From the fact that we are able spontaneously to assign and determine the
laws of relations in space without having recourse to experience, Plato
concludes (_Meno_, p. 353, Bip.) that all learning is mere recollection.
Kant, on the other hand, concludes that space is subjectively conditioned,
and merely a form of the faculty of knowledge. How far, in this regard,
does Kant stand above Plato!
_Cogito, ergo sum_, is an analytical judgment. Indeed Parmenides held it
to be an identical judgment: “το γαρ αυτο νοειν εστι τε και ειναι” (_nam
intelligere et esse idem est_, _Clem. Alex. Strom._, vi. 2, § 23). As
such, however, or indeed even as an analytical judgment, it cannot contain
any special wisdom; nor yet if, to go still deeper, we seek to deduce it
as a conclusion from the major premise, _non-entis nulla sunt prædicata_.
But with this proposition what Descartes really wished to express was the
great truth that immediate certainty belongs only to self-consciousness,
to what is subjective. To what is objective, on the other hand, thus to
everything else, only indirect certainty belongs; for it is arrived at
through self-consciousness; and being thus merely at second hand, it is to
be regarded as problematical. Upon this depends the value of this
celebrated proposition. As its opposite we may set up, in the sense of the
Kantian philosophy, _cogito, ergo est_, that is, exactly as I think
certain relations in things (the mathematical), they must always occur in
all possible experience;—this was an important, profound, and a late
_apperçu_, which appeared in the form of the problem as to the
_possibility of synthetic judgments a priori_, and has actually opened up
the way to a deeper knowledge. This problem is the watchword of the
Kantian philosophy, as the former proposition is that of the Cartesian,
and shows εξ οἱων εισ οἱα.
Kant very fitly places his investigations concerning time and space at the
head of all the rest. For to the speculative mind these questions present
themselves before all others: what is time?—what is this that consists of
mere movement, without anything that moves it?—and what is space? this
omnipresent nothing, out of which nothing that exists can escape without
ceasing to be anything at all?
That time and space depend on the subject, are the mode in which the
process of objective apperception is brought about in the brain, has
already a sufficient proof in the absolute impossibility of thinking away
time and space, while we can very easily think away everything that is
presented in them. The hand can leave go of everything except itself.
However, I wish here to illustrate by a few examples and deductions the
more exact proofs of this truth which are given by Kant, not for the
purpose of refuting stupid objections, but for the use of those who may
have to expound Kant’s doctrine in future.
“A right-angled equilateral triangle” contains no logical contradiction;
for the predicates do not by any means cancel the subject, nor are they
inconsistent with each other. It is only when their object is constructed
in pure perception that the impossibility of their union in it appears.
Now if on this account we were to regard this as a contradiction, then so
would every physical impossibility, only discovered to be such after the
lapse of centuries, be a contradiction; for example, the composition of a
metal from its elements, or a mammal with more or fewer than seven
cervical vertebra,(14) or horns and upper incisors in the same animal. But
only _logical_ impossibility is a contradiction, not physical, and just as
little mathematical. Equilateral and rectangled do not contradict each
other (they coexist in the square), nor does either of them contradict a
triangle. Therefore the incompatibility of the above conceptions can never
be known by mere _thinking_, but is only discovered by perception—merely
mental perception, however, which requires no experience, no real object.
We should also refer here to the proposition of Giordano Bruno, which is
also found in Aristotle: “An infinitely large body is necessarily
immovable”—a proposition which cannot rest either upon experience or upon
the principle of contradiction, since it speaks of things which cannot
occur in any experience, and the conceptions “infinitely large” and
“movable” do not contradict each other; but it is only pure perception
that informs us that motion demands a space outside the body, while its
infinite size leaves no space over. Suppose, now, it should be objected to
the first mathematical example that it is only a question of how complete
a conception of a triangle the person judging has: if the conception is
quite complete it will also contain the impossibility of a triangle being
rectangular and also equilateral. The answer to this is: assume that his
conception is not so complete, yet without recourse to experience he can,
by the mere construction of the triangle in his imagination, extend his
conception of it and convince himself for ever of the impossibility of
this combination of these conceptions. This process, however, is a
synthetic judgment _a priori_, that is, a judgment through which,
independently of all experience, and yet with validity for all experience,
we form and perfect our conceptions. For, in general, whether a given
judgment is analytical or synthetical can only be determined in the
particular case according as the conception of the subject in the mind of
the person judging is more or less complete. The conception “cat” contains
in the mind of a Cuvier a hundred times more than in that of his servant;
therefore the same judgments about it will be synthetical for the latter,
and only analytical for the former. But if we take the conceptions
objectively, and now wish to decide whether a given judgment is analytical
or synthetical, we must change the predicate into its contradictory
opposite, and apply this to the subject without a copula. If this gives a
_contradictio in adjecto_, then the judgment was analytical; otherwise it
was synthetical.
That Arithmetic rests on the pure intuition or perception of time is not
so evident as that Geometry is based upon that of space.(15) It can be
proved, however, in the following manner. All counting consists in the
repeated affirmation of unity. Only for the purpose of always knowing how
often we have already affirmed unity do we mark it each time with another
word: these are the numerals. Now repetition is only possible through
succession. But succession, that is, being after one another, depends
directly upon the intuition or perception of _time_. It is a conception
which can only be understood by means of this; and thus counting also is
only possible by means of time. This dependence of all counting upon time
is also betrayed by the fact that in all languages multiplication is
expressed by “time,” thus by a time-concept: _sexies_, ἑξακις, _six fois_,
_sex mal_. But simple counting is already a multiplication by one, and for
this reason in Pestalozzi’s educational establishment the children are
always made to multiply thus: “Two times two is four times one.” Aristotle
already recognised the close relationship of number and time, and
expounded it in the fourteenth chapter of the fourth book of the
“Physics.” Time is for him “the number of motion” (“ὁ χρονος αριθμος εστι
κινησεως”). He very profoundly suggests the question whether time could be
if the soul were not, and answers it in the negative. If arithmetic had
not this pure intuition or perception of time at its foundation, it would
be no science _a priori_, and therefore its propositions would not have
infallible certainty.
