law may be expressed:
o' = Sn_Q"" jin which S = the aggregate amount sup-



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14 FUNDAMENTAL PRINCIPLES.

pressed, t = the time elapsed during the encounter, <r = the
suppressed portion of all the concepts in the time indicated
byt.

As the latter quantity is apportioned among the individual
concepts, it is found that those which fall directly beneath the
statical threshold (16) are very quickly driven thence, while the
rest do not reach exactly their statical point in any given finite
time. On account of this latter circumstance, the concepts in
the mind of a man of most equable temperament are, while he
is awake, always in a state of gentle motion. This is also the
primary reason why the inner perception never meets an object
which holds it quite motionless.

18. When to several concepts already near equi-
librium a new one comes, a movement arises which
causes them to sink for a short time beneath their
statical point, after which they quickly and entirely of
themselves rise again — something as a liquid, when
an object is thrown into it, first sinks and then rises.
In this connection several remarkable circumstances
occur :

19. First, upon an occasion of this kind, one of the
older concepts may be removed entirely out of con-
sciousness even by a new concept that is much weaker
than itself. In this case, however, the striving of the
suppressed concept is not to be considered wholly in-
effective, as shown above (see 16) ; it works with all
its force against the concepts in consciousness. Al-
though its object is not conceived, it produces a certain
condition of consciousness. The way in which these
concepts are removed out of consciousness and yet are
effective therein may be indicated by the expression,
" They are on the mechanical threshold." The thresh-
old mentioned above (16) is called for the sake of dis-
tinction the statical threshold.



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EQUILIBRIUM AND MOVEMENT OF CONCEPTS. 15

Note. — If the concepts on the statical threshold acted in the
same way as on the mechanical threshold we should find onr-
selves in a state of the most intolerable uneasiness, or rather
the body would be subjected to a condition of tension that must
in a few moments prove fatal, even as under present conditions
sudden fright will sometimes cause death ; for all the concepts
which, as we are accustomed to say, the memory preserves, and
which we well know can upon the slightest occasion be repro-
duced, are in a state of incessant striving to rise, although the
condition of consciousness is not at all affected by them.

20. Second, the time during which one or more
concepts linger upon the mechanical threshold can be
extended if a series of new, although weaker, concepts
come in succession to them.

Every employment to which we are unaccustomed
puts us in this condition. The earlier concepts are
pressed back of the later ones. The former, however,
because they are the stronger, remain tense, affect the
physical organism more and more, and finally make
it necessary that the employment cease, when the old
concepts immediately rise, and we experience what is
called a feeling of relief which depends in part upon
the physical organism, although the first cause is pure-
ly psychological.

21. Third, when several concepts are driven in
succession to the mechanical threshold, several sudden
successive changes in the laws of reciprocal move-
ments arise.

In this way is to be explained the fact that the
course of our thoughts is so often inconsequent,
abrupt, and apparently irregular. This appearance
deceives in the same way as the wandering of the
planets. The conformity to law in the human mind
resembles exactly that in the firmament.



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16 FUNDAMENTAL PRINCIPLES.

NoTB. — ^As'a counterpart to the concepts which sink simul-
taneously are to be observed those which rise simultaneously,,
especially when they rise free — i. e., when a restricting environ-
ment or a general pressure suddenly disappears. With the ris-
ing the amount of suppression increases. Hence, in the case of
three, one may be, as it were, bent back, and under certain con-
ditions may sink quite to the threshold. Their elevation is
greater than the depression to which, sinking together, they
would have pressed one another, because in sinking the sum of
their mutual limitation depends upon the total strength, which
in the gradual rising is not the case.



CHAPTER IIL

COMPLICATIONS AND BLENDINQS.

