they stand in a necessary relation to them, without which they would be
nothing. This relation therefore constitutes the whole nature and
existence of concepts. Reflection is the necessary copy or repetition of
the originally presented world of perception, but it is a special kind of
copy in an entirely different material. Thus concepts may quite properly
be called ideas of ideas. The principle of sufficient reason has here also
a special form. Now we have seen that the form under which the principle
of sufficient reason appears in a class of ideas always constitutes and
exhausts the whole nature of the class, so far as it consists of ideas, so
that time is throughout succession, and nothing more; space is throughout
position, and nothing more; matter is throughout causation, and nothing
more. In the same way the whole nature of concepts, or the class of
abstract ideas, consists simply in the relation which the principle of
sufficient reason expresses in them; and as this is the relation to the
ground of knowledge, the whole nature of the abstract idea is simply and
solely its relation to another idea, which is its ground of knowledge.
This, indeed, may, in the first instance, be a concept, an abstract idea,
and this again may have only a similar abstract ground of knowledge; but
the chain of grounds of knowledge does not extend _ad infinitum_; it must
end at last in a concept which has its ground in knowledge of perception;
for the whole world of reflection rests on the world of perception as its
ground of knowledge. Hence the class of abstract ideas is in this respect
distinguished from other classes; in the latter the principle of
sufficient reason always demands merely a relation to another idea of the
_same_ class, but in the case of abstract ideas, it at last demands a
relation to an idea of _another_ class.
Those concepts which, as has just been pointed out, are not immediately
related to the world of perception, but only through the medium of one, or
it may be several other concepts, have been called by preference
_abstracta_, and those which have their ground immediately in the world of
perception have been called _concreta_. But this last name is only loosely
applicable to the concepts denoted by it, for they are always merely
_abstracta_, and not ideas of perception. These names, which have
originated in a very dim consciousness of the distinctions they imply, may
yet, with this explanation, be retained. As examples of the first kind of
concepts, _i.e._, _abstracta_ in the fullest sense, we may take
“relation,” “virtue,” “investigation,” “beginning,” and so on. As examples
of the second kind, loosely called _concreta_, we may take such concepts
as “man,” “stone,” “horse,” &c. If it were not a somewhat too pictorial
and therefore absurd simile, we might very appropriately call the latter
the ground floor, and the former the upper stories of the building of
reflection.(13)
It is not, as is commonly supposed, an essential characteristic of a
concept that it should contain much under it, that is to say, that many
ideas of perception, or it may be other abstract ideas, should stand to it
in the relation of its ground of knowledge, _i.e._, be thought through it.
This is merely a derived and secondary characteristic, and, as a matter of
fact, does not always exist, though it must always exist potentially. This
characteristic arises from the fact that a concept is an idea of an idea,
_i.e._, its whole nature consists in its relation to another idea; but as
it is not this idea itself, which is generally an idea of perception and
therefore belongs to quite a different class, the latter may have
temporal, spacial, and other determinations, and in general many relations
which are not thought along with it in the concept. Thus we see that
several ideas which are different in unessential particulars may be
thought by means of one concept, _i.e._, may be brought under it. Yet this
power of embracing several things is not an essential but merely an
accidental characteristic of the concept. There may be concepts through
which only one real object is thought, but which are nevertheless abstract
and general, by no means capable of presentation individually and as
perceptions. Such, for example, is the conception which any one may have
of a particular town which he only knows from geography; although only
this one town is thought under it, it might yet be applied to several
towns differing in certain respects. We see then that a concept is not
general because of being abstracted from several objects; but conversely,
because generality, that is to say, non-determination of the particular,
belongs to the concept as an abstract idea of the reason, different things
can be thought by means of the same one.
It follows from what has been said that every concept, just because it is
abstract and incapable of presentation in perception, and is therefore not
a completely determined idea, has what is called extension or sphere, even
in the case in which only one real object exists that corresponds to it.
Now we always find that the sphere of one concept has something in common
with the sphere of other concepts. That is to say, part of what is thought
under one concept is the same as what is thought under other concepts; and
conversely, part of what is thought under these concepts is the same as
what is thought under the first; although, if they are really different
concepts, each of them, or at least one of them, contains something which
the other does not contain; this is the relation in which every subject
stands to its predicate. The recognition of this relation is called
judgment. The representation of these spheres by means of figures in
space, is an exceedingly happy idea. It first occurred to Gottfried
Plouquet, who used squares for the purpose. Lambert, although later than
him, used only lines, which he placed under each other. Euler carried out
the idea completely with circles. Upon what this complete analogy between
the relations of concepts, and those of figures in space, ultimately
rests, I am unable to say. It is, however, a very fortunate circumstance
for logic that all the relations of concepts, according to their
possibility, _i.e._, _a priori_, may be made plain in perception by the
use of such figures, in the following way:—
(1.) The spheres of two concepts coincide: for example the concept of
necessity and the concept of following from given grounds, in the same way
the concepts of _Ruminantia_ and _Bisulca_ (ruminating and cloven-hoofed
animals), also those of vertebrate and red-blooded animals (although there
might be some doubt about this on account of the annelida): they are
convertible concepts. Such concepts are represented by a single circle
which stands for either of them.