Although time, like space, is the form of knowledge of the subject, yet,
just like space, it presents itself as independent of the subject and
completely objective. Against our will, or without our knowledge, it goes
fast or slow. We ask what o’clock it is; we investigate time, as if it
were something quite objective. And what is this objective existence? Not
the progress of the stars, or of the clocks, which merely serve to measure
the course of time itself, but it is something different from all things,
and yet, like them, independent of our will and knowledge. It exists only
in the heads of percipient beings, but the uniformity of its course and
its independence of the will give it the authority of objectivity.
Time is primarily the form of inner sense. Anticipating the following
book, I remark that the only object of inner sense is the individual will
of the knowing subject. Time is therefore the form by means of which
self-consciousness becomes possible for the individual will, which
originally and in itself is without knowledge. In it the nature of the
will, which in itself is simple and identical, appears drawn out into a
course of life. But just on account of this original simplicity and
identity of what thus exhibits itself, its _character_ remains always
precisely the same, and hence also the course of life itself retains
throughout the same key-note, indeed its multifarious events and scenes
are at bottom just like variations of one and the same theme.
The _a priori nature of the law of causality_ has, by Englishmen and
Frenchmen, sometimes not been seen at all, sometimes not rightly conceived
of; and therefore some of them still prosecute the earlier attempts to
find for it an _empirical_ origin. Maine de Biran places this in the
experience that the act of will as cause is followed by the movement of
the body as effect. But this fact itself is untrue. We certainly do not
recognise the really immediate act of will as something different from the
action of the body, and the two as connected by the bond of causality; but
both are one and indivisible. Between them there is no succession; they
are simultaneous. They are one and the same thing, apprehended in a double
manner. That which makes itself known to inner apprehension
(self-consciousness) as the real _act of will_ exhibits itself at once in
external perception, in which the body exists objectively as an _action_
of the body. That physiologically the action of the nerve precedes that of
the muscle is here immaterial, for it does not come within
self-consciousness; and we are not speaking here of the relation between
muscle and nerve, but of that between the act of will and the action of
the body. Now this does not present itself as a causal relation. If these
two presented themselves to us as cause and effect their connection would
not be so incomprehensible to us as it actually is; for what we understand
from its cause we understand as far as there is an understanding of things
generally. On the other hand, the movement of our limbs by means of mere
acts of will is indeed a miracle of such common occurrence that we no
longer observe it; but if we once turn our attention to it we become
keenly conscious of the incomprehensibility of the matter, just because in
this we have something before us which we do _not_ understand as the
effect of a cause. This apprehension, then, could never lead us to the
idea of causality, for that never appears in it at all. Maine de Biran
himself recognises the perfect simultaneousness of the act of will and the
movement (_Nouvelles Considérations des Rapports du Physique au Moral_, p.
377, 378). In England Thomas Reid (On the First Principles of Contingent
Truths, Essay IV. c. 5) already asserted that the knowledge of the causal
relation has its ground in the nature of the faculty of knowledge itself.
Quite recently Thomas Brown, in his very tediously composed book, “Inquiry
into the Relation of Cause and Effect,” 4th edit., 1835, says much the
same thing, that that knowledge springs from an innate, intuitive, and
instinctive conviction; thus he is at bottom upon the right path. Quite
unpardonable, however, is the crass ignorance on account of which in this
book of 476 pages, of which 130 are devoted to the refutation of Hume,
absolutely no mention is made of Kant, who cleared up the question more
than seventy years ago. If Latin had remained the exclusive language of
science such a thing would not have occurred. In spite of Brown’s
exposition, which in the main is correct, a modification of the doctrine
set up by Maine de Biran, of the empirical origin of the fundamental
knowledge of the causal relation, has yet found acceptance in England; for
it is not without a certain degree of plausibility. It is this, that we
abstract the law of causality from the perceived effect of our own body
upon other bodies. This was already refuted by Hume. I, however, have
shown that it is untenable in my work, “_Ueber den Willen in der Natur_”
(p. 75 of the second edition, p. 82 of the third), from the fact that
since we apprehend both our own and other bodies objectively in spatial
perception, the knowledge of causality must already be there, because it
is a condition of such perception. The one genuine proof that we are
conscious of the law of causality _before all experience_ lies in the
necessity of making a _transition_ from the sensation, which is only
empirically given, to its _cause_, in order that it may become perception
of the external world. Therefore I have substituted this proof for the
Kantian, the incorrectness of which I have shown. A most full and thorough
exposition of the whole of this important subject, which is only touched
on here, the _a priori_ nature of the law of causality and the
intellectual nature of empirical perception, will be found in my essay on
the principle of sufficient reason, § 21, to which I refer, in order to
avoid the necessity of repeating here what is said there. I have also
shown there the enormous difference between the mere sensation of the
senses and the perception of an objective world, and discovered the wide
gulf that lies between the two. The law of causality alone can bridge
across this gulf, and it presupposes for its application the two other
forms which are related to it, space and time. Only by means of these
three combined is the objective idea attained to. Now whether the
sensation from which we start to arrive at apprehension arises through the
resistance which is suffered by our muscular exertion, or through the
impression of light upon the retina, or of sound upon the nerves of the
brain, &c. &c., is really a matter of indifference. The _sensation_ always
remains a mere _datum_ for the _understanding_, which alone is capable of
apprehending it as the effect of a cause different from itself, which the
understanding now perceives as external, _i.e._, as something occupying
and filling space, which is also a form inherent in the intellect prior to
all experience. Without this intellectual operation, for which the forms
must lie ready in us, the perception of an _objective, external world_
could never arise from a mere _sensation_ within our skin. How can it ever
be supposed that the mere feeling of being hindered in intended motion,
which occurs also in lameness, could be sufficient for this? We may add to
this that before I attempt to affect external things _they_ must
necessarily have affected me as motives. But this almost presupposes the
apprehension of the external world. According to the theory in question
(as I have remarked in the place referred to above), a man born without
arms and legs could never attain to the idea of causality, and
consequently could never arrive at the apprehension of the external world.