22. The easily conceivable metaphysical reason
why opposed concepts resist one another is the unity
of the soul, of which they are the self-preservations.
This reason explains without difficulty the combina-
tion of our concepts (which combination is known to
exist). If, on account of their opposition, they did
not suppress one another, all concepts would compose
but one act of one soul ; and, indeed, in so far as they
are not divided into a manifold by any kind of arrests
whatever, they really constitute but one act. Con-
cepts that are on the threshold of consciousness can
not enter into combination with others, as they are
completely transformed into effort directed against
other de&iite concepts, and are thereby, as it were,
isolated. In consciousness, howevei*, concepts combine
in two ways : First, concepts which are not opposed or



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COMPLICATIONS AND BLENDINGS. 17

contrasted with one another (as a tone and a color) so
far as they meet unhindered, form a complex ; second,
contrasted concepts [e. g., red and yellow], in so far
as they are affected neither by accidental foreign con-
cepts nor by unavoidable opposition, become blended
(fused).

Complexes may be complete; blendings (fusions)
from their nature must always be (more or less) in-
complete.

Note. — Of such complexes as are partially or almost com-
plete, we have remarkable instances in the concepts of things
with several characteristics and of words used as signs of
thoughts. In the mother-tongue the latter, words and thoughts,
are so closely connected that it would appear that we think by
means of words. (Concerning both examples more hereafter.)
Among the blendings are especially remarkable, partly those
which include in themselves an aesthetic relation (whicli, taken
psychologically, is created at the same time with the blending),
partly those which involve succession, in which serial forms
have their origin.

23. That which is complicated or blended out of
several concepts furnishes an aggregate of force, and
for this reason works according to quite other statical
and mechanical laws than those according to which
the individual concepts would have acted. Also the
thresholds of consciousness change according to the
complex or blending (fusion), so that on account of a
combination a concept of the very weakest kind may
be able to remain and exert an influence in conscious-
ness.

Note 1. — ^The computation for complexes and blendings de-
pends upon the same principles as that for simple concepts ; it
is, however, much more intricate, especially for the reason that
5



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18 FUNDAMENTAL PRINCIPLES.

in the case of incomplete combinations the forces as well as their
arrests are only partially interwoven with one another (and do
not fully enter as factors into the product).

Note 2. — Combinations of concepts consist not only of two
or three members, but they often contain many members in very
unequal degrees of complication, or blending, in which case no
calculation can estimate the multiplicity. Nevertheless, from
the latter, the simplest cases may be chosen and the more intri-
cate ones estimated according to them. For every science the
simplest laws are the most important.

24. Problem: After an encounter between two
concepts, P and n, the remainders, r and p, are blended
(or incompletely united). The problem is to indicate
what help one of the two concepts, in case it should
be still more suppressed, would receive from the other.

Note. — Solution: Let P be the helping concept; it helps
with a force equal to r, but 11 can only appropriate this force in

thi3 ratio of p : n. Hence through P, n receives the help ^,
and in the same way P receives from n the help -^

The proof lies immediately in the analysis of the
ideas. It is plain that the two remainders, r and p, ,
taken together, determine the degree of union between
the two concepts. One of them is the helping force ;
the other, compared with the concept to which it be-
longs, is to be considered as a fraction of the whole ;
and, of the totality of help which could be rendered
by the first remainder, it yields that portion which
here attains efficient activity.

25. The following principles may be observed
here :

a. Beyond the point of union no help extends its
influence.



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COMPLICATION'S AND BLENDINGS. 19

If the concept 11 has more clearness in conscious-
ness than the remainder p indicates, then by the striv-
ing of the concept P, which might coiSd to the help
of the former, already more than enough has been
done ; hence for the present it exerts no more influ-
ence.

S. The farther the one of the concepts is below the
point of union, so much the more effectively does the
other help.

Note. — ^This gives the following differential equation :

n p

whence by integration u = p ( " — j

This equation contains the germ of manifold investigations
which penetrate the whole of psychology. It is indeed so sim-
ple that it can never really occur in the human soul, but all in-
vestigations into applied mathematics begin with such simple
presuppositions as only exist in abstraction— e. g., the mathe-
matical lever, or the laws of bodies falling in a vacuum. Here
merely the influence of the help is considered, which, if every-
thing depended upon it alone, would bring into consciousness
during the time t a quantity « from n. Besides, if we take into
. consideration the single circumstance that n meets with an un-
avoidable arrest from other concepts, then the calculation be-
comes so complicated that it can be only approximately solved
by an integration of the following form :

d*» = ad^wdt 4- hdmdfi + cwdf^.

