mathematics, which has become the pattern and symbol of all evidence,
rests essentially not upon demonstration, but upon immediate perception,
which is thus here, as everywhere else, the ultimate ground and source of
truth. Yet the perception which lies at the basis of mathematics has a
great advantage over all other perception, and therefore over empirical
perception. It is _a priori_, and therefore independent of experience,
which is always given only in successive parts; therefore everything is
equally near to it, and we can start either from the reason or from the
consequent, as we please. Now this makes it absolutely reliable, for in it
the consequent is known from the reason, and this is the only kind of
knowledge that has necessity; for example, the equality of the sides is
known as established by the equality of the angles. All empirical
perception, on the other hand, and the greater part of experience,
proceeds conversely from the consequent to the reason, and this kind of
knowledge is not infallible, for necessity only attaches to the consequent
on account of the reason being given, and no necessity attaches to the
knowledge of the reason from the consequent, for the same consequent may
follow from different reasons. The latter kind of knowledge is simply
induction, _i.e._, from many consequents which point to one reason, the
reason is accepted as certain; but as the cases can never be all before
us, the truth here is not unconditionally certain. But all knowledge
through sense-perception, and the great bulk of experience, has only this
kind of truth. The affection of one of the senses induces the
understanding to infer a cause of the effect, but, as a conclusion from
the consequent to the reason is never certain, illusion, which is
deception of the senses, is possible, and indeed often occurs, as was
pointed out above. Only when several of the senses, or it may be all the
five, receive impressions which point to the same cause, the possibility
of illusion is reduced to a minimum; but yet it still exists, for there
are cases, for example, the case of counterfeit money, in which all the
senses are deceived. All empirical knowledge, and consequently the whole
of natural science, is in the same position, except only the pure, or as
Kant calls it, metaphysical part of it. Here also the causes are known
from the effects, consequently all natural philosophy rests upon
hypotheses, which are often false, and must then gradually give place to
more correct ones. Only in the case of purposely arranged experiments,
knowledge proceeds from the cause to the effect, that is, it follows the
method that affords certainty; but these experiments themselves are
undertaken in consequence of hypotheses. Therefore, no branch of natural
science, such as physics, or astronomy, or physiology could be discovered
all at once, as was the case with mathematics and logic, but required and
requires the collected and compared experiences of many centuries. In the
first place, repeated confirmation in experience brings the induction,
upon which the hypothesis rests, so near completeness that in practice it
takes the place of certainty, and is regarded as diminishing the value of
the hypothesis, its source, just as little as the incommensurability of
straight and curved lines diminishes the value of the application of
geometry, or that perfect exactness of the logarithm, which is not
attainable, diminishes the value of arithmetic. For as the logarithm, or
the squaring of the circle, approaches infinitely near to correctness
through infinite fractions, so, through manifold experience, the
induction, _i.e._, the knowledge of the cause from the effects,
approaches, not infinitely indeed, but yet so near mathematical evidence,
_i.e._, knowledge of the effects from the cause, that the possibility of
mistake is small enough to be neglected, but yet the possibility exists;
for example, a conclusion from an indefinite number of cases to all cases,
_i.e._, to the unknown ground on which all depend, is an induction. What
conclusion of this kind seems more certain than that all men have the
heart on the left side? Yet there are extremely rare and quite isolated
exceptions of men who have the heart upon the right side. Sense-perception
and empirical science have, therefore, the same kind of evidence. The
advantage which mathematics, pure natural science, and logic have over
them, as _a priori_ knowledge, rests merely upon this, that the formal
element in knowledge upon which all that is _a priori_ is based, is given
as a whole and at once, and therefore in it we can always proceed from the
cause to the effect, while in the former kind of knowledge we are
generally obliged to proceed from the effect to the cause. In other
respects, the law of causality, or the principle of sufficient reason of
change, which guides empirical knowledge, is in itself just as certain as
the other forms of the principle of sufficient reason which are followed
by the _a priori_ sciences referred to above. Logical demonstrations from
concepts or syllogisms have the advantage of proceeding from the reason to
the consequent, just as much as knowledge through perception _a priori_,
and therefore in themselves, _i.e._, according to their form, they are
infallible. This has greatly assisted to bring demonstration in general
into such esteem. But this infallibility is merely relative; the
demonstration merely subsumes under the first principles of the science,
and it is these which contain the whole material truth of science, and
they must not themselves be demonstrated, but must be founded on
perception. In the few _a priori_ sciences we have named above, this
perception is pure, but everywhere else it is empirical, and is only
raised to universality through induction. If, then, in the empirical
sciences also, the particular is proved from the general, yet the general,
on the other hand, has received its truth from the particular; it is only
a store of collected material, not a self-constituted foundation.