But that this is not the case is proved by a fact communicated in
Froriep’s _Notizen_, July 1838, No. 133—the detailed account, accompanied
by a likeness, of an Esthonian girl, Eva Lauk, then fourteen years old,
who was born entirely without arms or legs. The account concludes with
these words: “According to the evidence of her mother, her mental
development had been quite as quick as that of her brothers and sisters;
she attained just as soon as they did to a correct judgment of size and
distance, yet without the assistance of hands.—Dorpat, 1st March 1838, Dr.
A. Hueck.”
Hume’s doctrine also, that the conception of causality arises from the
custom of seeing two states constantly following each other, finds a
practical refutation in the oldest of all successions, that of day and
night, which no one has ever held to be cause and effect of each other.
And the same succession also refutes Kant’s false assertion that the
_objective_ reality of a succession is only known when we apprehend the
two succeeding events as standing in the relation of cause and effect to
each other. Indeed the converse of this doctrine of Kant’s is true. We
know which of the two connected events is the cause and which the effect,
_empirically_, only in the succession. Again, on the other hand, the
absurd assertion of several professors of philosophy in our own day that
cause and effect are simultaneous can be refuted by the fact that in cases
in which the succession cannot be perceived on account of its great
rapidity, we yet assume it with certainty _a priori_, and with it the
lapse of a certain time. Thus, for example, we know that a certain time
must elapse between the falling of the flint and the projection of the
bullet, although we cannot perceive it, and that this time must further be
divided between several events that occur in a strictly determined
succession—the falling of the flint, the striking of the spark, ignition,
the spread of the fire, the explosion, and the projection of the bullet.
No man ever perceived this succession of events; but because we know which
is the cause of the others, we thereby also know which must _precede the
others in time_, and consequently also that during the course of the whole
series a certain time must elapse, although it is so short that it escapes
our empirical apprehension; for no one will assert that the projection of
the bullet is actually simultaneous with the falling of the flint. Thus
not only the law of causality, but also its relation to _time_, and the
necessity of the _succession_ of cause and effect, is known to us _a
priori_. If we know which of two events is the cause and which is the
effect, we also know which precedes the other in time; if, on the
contrary, we do not know which is cause and which effect, but only know in
general that they are causally connected, we seek to discover the
succession empirically, and according to that we determine which is the
cause and which the effect. The falseness of the assertion that cause and
effect are simultaneous further appears from the following consideration.
An unbroken chain of causes and effects fills the whole of time. (For if
this chain were broken the world would stand still, or in order to set it
in motion again an effect without a cause would have to appear.) Now if
every effect were simultaneous with its cause, then every effect would be
moved up into the time of its cause, and a chain of causes and effects
containing as many links as before would fill no time at all, still less
an infinite time, but would be all together in one moment. Thus, under the
assumption that cause and effect are simultaneous, the course of the world
shrinks up into an affair of a moment. This proof is analogous to the
proof that every sheet of paper must have a certain thickness, because
otherwise the whole book would have none. To say _when_ the cause ceases
and the effect begins is in almost all cases difficult, and often
impossible. For the _changes_ (_i.e._, the succession of states) are
continuous, like the time which they fill, and therefore also, like it,
they are infinitely divisible. But their succession is as necessarily
determined and as unmistakable as that of the moments of time itself, and
each of them is called, with reference to the one which precedes it,
“effect,” and with reference to the one which follows it, “cause.”
_Every change in the material world can only take place because another
has immediately preceded it_: this is the true and the whole content of
the law of causality. But no conception has been more misused in
philosophy than that of _cause_, by means of the favourite trick or
blunder of conceiving it too widely, taking it too generally, through
abstract thinking. Since Scholasticism, indeed properly since Plato and
Aristotle, philosophy has been for the most part a _systematic misuse of
general conceptions_. Such, for example, are substance, ground, cause, the
good, perfection, necessity, and very many others. A tendency of the mind
to work with such abstract and too widely comprehended conceptions has
shown itself almost at all times. It may ultimately rest upon a certain
indolence of the intellect, which finds it too difficult a task to be
constantly controlling thought by perception. By degrees such unduly wide
conceptions come to be used almost like algebraical symbols, and tossed
about like them, and thus philosophy is reduced to a mere process of
combination, a kind of reckoning which (like all calculations) employs and
demands only the lower faculties. Indeed there finally results from this a
mere juggling with words, of which the most shocking example is afforded
us by the mind-destroying Hegelism, in which it is carried to the extent
of pure nonsense. But Scholasticism also often degenerated into
word-juggling. Nay even the “Topi” of Aristotle—very abstract principles,
conceived with absolute generality, which one could apply to the most
different kinds of subjects, and always bring into the field in arguing
either _pro_ or _contra_—have also their origin in this misuse of general
conceptions. We find innumerable examples of the way the Schoolmen worked
with such abstractions in their writings, especially in those of Thomas
Aquinas. But philosophy really pursued the path which was entered on by
the Schoolmen down to the time of Locke and Kant, who at last bethought
themselves as to the origin of conceptions. Indeed we find Kant himself,
in his earlier years, still upon that path, in his “Proof of the Existence
of God” (p. 191 of the first volume of Rosenkranz’s edition), where the
conceptions substance, ground, reality, are used in such a way as would
never have been possible if he had gone back to the _source_ of these
conceptions and to their _true content_ which is determined thereby. For
then he would have found as the source and content of _substance_ simply
matter, of ground (if things of the real world are in question) simply
cause, that is, the prior change which brings about the later change, &c.