It is self-evident that it much more nearly expresses the
facts which are to be observed experimentally.

26. The foregoing contains the foundation of the
theory of mediate reproduction, which, according to
ordinary language, is derived from the association of
ideaa or concepts. Before pursuing this further we
must mention immediate reproduction — i. e., that re-



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20 FUNDAMENTAL PRINCIPLES.

production which, by its own force follows upon the
yielding of the hindrances. The ordinary case is that
a concept grfffied by a new act of perception causes the
old concept of the same or of a similar object to rise
into consciousness. This occurs when the concept
furnished by the new act of perception presses back
everything present in consciousness opposed to the
old concept, which is similar to the new one. Then,
without further difficulty, the old concept rises of it-
self. From this are to be observed the following con-
ditions, which are to be found by calculation, of which,
however, no idea can be given here :

a. In the beginning the rising is in proportion to
the square of the time, if the new act of perception
occurs suddenly ; but to the cube of the time, if the
latter (as is usual) is formed by a gradual and linger-
ing act of apprehension.

h. The course of the rising is adjusted principally
to the strength of the concept furnished by the new
act of perception in proportion to the opposing one
which it has pressed back ; but the individual strength
of the- rising concept only has influence under special
conditions. It can, as it were, only use this strength
in the free space which is given to it.

c. The rising concept blends as such with the con-
cept, similar to it, furnished by the new act of percep-
tion. Since it does not rise entirely, however, th©
blending is incomplete.

d» The fact that immediate reproduction is not
limited entirely to the old concept of exactly the same
kind, but extends to the more or less similar so far
as to receive partial freedom from the new act of per-
ception, is of special importance. The whole repro-



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COMPLICATIONS AND BLENDINGS. 21

duction may be indicated by the name of vaulting
(or arching). In the case of a long duration, or of
a. frequent repetition of a new act of perception, a
second important process, which we call tapering (or
pointing), follows. The peculiarity of this latter con-
sists in the fact that the concepts ^hich are less
similar are again arrested by the concepts received
through the new act of perception, as the old con-
cepts bring with them into consciousness others which
are opposed to the new, so that finally the concept
that is entirely homogeneous finds itself alone favored,
and forms, as it were, a tapering summit where the
highest point of the vault (or arch) was heretofore.

27. Where the circumstances allow, with this im-
mediate reproduction is united that mediate repro-
duction mentioned in 25. The concept P, mentioned
above, is reproduced immediately (i. e., without the
mediation of others), then the free space allowed it may
be regarded as that r (spoken of in 25) or as a force
which strives to raise the n blended with it to its point
of blending p.

Note.— As the free space gradually increasing (and again
decreasing) is given, we must for the present observation regard

r in the formula « = pM_g""^^asa variable quantity, and

indeed as a function of that quantity upon which the proposi-
tions in 26 depend.

28. The most important applications of the previ-
ous theories are, if with different remainders r, r\ r",
etc., of one and the same concept P several U, U', U",
etc., are united, by which, for the sake of brevity, we
may assume the remainders of the latter, viz., p, p', p",
to be equal ; also, IT, II', etc., may be equal.



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22 FUNDAMENTAL PRINCIPLES.

A concept acts upon several united with it in the
same series according to the time in which its remain-
ders {by which it is united with those others according
to quantity) stand.

Note. — In order to avoid diffuseness, this most important
law is here only very incompletely expressed in words. We
recognize it better and more clearly in the formula given:

« = p/ "" — ),if instead of one r we substitute different

smaller and greater, r, r', r", etc. But the more exact calcula-
tion mentioned in 25 shows that the*n, n', n", etc., blended
with them, not only rise, but sink again, as it were, to make
place for each other, and in the order of r, r,' r", etc.