(2.) The sphere of one concept includes that of the other.
[Illustration: Category "horse" within category "animal".]
(3.) A sphere includes two or more spheres which exclude each other and
fill it.
[Illustration: Circle divided into thirds "right", "acute", and "obtuse".]
(4.) Two spheres include each a part of the other.
[Illustration: Two overlapping circles, one "flower" and one "red".]
(5.) Two spheres lie in a third, but do not fill it.
[Illustration: A large circle, "matter", within which are two other
circles, "water" and "earth".]
This last case applies to all concepts whose spheres have nothing
immediately in common, for there is always a third sphere, often a much
wider one, which includes both.
To these cases all combinations of concepts may be referred, and from them
the entire doctrine of the judgment, its conversion, contraposition,
equipollence, disjunction (this according to the third figure) may be
deduced. From these also may be derived the properties of the judgment,
upon which Kant based his pretended categories of the understanding, with
the exception however of the hypothetical form, which is not a combination
of concepts, but of judgments. A full account is given in the Appendix of
“Modality,” and indeed of every property of judgments on which the
categories are founded.
With regard to the possible combinations of concepts which we have given,
it has only further to be remarked that they may also be combined with
each other in many ways. For example, the fourth figure with the second.
Only if one sphere, which partly or wholly contains another, is itself
contained in a third sphere, do these together exemplify the syllogism in
the first figure, _i.e._, that combination of judgments, by means of which
it is known that a concept which is partly or wholly contained in another
concept, is also contained in a third concept, which again contains the
first: and also, conversely, the negation; the pictorial representation of
which can, of course, only be two connected spheres which do not lie
within a third sphere. If many spheres are brought together in this way we
get a long train of syllogisms. This schematism of concepts, which has
already been fairly well explained in more than one textbook, may be used
as the foundation of the doctrine of the judgment, and indeed of the whole
syllogistic theory, and in this way the treatment of both becomes very
easy and simple. Because, through it, all syllogistic rules may be seen in
their origin, and may be deduced and explained. It is not necessary,
however, to load the memory with these rules, as logic is never of
practical use, but has only a theoretical interest for philosophy. For
although it may be said that logic is related to rational thinking as
thorough-bass is to music, or less exactly, as ethics is to virtue, or
æsthetics to art; we must yet remember that no one ever became an artist
by the study of æsthetics; that a noble character was never formed by the
study of ethics; that long before Rameau, men composed correctly and
beautifully, and that we do not need to know thorough-bass in order to
detect discords: and just as little do we need to know logic in order to
avoid being misled by fallacies. Yet it must be conceded that
thorough-bass is of the greatest use in the practice of musical
composition, although it may not be necessary for the understanding of it;
and indeed æsthetics and even ethics, though in a much less degree, and
for the most part negatively, may be of some use in practice, so that we
cannot deny them all practical worth, but of logic even this much cannot
be conceded. It is nothing more than the knowledge in the abstract of what
every one knows in the concrete. Therefore we call in the aid of logical
rules, just as little to enable us to construct a correct argument as to
prevent us from consenting to a false one, and the most learned logician
lays aside the rules of logic altogether in his actual thought. This may
be explained in the following way. Every science is a system of general
and therefore abstract truths, laws, and rules with reference to a special
class of objects. The individual case coming under these laws is
determined in accordance with this general knowledge, which is valid once
for all; because such application of the general principle is far easier
than the exhaustive investigation of the particular case; for the general
abstract knowledge which has once been obtained is always more within our
reach than the empirical investigation of the particular case. With logic,
however, it is just the other way. It is the general knowledge of the mode
of procedure of the reason expressed in the form of rules. It is reached
by the introspection of reason, and by abstraction from all content. But
this mode of procedure is necessary and essential to reason, so that it
will never depart from it if left to itself. It is, therefore, easier and
surer to let it proceed itself according to its nature in each particular
case, than to present to it the knowledge abstracted from this procedure
in the form of a foreign and externally given law. It is easier, because,
while in the case of all other sciences, the general rule is more within
our reach than the investigation of the particular case taken by itself;
with the use of reason, on the contrary, its necessary procedure in a
given case is always more within our reach than the general rule
abstracted from it; for that which thinks in us is reason itself. It is
surer, because a mistake may more easily occur in such abstract knowledge,
or in its application, than that a process of reason should take place
which would run contrary to its essence and nature. Hence arises the
remarkable fact, that while in other sciences the particular case is
always proved by the rule, in logic, on the contrary, the rule must always
be proved from the particular case; and even the most practised logician,
if he remark that in some particular case he concludes otherwise than the
rule prescribes, will always expect to find a mistake in the rule rather
than in his own conclusion. To desire to make practical use of logic
means, therefore, to desire to derive with unspeakable trouble, from
general rules, that which is immediately known with the greatest certainty