It is true that in this case such an investigation would not have led to
the intended result. But everywhere, as here, such unduly wide
conceptions, under which, therefore, more was subsumed than their true
content would have justified, there have arisen false principles, and from
these false systems. Spinoza’s whole method of demonstration rests upon
such uninvestigated and too widely comprehended conceptions. Now here lies
the great merit of Locke, who, in order to counteract all that dogmatic
unreality, insisted upon the investigation of the _origin of the
conceptions_, and thus led back to _perception and experience_. Bacon had
worked in a similar frame of mind, yet more with reference to Physics than
to Metaphysics. Kant followed the path entered upon by Locke, but in a
higher sense and much further, as has already been mentioned above. To the
men of mere show who succeeded in diverting the attention of the public
from Kant to themselves the results obtained by Locke and Kant were
inconvenient. But in such a case they know how to ignore both the dead and
the living. Thus without hesitation they forsook the only right path which
had at last been found by those wise men, and philosophised at random with
all kinds of indiscriminately collected conceptions, unconcerned as to
their origin and content, till at last the substance of the Hegelian
philosophy, wise beyond measure, was that the conceptions had no origin at
all, but were rather themselves the origin and source of things. But Kant
has erred in this respect. He has too much neglected empirical perception
for the sake of _pure_ perception—a point which I have fully discussed in
my criticism of his philosophy. With me perception is throughout the
source of all knowledge. I early recognised the misleading and insidious
nature of abstractions, and in 1813, in my essay on the principle of
sufficient reason, I pointed out the difference of the relations which are
thought under _this_ conception. General conceptions must indeed be the
material in which philosophy deposits and stores up its knowledge, but not
the source from which it draws it; the _terminus ad quem_, not _a quo_. It
is not, as Kant defines it, a science _drawn from_ conceptions, but a
science _in_ conceptions. Thus the conception of causality also, with
which we are here concerned, has always been taken far too widely by
philosophers for the furtherance of their dogmatic ends, and much was
imported into it which does not belong to it at all. Hence arose
propositions such as the following: “All that is has its cause”—“the
effect cannot contain more than the cause, thus nothing that was not also
in the cause”—“_causa est nobilior suo effectu_,” and many others just as
unwarranted. The following subtilty of that insipid gossip Proclus affords
an elaborate and specially lucid example of this. It occurs in his
“_Institutio Theologica_,” § 76: “Παν το απο ακινητου γιγνομενον αιτιας,
αμεταβλητον εχει την ὑπαρξιν; παν δε το απο κινουμενης, μεταβλητην; ει γαρ
ακινητον εστι παντῃ το ποιουν, ου δια κινησεως, αλλ᾽ αυτῳ τῳ ειναι παραγει
το δευτερον αφ᾽ ἑαυτου.” (_Quidquid ab immobili causa manat, immutabilem
habet essentiam [substantiam]. Quidquid vero a mobili causa manat,
essentiam habet mutabilem. Si enim illud, quod aliquid facit, est prorsus
immobile, non per motum, sed per ipsum Esse producit ipsum secundum ex se
ipso._) Excellent! But just show me a cause which is not itself set in
motion: it is simply impossible. But here, as in so many cases,
abstraction has thought away all determinations down to that one which it
is desired to make use of without regard to the fact that the latter
cannot exist without the former. The only correct expression of the law of
causality is this: _Every change has its cause in another change which
immediately precedes it_. If something _happens_, _i.e._, if a new state
of things appears, _i.e._, if something is _changed_, then something else
must have _changed_ immediately before, and something else again before
this, and so on _ad infinitum_, for a _first_ cause is as impossible to
conceive as a beginning of time or a limit of space. More than this the
law of causality does not assert. Thus its claims only arise in the case
of _changes_. So long as nothing changes there can be no question of a
cause. For there is no _a priori_ ground for inferring from the existence
of given things, _i.e._, states of matter, their previous non-existence,
and from this again their coming into being, that is to say, there is no
_a priori_ ground for inferring a change. Therefore the mere existence of
a thing does not justify us in inferring that it has a cause. Yet there
may be _a posteriori_ reasons, that is, reasons drawn from previous
experience, for the assumption that the present state or condition did not
always exist, but has only come into existence in consequence of another
state, and therefore by means of a change, the cause of which is then to
be sought, and also the cause of this cause. Here then we are involved in
the _infinite regressus_ to which the application of the law of causality
always leads. We said above: “_Things_, _i.e._, _states or conditions of
matter,_” for _change_ and _causality_ have only to do with states or
conditions. It is these states which we understand by _form_, in the wider
sense; and only the forms change, the matter is permanent. Thus it is only
the form which is subject to the law of causality. But the form
constitutes the _thing_, _i.e._, it is the ground of _the difference_ of
things; while matter must be thought as the same in all. Therefore the
Schoolmen said, “_Forma dat esse rei;_” more accurately this proposition
would run: _Forma dat rei essentiam, materia existentiam_. Therefore the
question as to the cause of a _thing_ always concerns merely its form,
_i.e._, its state or quality, and not its matter, and indeed only the
former so far as we have grounds for assuming that it has not _always_
existed, but has come into being by means of a _change_. The union of
_form_ and _matter_, or of _essentia_ and _existentia_, gives the
_concrete_, which is always particular; thus, the _thing_. And it is the
_forms_ whose union with _matter_, _i.e._, whose appearance in matter by
means of a _change_, are subject to the law of causality. By taking the
conception _too widely_ in the abstract the mistake slipped in of
extending causality to the thing absolutely, that is, to its whole inner
nature and existence, thus also to matter, and ultimately it was thought
justifiable to ask for a cause of the world itself. This is the origin of
the _cosmological proof_. This proof begins by inferring from the
existence of the world its non-existence, which preceded its existence,
and such an inference is quite unjustifiable; it ends, however, with the
most fearful inconsistency, for it does away altogether with the law of
causality, from which alone it derives all its evidencing power, for it
stops at a first cause, and will not go further; thus ends, as it were, by
committing parricide, as the bees kill the drones after they have served
their end. All the talk about the _absolute_ is referable to a shamefast,
and therefore disguised cosmological proof, which, in the face of the
“Critique of Pure Reason,” has passed for philosophy in Germany for the
last sixty years. What does the absolute mean? Something that is, and of
which (under pain of punishment) we dare not ask further whence and why it
is. A precious rarity for professors of philosophy! In the case, however,
of the honestly expressed cosmological proof, through the assumption of a
first cause, and therefore of a first beginning in a time which has
absolutely no beginning, this beginning is always pushed further back by
the question: Why not earlier? And so far back indeed that one never gets
down from it to the present, but is always marvelling that the present
itself did not occur already millions of years ago. In general, then, the
law of causality applies to all things in the world, but not to the world
itself, for it is _immanent_ in the world, not _transcendent; with_ it it
comes into action, and _with_ it it is abolished. This depends ultimately
upon the fact that it belongs to the mere form of our understanding, like
the whole of the objective world, which accordingly is merely phenomenal,
and is conditioned by the understanding. Thus the law of causality has
full application, without any exception, to all things in the world, of
course in respect of their form, to the variation of these forms, and thus
to their changes. It is valid for the actions of men as for the impact of
a stone, yet, as we have said always, merely with regard to events, to
_changes_. But if we abstract from its origin in the understanding and try
to look at it as purely objective, it will be found in ultimate analysis
to depend upon the fact that everything that acts does so by virtue of its
original, and therefore eternal or timeless, power; therefore its present
effect would necessarily have occurred infinitely earlier, that is, before
all conceivable time, but that it lacked the temporal condition. This
temporal condition is the occasion, _i.e._, the cause, on account of which
alone the effect only takes place _now_, but now takes place necessarily;
the cause assigns it its place in time.