So much for the foundation of truth. Of the source and possibility of
error many explanations have been tried since Plato’s metaphorical
solution of the dove-cot where the wrong pigeons are caught, &c.
(Theætetus, p. 167, _et seq._) Kant’s vague, indefinite explanation of the
source of error by means of the diagram of diagonal motion, will be found
in the “Critique of Pure Reason,” p. 294 of the first edition, and p. 350
of the fifth. As truth is the relation of a judgment to its ground of
knowledge, it is always a problem how the person judging can believe that
he has such a ground of knowledge and yet not have it; that is to say, how
error, the deception of reason, is possible. I find this possibility quite
analogous to that of illusion, or the deception of the understanding,
which has been explained above. My opinion is (and this is what gives this
explanation its proper place here) that _every error is an inference from
the consequent to the reason_, which indeed is valid when we know that the
consequent has that reason and can have no other; but otherwise is not
valid. The person who falls into error, either attributes to a consequent
a reason which it cannot have, in which case he shows actual deficiency of
understanding, _i.e._, deficiency in the capacity for immediate knowledge
of the connection between the cause and the effect, or, as more frequently
happens, he attributes to the effect a cause which is possible, but he
adds to the major proposition of the syllogism, in which he infers the
cause from the effect, that this effect _always_ results only from this
cause. Now he could only be assured of this by a complete induction,
which, however, he assumes without having made it. This “always” is
therefore too wide a concept, and instead of it he ought to have used
“sometimes” or “generally.” The conclusion would then be problematical,
and therefore not erroneous. That the man who errs should proceed in this
way is due either to haste, or to insufficient knowledge of what is
possible, on account of which he does not know the necessity of the
induction that ought to be made. Error then is quite analogous to
illusion. Both are inferences from the effect to the cause; the illusion
brought about always in accordance with the law of causality, and by the
understanding alone, thus directly, in perception itself; the error in
accordance with all the forms of the principle of sufficient reason, and
by the reason, thus in thought itself; yet most commonly in accordance
with the law of causality, as will appear from the three following
examples, which may be taken as types or representatives of the three
kinds of error. (1.) The illusion of the senses (deception of the
understanding) induces error (deception of the reason); for example, if
one mistakes a painting for an alto-relief, and actually takes it for
such; the error results from a conclusion from the following major
premise: “If dark grey passes regularly through all shades to white; the
cause is _always_ the light, which strikes differently upon projections
and depressions, _ergo_—.” (2.) “If there is no money in my safe, the
cause is _always_ that my servant has got a key for it: _ergo_—.” (3.) “If
a ray of sunlight, broken through a prism, _i.e._, bent up or down,
appears as a coloured band instead of round and white as before, the cause
must always be that light consists of homogeneous rays, differently
coloured and refrangible to different degrees, which, when forced asunder
on account of the difference of their refrangibility, give an elongated
and variously-coloured spectrum: _ergo—bibamus!_”—It must be possible to
trace every error to such a conclusion, drawn from a major premise which
is often only falsely generalised, hypothetical, and founded on the
assumption that some particular cause is that of a certain effect. Only
certain mistakes in counting are to be excepted, and they are not really
errors, but merely mistakes. The operation prescribed by the concepts of
the numbers has not been carried out in pure intuition or perception, in
counting, but some other operation instead of it.
As regards the _content_ of the sciences generally, it is, in fact, always
the relation of the phenomena of the world to each other, according to the
principle of sufficient reason, under the guidance of the _why_, which has
validity and meaning only through this principle. _Explanation_ is the
establishment of this relation. Therefore explanation can never go further
than to show two ideas standing to each other in the relation peculiar to
that form of the principle of sufficient reason which reigns in the class
to which they belong. If this is done we cannot further be asked the
question, _why_: for the relation proved is that one which absolutely
cannot be imagined as other than it is, _i.e._, it is the form of all
knowledge. Therefore we do not ask why 2 + 2 = 4; or why the equality of
the angles of a triangle determines the equality of the sides; or why its
effect follows any given cause; or why the truth of the conclusion is
evident from the truth of the premises. Every explanation which does not
ultimately lead to a relation of which no “why” can further be demanded,
stops at an accepted _qualitas occulta_; but this is the character of
every original force of nature. Every explanation in natural science must
ultimately end with such a _qualitas occulta_, and thus with complete
obscurity. It must leave the inner nature of a stone just as much
unexplained as that of a human being; it can give as little account of the
weight, the cohesion, the chemical qualities, &c., of the former, as of
the knowing and acting of the latter. Thus, for example, weight is a
_qualitas occulta_, for it can be thought away, and does not proceed as a
necessity from the form of knowledge; which, on the contrary, is not the
case with the law of inertia, for it follows from the law of causality,
and is therefore sufficiently explained if it is referred to that law.