in the particular case. It is just as if a man were to consult mechanics
as to the motion of his body, and physiology as to his digestion; and
whoever has learnt logic for practical purposes is like him who would
teach a beaver to make its own dam. Logic is, therefore, without practical
utility; but it must nevertheless be retained, because it has
philosophical interest as the special knowledge of the organisation and
action of reason. It is rightly regarded as a definite, self-subsisting,
self-contained, complete, and thoroughly safe discipline; to be treated
scientifically for itself alone and independently of everything else, and
therefore to be studied at the universities. But it has its real value, in
relation to philosophy as a whole, in the inquiry into the nature of
knowledge, and indeed of rational and abstract knowledge. Therefore the
exposition of logic should not have so much the form of a practical
science, should not contain merely naked arbitrary rules for the correct
formation of the judgment, the syllogism, &c., but should rather be
directed to the knowledge of the nature of reason and the concept, and to
the detailed investigation of the principle of sufficient reason of
knowing. For logic is only a paraphrase of this principle, and, more
exactly, only of that exemplification of it in which the ground that gives
truth to the judgment is neither empirical nor metaphysical, but logical
or metalogical. Besides the principle of sufficient reason of knowing, it
is necessary to take account of the three remaining fundamental laws of
thought, or judgments of metalogical truth, so nearly related to it; and
out of these the whole science of reason grows. The nature of thought
proper, that is to say, of the judgment and the syllogism, must be
exhibited in the combination of the spheres of concepts, according to the
analogy of the special schema, in the way shown above; and from all this
the rules of the judgment and the syllogism are to be deduced by
construction. The only practical use we can make of logic is in a debate,
when we can convict our antagonist of his intentional fallacies, rather
than of his actual mistakes, by giving them their technical names. By thus
throwing into the background the practical aim of logic, and bringing out
its connection with the whole scheme of philosophy as one of its chapters,
we do not think that we shall make the study of it less prevalent than it
is just now. For at the present day every one who does not wish to remain
uncultured, and to be numbered with the ignorant and incompetent
multitude, must study speculative philosophy. For the nineteenth century
is a philosophical age, though by this we do not mean either that it has
philosophy, or that philosophy governs it, but rather that it is ripe for
philosophy, and, therefore, stands in need of it. This is a sign of a high
degree of civilisation, and indeed, is a definite stage in the culture of
the ages.(14)
Though logic is of so little practical use, it cannot be denied that it
was invented for practical purposes. It appears to me to have originated
in the following way:—As the love of debating developed among the
Eleatics, the Megarics, and the Sophists, and by degrees became almost a
passion, the confusion in which nearly every debate ended must have made
them feel the necessity of a method of procedure as a guide; and for this
a scientific dialectic had to be sought. The first thing which would have
to be observed would be that both the disputing parties should always be
agreed on some one proposition, to which the disputed points might be
referred. The beginning of the methodical procedure consisted in this,
that the propositions admitted on both sides were formally stated to be
so, and placed at the head of the inquiry. But these propositions were at
first concerned only with the material of the inquiry. It was soon
observed that in the process of going back to the truth admitted on both
sides, and of deducing their assertions from it, each party followed
certain forms and laws about which, without any express agreement, there
was no difference of opinion. And from this it became evident that these
must constitute the peculiar and natural procedure of reason itself, the
form of investigation. Although this was not exposed to any doubt or
difference of opinion, some pedantically systematic philosopher hit upon
the idea that it would look well, and be the completion of the method of
dialectic, if this formal part of all discussion, this regular procedure
of reason itself, were to be expressed in abstract propositions, just like
the substantial propositions admitted on both sides, and placed at the
beginning of every investigation, as the fixed canon of debate to which
reference and appeal must always be made. In this way what had formerly
been followed only by tacit agreement, and instinctively, would be
consciously recognised and formally expressed. By degrees, more or less
perfect expressions were found for the fundamental principles of logic,
such as the principles of contradiction, sufficient reason, excluded
middle, the _dictum de omni et nullo_, as well as the special rules of the
syllogism, as for example, _ex meris particularibus aut negativis nihil
sequitur, a rationato ad rationem non valet consequentia_, and so on. That
all this was only brought about slowly, and with great pains, and up till
the time of Aristotle remained very incomplete, is evident from the
awkward and tedious way in which logical truths are brought out in many of
the Platonic dialogues, and still more from what Sextus Empiricus tells us
of the controversies of the Megarics, about the easiest and simplest
logical rules, and the laborious way in which they were brought into a
definite form (Sext. Emp. adv. Math. l. 8, p. 112). But Aristotle
collected, arranged, and corrected all that had been discovered before his
time, and brought it to an incomparably greater state of perfection. If we
thus observe how the course of Greek culture had prepared the way for, and
led up to the work of Aristotle, we shall be little inclined to believe
the assertion of the Persian author, quoted by Sir William Jones with much
approval, that Kallisthenes found a complete system of logic among the
Indians, and sent it to his uncle Aristotle (Asiatic Researches, vol. iv.