But in consequence of that unduly wide view in abstract thought of the
conception _cause_, which was considered above, it has been confounded
with the conception of _force_. This is something completely different
from the cause, but yet is that which imparts to every cause its
causality, _i.e._, the capability of producing an effect. I have explained
this fully and thoroughly in the second book of the first volume, also in
“The Will in Nature,” and finally also in the second edition of the essay
on the principle of sufficient reason, § 20, p. 44 (third edition, p. 45).
This confusion is to be found in its most aggravated form in Maine de
Biran’s book mentioned above, and this is dealt with more fully in the
place last referred to; but apart from this it is also very common; for
example, when people seek for the cause of any original force, such as
gravitation. Kant himself (_Über den Einzig Möglichen Beweisgrund_, vol.
i. p. 211-215 of Rosenkranz’s edition) calls the forces of nature
“efficient causes,” and says “gravity is a cause.” Yet it is impossible to
see to the bottom of his thought so long as force and cause are not
distinctly recognised as completely different. But the use of abstract
conceptions leads very easily to their confusion if the consideration of
their origin is set aside. The knowledge of causes and effects, always
_perceptive_, which rests on the form of the understanding, is neglected
in order to stick to the abstraction _cause_. In this way alone is the
conception of causality, with all its simplicity, so very frequently
wrongly apprehended. Therefore even in Aristotle (“Metaph.,” iv. 2) we
find causes divided into four classes which are utterly falsely, and
indeed crudely conceived. Compare with it my classification of causes as
set forth for the first time in my essay on sight and colour, chap. 1, and
touched upon briefly in the sixth paragraph of the first volume of the
present work, but expounded at full length in my prize essay on the
freedom of the will, p. 30-33. Two things in nature remain untouched by
that chain of causality which stretches into infinity in both directions;
these are matter and the forces of nature. They are both conditions of
causality, while everything else is conditioned by it. For the one
(matter) is that _in_ which the states and their changes appear; the other
(forces of nature) is that by virtue of which alone they can appear at
all. Here, however, one must remember that in the second book, and later
and more thoroughly in “The Will in Nature,” the natural forces are shown
to be identical with the will in us; but matter appears as the mere
_visibility of the will_; so that ultimately it also may in a certain
sense be regarded as identical with the will.
On the other hand, not less true and correct is what is explained in § 4
of the first book, and still better in the second edition of the essay on
the principle of sufficient reason at the end of § 21, p. 77 (third
edition, p. 82), that matter is causality itself objectively comprehended,
for its entire nature consists in _acting in general_, so that it itself
is thus the activity (ενεργεια = reality) of things generally, as it were
the abstraction of all their different kinds of acting. Accordingly, since
the essence, _essentia_, of matter consists in _action in general_, and
the reality, _existentia_, of things consists in their materiality, which
thus again is one with action in general, it may be asserted of matter
that in it _existentia_ and _essentia_ unite and are one, for it has no
other attribute than _existence itself_ in general and independent of all
fuller definitions of it. On the other hand, all _empirically_ given
matter, thus all material or matter in the special sense (which our
ignorant materialists at the present day confound with matter), has
already entered the framework of the _forms_ and manifests itself only
through their qualities and accidents, because in experience every action
is of quite a definite and special kind, and is never merely general.
Therefore pure matter is an object of _thought_ alone, not of
_perception_, which led Plotinus (_Enneas II._, lib. iv., c. 8 & 9) and
Giordano Bruno (_Della Causa_, dial. 4) to make the paradoxical assertion
that matter has no extension, for extension is inseparable from the form,
and that therefore it is _incorporeal_. Yet Aristotle had already taught
that it is not a body although it is corporeal: “σωμα μεν ουκ αν ειη,
σωματικη δε” (_Stob. Ecl._, lib. i., c. 12, § 5). In reality we think
under _pure matter_ only action, in the abstract, quite independent of the
_kind_ of action, thus _pure causality_ itself; and as such it is not an
_object_ but a _condition_ of experience, just like space and time. This
is the reason why in the accompanying table of our pure _a priori_
knowledge matter is able to take the place of causality, and therefore
appears along with space and time as the third pure form, and therefore as
dependent on our intellect.
This table contains all the fundamental truths which are rooted in our
perceptive or intuitive knowledge _a priori_, expressed as first
principles independent of each other. What is special, however, what forms
the content of arithmetic and geometry, is not given here, nor yet what
only results from the union and application of those formal principles of
knowledge. This is the subject of the “Metaphysical First Principles of
Natural Science” expounded by Kant, to which this table in some measure
forms the propædutic and introduction, and with which it therefore stands
in direct connection. In this table I have primarily had in view the very
remarkable _parallelism_ of those _a priori_ principles of knowledge which
form the framework of all experience, but specially also the fact that, as
I have explained in § 4 of the first volume, matter (and also causality)
is to be regarded as a combination, or if it is preferred, an
amalgamation, of space and time. In agreement with this, we find that what
geometry is for the pure perception or intuition of space, and arithmetic
for that of time, Kant’s _phoronomy_ is for the pure perception or
intuition of the two _united_. For matter is primarily that which is
movable in space. The mathematical point cannot even be conceived as
movable, as Aristotle has shown (“Physics,” vi. 10). This philosopher also
himself provided the first example of such a science, for in the fifth and
sixth books of his “Physics” he determined _a priori_ the laws of rest and
motion.