There are two things which are altogether inexplicable,—that is to say, do
not ultimately lead to the relation which the principle of sufficient
reason expresses. These are, first, the principle of sufficient reason
itself in all its four forms, because it is the principle of all
explanation, which has meaning only in relation to it; secondly, that to
which this principle does not extend, but which is the original source of
all phenomena; the thing-in-itself, the knowledge of which is not subject
to the principle of sufficient reason. We must be content for the present
not to understand this thing-in-itself, for it can only be made
intelligible by means of the following book, in which we shall resume this
consideration of the possible achievements of the sciences. But at the
point at which natural science, and indeed every science, leaves things,
because not only its explanation of them, but even the principle of this
explanation, the principle of sufficient reason, does not extend beyond
this point; there philosophy takes them up and treats them after its own
method, which is quite distinct from the method of science. In my essay on
the principle of sufficient reason, § 51, I have shown how in the
different sciences the chief guiding clue is one or other form of that
principle; and, in fact, perhaps the most appropriate classification of
the sciences might be based upon this circumstance. Every explanation
arrived at by the help of this clue is, as we have said, merely relative;
it explains things in relation to each other, but something which indeed
is presupposed is always left unexplained. In mathematics, for example,
this is space and time; in mechanics, physics, and chemistry it is matter,
qualities, original forces and laws of nature; in botany and zoology it is
the difference of species, and life itself; in history it is the human
race with all its properties of thought and will: in all it is that form
of the principle of sufficient reason which is respectively applicable. It
is peculiar to _philosophy_ that it presupposes nothing as known, but
treats everything as equally external and a problem; not merely the
relations of phenomena, but also the phenomena themselves, and even the
principle of sufficient reason to which the other sciences are content to
refer everything. In philosophy nothing would be gained by such a
reference, as one member of the series is just as external to it as
another; and, moreover, that kind of connection is just as much a problem
for philosophy as what is joined together by it, and the latter again is
just as much a problem after its combination has been explained as before
it. For, as we have said, just what the sciences presuppose and lay down
as the basis and the limits of their explanation, is precisely and
peculiarly the problem of philosophy, which may therefore be said to begin
where science ends. It cannot be founded upon demonstrations, for they
lead from known principles to unknown, but everything is equally unknown
and external to philosophy. There can be no principle in consequence of
which the world with all its phenomena first came into existence, and
therefore it is not possible to construct, as Spinoza wished, a philosophy
which demonstrates _ex firmis principiis_. Philosophy is the most general
rational knowledge, the first principles of which cannot therefore be
derived from another principle still more general. The principle of
contradiction establishes merely the agreement of concepts, but does not
itself produce concepts. The principle of sufficient reason explains the
connections of phenomena, but not the phenomena themselves; therefore
philosophy cannot proceed upon these principles to seek a _causa
efficiens_ or a _causa finalis_ of the whole world. My philosophy, at
least, does not by any means seek to know _whence_ or _wherefore_ the
world exists, but merely _what_ the world is. But the _why_ is here
subordinated to the _what_, for it already belongs to the world, as it
arises and has meaning and validity only through the form of its
phenomena, the principle of sufficient reason. We might indeed say that
every one knows what the world is without help, for he is himself that
subject of knowledge of which the world is the idea; and so far this would
be true. But that knowledge is empirical, is in the concrete; the task of
philosophy is to reproduce this in the abstract to raise to permanent
rational knowledge the successive changing perceptions, and in general,
all that is contained under the wide concept of feeling and merely
negatively defined as not abstract, distinct, rational knowledge. It must
therefore consist of a statement in the abstract, of the nature of the
whole world, of the whole, and of all the parts. In order then that it may
not lose itself in the endless multitude of particular judgments, it must
make use of abstraction and think everything individual in the universal,
and its differences also in the universal. It must therefore partly
separate and partly unite, in order to present to rational knowledge the
whole manifold of the world generally, according to its nature,
comprehended in a few abstract concepts. Through these concepts, in which
it fixes the nature of the world, the whole individual must be known as
well as the universal, the knowledge of both therefore must be bound
together to the minutest point. Therefore the capacity for philosophy
consists just in that in which Plato placed it, the knowledge of the one
in the many, and the many in the one. Philosophy will therefore be a
sum-total of general judgments, whose ground of knowledge is immediately
the world itself in its entirety, without excepting anything; thus all
that is to be found in human consciousness; it will be _a complete
recapitulation, as it were, a reflection, of the world in abstract
concepts_, which is only possible by the union of the essentially
identical in _one_ concept and the relegation of the different to another.