p. 163). It is easy to understand that in the dreary middle ages the
Aristotelian logic would be very acceptable to the controversial spirit of
the schoolmen, which, in the absence of all real knowledge, spent its
energy upon mere formulas and words, and that it would be eagerly adopted
even in its mutilated Arabian form, and presently established as the
centre of all knowledge. Though its authority has since declined, yet up
to our own time logic has retained the credit of a self-contained,
practical, and highly important science. Indeed, in our own day, the
Kantian philosophy, the foundation-stone of which is taken from logic, has
excited a new interest in it; which, in this respect, at any rate, that
is, as the means of the knowledge of the nature of reason, it deserves.
Correct and accurate conclusions may be arrived at if we carefully observe
the relation of the spheres of concepts, and only conclude that one sphere
is contained in a third sphere, when we have clearly seen that this first
sphere is contained in a second, which in its turn is contained in the
third. On the other hand, the art of sophistry lies in casting only a
superficial glance at the relations of the spheres of the concepts, and
then manipulating these relations to suit our purposes, generally in the
following way:—When the sphere of an observed concept lies partly within
that of another concept, and partly within a third altogether different
sphere, we treat it as if it lay entirely within the one or the other, as
may suit our purpose. For example, in speaking of passion, we may subsume
it under the concept of the greatest force, the mightiest agency in the
world, or under the concept of the irrational, and this again under the
concept of impotency or weakness. We may then repeat the process, and
start anew with each concept to which the argument leads us. A concept has
almost always several others, which partially come under it, and each of
these contains part of the sphere of the first, but also includes in its
own sphere something more, which is not in the first. But we draw
attention only to that one of these latter concepts, under which we wish
to subsume the first, and let the others remain unobserved, or keep them
concealed. On the possession of this skill depends the whole art of
sophistry and all finer fallacies; for logical fallacies such as
_mentiens_, _velatus_, _cornatus_, &c., are clearly too clumsy for actual
use. I am not aware that hitherto any one has traced the nature of all
sophistry and persuasion back to this last possible ground of its
existence, and referred it to the peculiar character of concepts, _i.e._,
to the procedure of reason itself. Therefore, as my exposition has led me
to it, though it is very easily understood, I will illustrate it in the
following table by means of a schema. This table is intended to show how
the spheres of concepts overlap each other at many points, and so leave
room for a passage from each concept to whichever one we please of several
other concepts. I hope, however, that no one will be led by this table to
attach more importance to this little explanation, which I have merely
given in passing, than ought to belong to it, from the nature of the
subject. I have chosen as an illustration the concept of travelling. Its
sphere partially includes four others, to any of which the sophist may
pass at will; these again partly include other spheres, several of them
two or more at once, and through these the sophist takes whichever way he
chooses, always as if it were the only way, till at last he reaches, in
good or evil, whatever end he may have in view. In passing from one sphere
to another, it is only necessary always to follow the direction from the
centre (the given chief concept) to the circumference, and never to
reverse this process. Such a piece of sophistry may be either an unbroken
speech, or it may assume the strict syllogistic form, according to what is
the weak side of the hearer. Most scientific arguments, and especially
philosophical demonstrations, are at bottom not much more than this, for
how else would it be possible, that so much, in different ages, has not
only been falsely apprehended (for error itself has a different source),
but demonstrated and proved, and has yet afterwards been found to be
fundamentally wrong, for example, the Leibnitz-Wolfian Philosophy,
Ptolemaic Astronomy, Stahl’s Chemistry, Newton’s Theory of Colours, &c.
&c.(15)
§ 10. Through all this, the question presses ever more upon us, how
_certainty_ is to be attained, how _judgments __ are to be established_,
what constitutes _rational knowledge_, (_wissen_), and _science_, which we
rank with language and deliberate action as the third great benefit
conferred by reason.