Now this table may be regarded at pleasure either as a collection of the
eternal laws of the world, and therefore as the basis of our ontology, or
as a chapter of the physiology of the brain, according as one assumes the
realistic or the idealistic point of view; but the second is in the last
instance right. On this point, indeed, we have already come to an
understanding in the first chapter; yet I wish further to illustrate it
specially by an example. Aristotle’s book “_De Xenophane_,” &c., commences
with these weighty words of Xenophanes: “Αϊδιον ειναι φησιν, ει τι εστιν,
ειπερ μη ενδεχεται γενεσθαι μηδεν εκ μηδενος.” (_Æternum esse, inquit,
quicquid est, siquidem fieri non potest, ut ex nihilo quippiam existat._)
Here, then, Xenophanes judges as to the origin of things, as regards its
possibility, and of this origin he can have had no experience, even by
analogy; nor indeed does he appeal to experience, but judges
apodictically, and therefore _a priori_. How can he do this if as a
stranger he looks from without into a world that exists purely
objectively, that is, independently of his knowledge? How can he, an
ephemeral being hurrying past, to whom only a hasty glance into such a
world is permitted, judge apodictically, _a priori_ and without experience
concerning that world, the possibility of its existence and origin? The
solution of this riddle is that the man has only to do with his own ideas,
which as such are the work of his brain, and the constitution of which is
merely the manner or mode in which alone the function of his brain can be
fulfilled, _i.e._, the form of his perception. He thus judges only as to
the _phenomena of his own brain_, and declares what enters into its forms,
time, space, and causality, and what does not. In this he is perfectly at
home and speaks apodictically. In a like sense, then, the following table
of the _Prædicabilia a priori_ of time, space, and matter is to be taken:—
Prædicabilia _A Priori_.
Of Time. Of Space. Of Matter.
(1) There is only (1) There is only (1) There is only
_one_ Time, and all _one_ Space, and all _one_ Matter, and
different times are different spaces are all different
parts of it. parts of it. materials are
different states of
matter; as such it
is called
_Substance_.
(2) Different times (2) Different spaces (2) Different
are not simultaneous are not successive matters (materials)
but successive. but simultaneous. are not so through
substance but
through accidents.
(3) Time cannot be (3) Space cannot be (3) Annihilation of
thought away, but thought away, but matter is
everything can be everything can be inconceivable, but
thought away from thought away from annihilation of all
it. it. its forms and
qualities is
conceivable.
(4) Time has three (4) Space has three (4) Matter exists,
divisions, the past, dimensions—height, _i.e._, acts in all
the present, and the breadth, and length. the dimensions of
future, which space and throughout
constitute two the whole length of
directions and a time, and thus these
centre of two are united and
indifference. thereby filled. In
this consists the
true nature of
matter; thus it is
through and through
causality.
(5) Time is (5) Space is (5) Matter is
infinitely infinitely infinitely
divisible. divisible. divisible.
(6) Time is (6) Space is (6) Matter is
homogeneous and a homogeneous and a homogeneous and a
_Continuum_, _i.e._, _Continuum_, _i.e._, _Continuum_, _i.e._,
no one of its parts no one of its parts it does not consist
is different from is different from of originally
the rest, nor the rest, nor different
separated from it by separated from it by (_homoiomeria_) or
anything that is not anything that is not originally separated
time. space. parts (atoms); it is
therefore not
composed of parts,
which would
necessarily be
separated by
something that was
not matter.
(7) Time has no (7) Space has no (7) Matter has no
beginning and no limits, but all origin and no end,
end, but all limits are in it. but all coming into
beginning and end is being and passing
in it. away are in it.
(8) By reason of (8) By reason of (8) By reason of
time we count. space we measure. matter we weigh.
(9) Rhythm is only (9) Symmetry is only (9) Equilibrium is
in time. in space. only in matter.
(10) We know the (10) We know the (10) We know the
laws of time _a laws of space _a laws of the
priori_. priori_. substance of all
accidents _a
priori_.
(11) Time can be (11) Space is (11) Matter can only
perceived _a immediately be thought _a
priori_, although perceptible _a priori_.
only in the form of priori_.
a line.
(12) Time has no (12) Space can never (12) The accidents
permanence, but pass away, but change; the
passes away as soon endures through all substance remains.
as it is there. time.
(13) Time never (13) Space is (13) Matter is
rests. immovable. indifferent to rest
and motion, _i.e._,
it is originally
disposed towards
neither of the two.
(14) Everything that (14) Everything that (14) Everything
exists in time has exists in space has material has the
duration. a position. capacity for action.
(15) Time has no (15) Space has no (15) Matter is what
duration, but all motion, but all is permanent in time
duration is in it, motion is in it, and and movable in
and is the it is the change of space; by the
persistence of what position of what is comparison of what
is permanent in moved, in contrast rests with what is
contrast with its with its unbroken moved we measure
restless course. rest. duration.
(16) All motion is (16) All motion is (16) All motion is
only possible in only possible in only possible to
time. space. matter.
(17) Velocity is, in (17) Velocity is, in (17) The magnitude
equal spaces, in equal times, in of the motion, the
inverse proportion direct proportion to velocity being
to the time. the space. equal, is in direct
geometrical
proportion to the
matter (mass).
(18) Time is not (18) Space is (18) Matter as such
measurable directly measurable directly (mass) is
through itself, but through itself, and measurable, _i.e._,
only indirectly indirectly through determinable as
through motion, motion, which is in regards its quantity
which is in space time and space only indirectly,
and time together: together; hence, for only through the
thus the motion of example, an hour’s amount of the motion
the sun and of the journey, and the which it receives
clock measure time. distance of the and imparts when it
fixed stars is repelled or
expressed as the attracted.
travelling of light
for so many years.
(19) Time is (19) Space is (19) Matter is
omnipresent. Every eternal. Every part absolute. That is,
part of time is of it exists always. it neither comes
everywhere, _i.e._, into being nor
in all space, at passes away, and
once. thus its quantity
can neither be
increased nor
diminished.
(20) In time taken (20) In space taken (20, 21) Matter
by itself everything by itself everything unites the ceaseless
would be in would be flight of time with
succession. simultaneous. the rigid immobility
of space; therefore
it is the permanent
substance of the
changing accidents.
Causality determines
this change for
every place at every
time, and thereby
combines time and
space, and
constitutes the
whole nature of
matter.