29. Here is discovered the ground of the genuine
reproduction or of memory so far as it brings to us a
series of concepts in the same order in which they
were first received. In order to comprehend this, we
must consider what union arises among several con-
cepts that are successively given.

Let a series, a, b, c, d, be given by perception ; then,
from the first movement of the perception and during
its continuance, a is exposed to an arrest from other
concepts already in consciousness. In the mean time,
a, already partially sunken in consciousness, became
more and more obscured when b came to it. This b
at first, unobscured, blended with the sinking a ; then
followed c, which itself unobscured, united with J,
which was becoming obscured, and also with a, which
was still more obscured. Similarly followed df, to be-
come united in different degrees with a, J, c. From
this arises a law for each of these concepts that states
how, after the whole series has been, for a time, removed
out of consciousness, upon the re-emergence of one of



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OF COMPLEXES AND BLENDINQS. 23

the concepts of such a series into consciousness, every
other concept of the same series is called up. Let it be
assumed that a rises first, then it is united more with
*, less with c, and still less with d ; backward, however,
J, c, and d are blended collectively in an unobscured
condition with the remainders of a ; hence a seeks to
bring them all again into an unobscured condition
[i. e., into full consciousness]. But a acts the most
quickly and strongly upon &, more slowly upon c, still
more slowly upon rf, etc., by which close investiga-
tion shows that h sinks again, while c rises, even as
c sinks when d rises; in short, the series follows in
the same order as first given. On the contrary, let us
assume that c is originally reproduced, then c acts
upon d and the following members of the series ex-
actly in the same way as was indicated in the case
of a — i. e., the series c, d, etc., unfolds gradually in the
order of its succession. On the contrary, h and a
experience quite another influence. The unobscured
c was blended with their different remainders. Then
c acts upon them with its whole strength, and without
delay, but only to call back the remainders of a and l
united with it, to bring a part of h and a smaller part
of a into consciousness. Thus it happens that when
we remember something in the middle of a known
series, the preceding part of the series presents itself all
at once in a lessened degree of clearness, while the por-
tion following comes before the mind in the same order
as the series it brings with tt. But the series never
runs backward ; an anagram from a well-comprehended
word never originates without intentional effort.

30. Several series may cross one another, e. g., a, J,
c, e2, e, and a, )3, c, 8, «, in which c is common to the two



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24 FUNDAMENTAL PRINCIPLES.

series. If c were reproduced alone, it would strive to
call up d and e as well as 8 and c If, howeyer, b
comes into consciousness first, then the first series
comes decidedly forward on account of the united help
of h and c, yet the oppositions among the members of
both series, in this case, have each their own influence.

We may remark that, to the simple type or model
here given, a variety of complicated psychological oc-
currences may be adjusted. The same c can be held
as the common point of intersection for many hun-
dred series. On account of the manifold oppositions
in these series, the common c may cause none of the
members to rise perceptibly, but so soon as h and a
come forward, determining c more closely, the inde-
cision will disappear, and the uppermost series will
really come before the mind.

31. The foregoing depends upon the difference
presupposed in the remainders r, r', r", etc. (28). But
in order that this difference may have its influence,
the concept to which these remainders belong must
come forward sufficiently into consciousness. Let it
be granted that it is arrested to such a degree that
its active representation amounts to no more than that
of the smallest among the remainders r, r', r", etc.,
then it works equally on the whole series of concepts
blended with it so that a vague total impression of all
comes into consciousness. The reason for this is ex-
plained in sections 27 and 12. The remainders are not
different parts severed from one and the same concept ;
hence if a little of the latter is in consciousness, we
must not first question whether this little may be one
and perhaps quite the smallest among those remainders,
but we must assume that it really is so, although at



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OF COMPLEXES AND BLENDlNGa 25

the same time it may be a part of every other greater
remainder. If the active concept gradually rises into
consciousness, then the remainders, from the smaller


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