This task was already prescribed to philosophy by Bacon of Verulam when he
said: _ea demum vera est philosophia, quae mundi ipsius voces fidelissime
reddit, et veluti dictante mundo conscripta est, et nihil aliud est, quam
ejusdem_ SIMULACRUM ET REFLECTIO, _neque addit quidquam de proprio, sed
tantum iterat et resonat_ (De Augm. Scient., L. 2, c. 13). But we take
this in a wider sense than Bacon could then conceive.
The agreement which all the sides and parts of the world have with each
other, just because they belong to a whole, must also be found in this
abstract copy of it. Therefore the judgments in this sum-total could to a
certain extent be deduced from each other, and indeed always reciprocally
so deduced. Yet to make the first judgment possible, they must all be
present, and thus implied as prior to it in the knowledge of the world in
the concrete, especially as all direct proof is more certain than indirect
proof; their harmony with each other by virtue of which they come together
into the unity of _one_ thought, and which arises from the harmony and
unity of the world of perception itself, which is their common ground of
knowledge, is not therefore to be made use of to establish them, as that
which is prior to them, but is only added as a confirmation of their
truth. This problem itself can only become quite clear in being
solved.(23)
§ 16. After this full consideration of reason as a special faculty of
knowledge belonging to man alone, and the results and phenomena peculiar
to human nature brought about by it, it still remains for me to speak of
reason, so far as it is the guide of human action, and in this respect may
be called _practical_. But what there is to say upon this point has found
its place elsewhere in the appendix to this work, where I controvert the
existence of the so-called practical reason of Kant, which he (certainly
very conveniently) explained as the immediate source of virtue, and as the
seat of an absolute (_i.e._, fallen from heaven) imperative. The detailed
and thorough refutation of this Kantian principle of morality I have given
later in the “Fundamental Problems of Ethics.” There remains, therefore,
but little for me to say here about the actual influence of reason, in the
true sense of the word, upon action. At the commencement of our treatment
of reason we remarked, in general terms, how much the action and behaviour
of men differs from that of brutes, and that this difference is to be
regarded as entirely due to the presence of abstract concepts in
consciousness. The influence of these upon our whole existence is so
penetrating and significant that, on account of them, we are related to
the lower animals very much as those animals that see are related to those
that have no eyes (certain larvae, worms, and zoophytes). Animals without
eyes know only by touch what is immediately present to them in space, what
comes into contact with them; those which see, on the contrary, know a
wide circle of near and distant objects. In the same way the absence of
reason confines the lower animals to the ideas of perception, _i.e._, the
real objects which are immediately present to them in time; we, on the
contrary, on account of knowledge in the abstract, comprehend not only the
narrow actual present, but also the whole past and future, and the wide
sphere of the possible; we view life freely on all its sides, and go far
beyond the present and the actual. Thus what the eye is in space and for
sensuous knowledge, reason is, to a certain extent, in time and for inner
knowledge. But as the visibility of objects has its worth and meaning only
in the fact that it informs us of their tangibility, so the whole worth of
abstract knowledge always consists in its relation to what is perceived.
Therefore men naturally attach far more worth to immediate and perceived
knowledge than to abstract concepts, to that which is merely thought; they
place empirical knowledge before logical. But this is not the opinion of
men who live more in words than in deeds, who have seen more on paper and
in books than in actual life, and who in their greatest degeneracy become
pedants and lovers of the mere letter. Thus only is it conceivable that
Leibnitz and Wolf and all their successors could go so far astray as to
explain knowledge of perception, after the example of Duns Scotus, as
merely confused abstract knowledge! To the honour of Spinoza, I must
mention that his truer sense led him, on the contrary, to explain all
general concepts as having arisen from the confusion of that which was
known in perception (Eth. II., prop. 40, Schol. 1). It is also a result of
perverted opinion that in mathematics the evidence proper to it was
rejected, and logical evidence alone accepted; that everything in general
which was not abstract knowledge was comprehended under the wide name of
feeling, and consequently was little valued; and lastly that the Kantian
ethics regarded the good will which immediately asserts itself upon
knowledge of the circumstances, and guides to right and good action as
mere feeling and emotion, and consequently as worthless and without merit,
and would only recognise actions which proceed from abstract maxims as
having moral worth.