(21) Time makes the (21) Space makes the
change of accidents permanence of
possible. substance possible.
(22) Every part of (22) No part of (22) For matter is
time contains all space contains the both permanent and
parts of matter. same matter as impenetrable.
another.
(23) Time is the (23) Space is the (23) Individuals are
_principium _principium material.
individuationis_. individuationis_.
(24) The now has no (24) The point has (24) The atom has no
duration. no extension. reality.
(25) Time in itself (25) Space in itself (25) Matter in
is empty and without is empty and without itself is without
properties. properties. form and quality,
and likewise inert,
_i.e._, indifferent
to rest or motion,
thus without
properties.
(26) Every moment is (26) By the position (26) Every change in
conditioned by the of every limit in matter can take
preceding moment, space with reference place only on
and is only because to any other limit, account of another
the latter has its position with change which
ceased to be. reference to every preceded it; and
(Principle of possible limit is therefore a first
sufficient reason of precisely change, and thus
existence in determined. also a first state
time.—See my essay (Principle of of matter, is just
on the principle of sufficient reason of as inconceivable as
sufficient reason.) existence in space.) a beginning of time
or a limit of space.
(Principle of
sufficient reason of
becoming.)
(27) Time makes (27) Space makes (27) Matter, as that
arithmetic possible. geometry possible. which is movable in
space, makes
phoronomy possible.
(28) The simple (28) The simple (28) The simple
element in element in geometry element in phoronomy
arithmetic is unity. is the point. is the atom.
Notes to the Annexed Table.
(1) To No. 4 of Matter.
The essence of matter is acting, it is acting itself, in the abstract,
thus acting in general apart from all difference of the kind of action: it
is through and through causality. On this account it is itself, as regards
its existence, not subject to the law of causality, and thus has neither
come into being nor passes away, for otherwise the law of causality would
be applied to itself. Since now causality is known to us _a priori_, the
conception of matter, as the indestructible basis of all that exists, can
so far take its place in the knowledge we possess _a priori_, inasmuch as
it is only the realisation of an _a priori_ form of our knowledge. For as
soon as we see anything that acts or is causally efficient it presents
itself _eo ipso_ as material, and conversely anything material presents
itself as necessarily active or causally efficient. They are in fact
interchangeable conceptions. Therefore the word “actual” is used as
synonymous with “material;” and also the Greek κατ᾽ ενεργειαν, in
opposition to κατα δυναμιν, reveals the same source, for ενεργεια
signifies action in general; so also with _actu_ in opposition to
_potentia_, and the English “actually” for “_wirklich_.” What is called
space-occupation, or impenetrability, and regarded as the essential
predicate of body (_i.e._ of what is material), is merely that _kind of
action_ which belongs to _all_ bodies without exception, the mechanical.
It is this universality alone, by virtue of which it belongs to the
conception of body, and follows _a priori_ from this conception, and
therefore cannot be thought away from it without doing away with the
conception itself—it is this, I say, that distinguishes it from any other
kind of action, such as that of electricity or chemistry, or light or
heat. Kant has very accurately analysed this space-occupation of the
mechanical mode of activity into repulsive and attractive force, just as a
given mechanical force is analysed into two others by means of the
parallelogram of forces. But this is really only the thoughtful analysis
of the phenomenon into its two constituent parts. The two forces in
conjunction exhibit the body within its own limits, that is, in a definite
volume, while the one alone would diffuse it into infinity, and the other
alone would contract it to a point. Notwithstanding this reciprocal
balancing or neutralisation, the body still acts upon other bodies which
contest its space with the first force, repelling them, and with the other
force, in gravitation, attracting all bodies in general. So that the two
forces are not extinguished in their product, as, for instance, two equal
forces acting in different directions, or +E and -E, or oxygen and
hydrogen in water. That impenetrability and gravity really exactly
coincide is shown by their empirical inseparableness, in that the one
never appears without the other, although we can separate them in thought.
I must not, however, omit to mention that the doctrine of Kant referred
to, which forms the fundamental thought of the second part of his
“Metaphysical First Principles of Natural Science,” thus of the Dynamics,
was distinctly and fully expounded before Kant by Priestley, in his
excellent “Disquisitions on Matter and Spirit,” § 1 and 2, a book which
appeared in 1777, and the second edition in 1782, while Kant’s work was
published in 1786. Unconscious recollection may certainly be assumed in
the case of subsidiary thoughts, flashes of wit, comparisons, &c., but not
in the case of the principal and fundamental thought. Shall we then
believe that Kant silently appropriated such important thoughts of another
man? and this from a book which at that time was new? Or that this book
was unknown to him, and that the same thoughts sprang up in two minds
within a short time? The explanation, also, which Kant gives, in the
“Metaphysical First Principles of Natural Science” (first edition, p. 88;
Rosenkranz’s edition, p. 384), of the real difference between fluids and
solids, is in substance already to be found in Kaspar Freidr. Wolff’s
“Theory of Generation,” Berlin 1764, p. 132. But what are we to say if we
find Kant’s most important and brilliant doctrine, that of the ideality of
space and the merely phenomenal existence of the corporeal world, already
expressed by Maupertuis thirty years earlier? This will be found more
fully referred to in Frauenstädt’s letters on my philosophy, Letter 14.
Maupertuis expresses this paradoxical doctrine so decidedly, and yet
without adducing any proof of it, that one must suppose that he also took
it from somewhere else. It is very desirable that the matter should be
further investigated, and as this would demand tiresome and extensive
researches, some German Academy might very well make the question the
subject of a prize essay. Now in the same relation as that in which Kant
here stands to Priestley, and perhaps also to Kaspar Wolff, and Maupertuis
or his predecessor, Laplace stands to Kant. For the principal and
fundamental thought of Laplace’s admirable and certainly correct theory of
the origin of the planetary system, which is set forth in his “_Exposition
du Système du Monde_,” liv. v. c. 2, was expressed by Kant nearly fifty
years before, in 1755, in his “_Naturgeschichte und Theorie des Himmels_,”
and more fully in 1763 in his “_Einzig möglichen Beweisgrund des Daseyns
Gottes_,” ch. 7. Moreover, in the later work he gives us to understand
that Lambert in his “_Kosmologischen Briefen_,” 1761, tacitly adopted that
doctrine from him, and these letters at the same time also appeared in
French (_Lettres Cosmologiques sur la Constitution de l’Univers_). We are
therefore obliged to assume that Laplace knew that Kantian doctrine.
Certainly he expounds the matter more thoroughly, strikingly, and fully,
and at the same time more simply than Kant, as is natural from his more
profound astronomical knowledge; yet in the main it is to be found clearly
expressed in Kant, and on account of the importance of the matter, would
alone have been sufficient to make his name immortal. It cannot but
disturb us very much if we find minds of the first order under suspicion
of dishonesty, which would be a scandal to those of the lowest order. For
we feel that theft is even more inexcusable in a rich man than in a poor
one. We dare not, however, be silent; for here we are posterity, and must
be just, as we hope that posterity will some day be just to us. Therefore,
as a third example, I will add to these cases, that the fundamental
thoughts of the “Metamorphosis of Plants,” by Goethe, were already
expressed by Kaspar Wolff in 1764 in his “Theory of Generation,” p. 148,
229, 243, &c. Indeed, is it otherwise with the _system of gravitation_?
the discovery of which is on the Continent of Europe always ascribed to
Newton, while in England the learned at least know very well that it
belongs to Robert Hooke, who in the year 1666, in a “Communication to the
Royal Society,” expounds it quite distinctly, although only as an
hypothesis and without proof. The principal passage of this communication
is quoted in Dugald Stewart’s “Philosophy of the Human Mind,” and is
probably taken from Robert Hooke’s Posthumous Works. The history of the
matter, and how Newton got into difficulty by it, is also to be found in
the “_Biographie Universelle_,” article Newton. Hooke’s priority is
treated as an established fact in a short history of astronomy, _Quarterly
Review_, August 1828. Further details on this subject are to be found in
my “_Parerga_,” vol. ii., § 86 (second edition, § 88). The story of the
fall of an apple is a fable as groundless as it is popular, and is quite
without authority.
(2) To No. 18 of Matter.
_The quantity of a motion_ (_quantitas motus_, already in Descartes) is
the product of the mass into the velocity.
This law is the basis not only of the doctrine of impact in mechanics, but
also of that of equilibrium in statics. From the force of impact which two
bodies with the same velocity exert the relation of their masses to each
other may be determined. Thus of two hammers striking with the same
velocity, the one which has the greater mass will drive the nail deeper
into the wall or the post deeper into the earth. For example, a hammer
weighing six pounds with a velocity = 6 effects as much as a hammer
weighing three pounds with a velocity = 12, for in both cases the quantity
of motion or the momentum = 36. Of two balls rolling at the same pace, the
one which has the greater mass will impel a third ball at rest to a
greater distance than the ball of less mass can. For the mass of the first
multiplied by the same velocity gives a _greater quantity of motion_, or a
_greater momentum_. The cannon carries further than the gun, because an
equal velocity communicated to a much greater mass gives a much _greater
quantity of motion_, which resists longer the retarding effect of gravity.
For the same reason, the same arm will throw a lead bullet further than a
stone one of equal magnitude, or a large stone further than quite a small
one. And therefore also a case-shot does not carry so far as a ball-shot.
The same law lies at the foundation of the theory of the lever and of the
balance. For here also the smaller mass, on the longer arm of the lever or
beam of the balance, has a greater velocity in falling; and multiplied by
this it may be equal to, or indeed exceed, the _quantity of motion_ or the
_momentum_ of the greater mass at the shorter arm of the lever. In the
state of rest brought about by _equilibrium_ this velocity exists merely
in intention or virtually, _potentiâ_, not _actu_; but it acts just as
well as _actu_, which is very remarkable.
The following explanation will be more easily understood now that these
truths have been called to mind.
The quantity of a given matter can only be estimated in general according
to its force, and its force can only be known in its _expression_. Now
when we are considering matter only as regards its quantity, not its
quality, this expression can only be mechanical, _i.e._, it can only
consist in motion which it imparts to other matter. For only in motion
does the force of matter become, so to speak, _alive_; hence the
expression _vis viva_ for the manifestation of force of matter in motion.
Accordingly the only measure of the quantity of a given matter is the
_quantity of its motion_, or its _momentum_. In this, however, if it is
given, the _quantity_ of matter still appears in conjunction and
amalgamated with its other factor, _velocity_. Therefore if we want to
know the quantity of matter (the mass) this other factor must be
eliminated. Now the velocity is known directly; for it is _S/T_. But the
other factor, which remains when this is eliminated, can always be known
only _relatively_ in comparison with other masses, which again can only be
known themselves by means of the _quantity of their motion_, or their
_momentum_, thus in their combination with velocity. We must therefore
compare one _quantity of motion_ with the other, and then subtract the
velocity from both, in order to see how much each of them owed to its
mass. This is done by weighing the masses against each other, in which
that _quantity of motion_ is compared which, in each of the two masses,
calls forth the attractive power of the earth that acts upon both only in
proportion to their _quantity_. Therefore there are two kinds of weighing.
Either we impart to the two masses to be compared _equal_ velocity, in
order to find out which of the two now _communicates_ motion to the other,
thus itself _has_ a greater quantity of motion, which, since the velocity
is the same on both sides, is to be ascribed to the other factor of the
_quantity of motion_ or the _momentum_, thus to the mass (common balance).
Or we weigh, by investigating how much _more velocity_ the one mass must
receive than the other has, in order to be equal to the latter in
_quantity of motion_ or _momentum_, and therefore allow no more motion to
be communicated to itself by the other; for then in proportion as its
velocity must exceed that of the other, its mass, _i.e._, the quantity of
its matter, is less than that of the other (steelyard). This estimation of
masses by weighing depends upon the favourable circumstance that the
moving force, in itself, acts upon both quite equally, and each of the two
is in a position to _communicate_ to the other directly its surplus
_quantity of motion_ or _momentum_, so that it becomes visible.
The substance of these doctrines has long ago been expressed by Newton and
Kant, but through the connection and the clearness of this exposition I
believe I have made it more intelligible, so that that insight is possible
for all which I regarded as necessary for the justification of proposition
No. 18.
Second Half. The Doctrine of the Abstract Idea, or Thinking.