APPLICATION TO KANT’S THEORY OF EXPERIENCE
When we observe the heavenly bodies we become aware that they all
participate in one universal motion—a diurnal revolution round the
polar axis.
In the case of fixed stars this is most unqualifiedly true, but in the
case of the sun, and the planets also, the single motion of revolution
can be discerned, modified, and slightly altered by other and secondary
motions.
Hence the universal characteristic of the celestial bodies is that they
move in a diurnal circle.
But we know that this one great fact which is true of them all has in
reality nothing to do with them. The diurnal revolution which they
visibly perform is the result of the condition of the observer. It is
because the observer is on a rotating earth that a universal statement
can be made about all the celestial bodies.
The universal statement which is valid about every one of the celestial
bodies is that which does not concern them at all, and is but a
statement of the condition of the observer.
Now there are universal statements of other kinds which we can make. We
can say that all objects of experience are in space and subject to the
laws of geometry.
Does this mean that space and all that it means is due to a condition
of the observer?
If a universal law in one case means nothing affecting the objects
themselves, but only a condition of observation, is this true in every
case? There is shown us in astronomy a _vera causa_ for the assertion
of a universal. Is the same cause to be traced everywhere?
Such is a first approximation to the doctrine of Kant’s critique.
It is the apprehension of a relation into which, on the one side and
the other, perfectly definite constituents enter—the human observer and
the stars—and a transference of this relation to a region in which the
constituents on either side are perfectly unknown.
If spatiality is due to a condition of the observer, the observer
cannot be this bodily self of ours—the body, like the objects around
it, are equally in space.
This conception Kant applied, not only to the intuitions of sense, but
to the concepts of reason—wherever a universal statement is made there
is afforded him an opportunity for the application of his principle.
He constructed a system in which one hardly knows which the most to
admire, the architectonic skill, or the reticence with regard to things
in themselves, and the observer in himself.
His system can be compared to a garden, somewhat formal perhaps, but
with the charm of a quality more than intellectual, a _besonnenheit_,
an exquisite moderation over all. And from the ground he so carefully
prepared with that buried in obscurity, which it is fitting should be
obscure, science blossoms and the tree of real knowledge grows.
The critique is a storehouse of ideas of profound interest. The one
of which I have given a partial statement leads, as we shall see
on studying it in detail, to a theory of mathematics suggestive of
enquiries in many directions.
The justification for my treatment will be found amongst other passages
in that part of the transcendental analytic, in which Kant speaks of
objects of experience subject to the forms of sensibility, not subject
to the concepts of reason.
Kant asserts that whenever we think we think of objects in space and
time, but he denies that the space and time exist as independent
entities. He goes about to explain them, and their universality, not by
assuming them, as most other philosophers do, but by postulating their
absence. How then does it come to pass that the world is in space and
time to us?
Kant takes the same position with regard to what we call nature—a great
system subject to law and order. “How do you explain the law and order
in nature?” we ask the philosophers. All except Kant reply by assuming
law and order somewhere, and then showing how we can recognise it.
In explaining our notions, philosophers from other than the Kantian
standpoint, assume the notions as existing outside us, and then it is
no difficult task to show how they come to us, either by inspiration or
by observation.
We ask “Why do we have an idea of law in nature?” “Because natural
processes go according to law,” we are answered, “and experience
inherited or acquired, gives us this notion.”
But when we speak about the law in nature we are speaking about a
notion of our own. So all that these expositors do is to explain our
notion by an assumption of it.
Kant is very different. He supposes nothing. An experience such as ours
is very different from experience in the abstract. Imagine just simply
experience, succession of states, of consciousness! Why, there would be
no connecting any two together, there would be no personal identity,
no memory. It is out of a general experience such as this, which, in
respect to anything we call real, is less than a dream, that Kant shows
the genesis of an experience such as ours.
Kant takes up the problem of the explanation of space, time, order, and
so quite logically does not presuppose them.
But how, when every act of thought is of things in space, and time,
and ordered, shall we represent to ourselves that perfectly indefinite
somewhat which is Kant’s necessary hypothesis—that which is not in
space or time and is not ordered. That is our problem, to represent
that which Kant assumes not subject to any of our forms of thought, and
then show some function which working on that makes it into a “nature”
subject to law and order, in space and time. Such a function Kant
calls the “Unity of Apperception”; _i.e._, that which makes our state
of consciousness capable of being woven into a system with a self, an
outer world, memory, law, cause, and order.
The difficulty that meets us in discussing Kant’s hypothesis is that
everything we think of is in space and time—how then shall we represent
in space an existence not in space, and in time an existence not in
time? This difficulty is still more evident when we come to construct
a poiograph, for a poiograph is essentially a space structure. But
because more evident the difficulty is nearer a solution. If we always
think in space, _i.e._ using space concepts, the first condition
requisite for adapting them to the representation of non-spatial
existence, is to be aware of the limitation of our thought, and so be
able to take the proper steps to overcome it. The problem before us,
then, is to represent in space an existence not in space.
The solution is an easy one. It is provided by the conception of
alternativity.
To get our ideas clear let us go right back behind the distinctions of
an inner and an outer world. Both of these, Kant says, are products.
Let us take merely states of consciousness, and not ask the question
whether they are produced or superinduced—to ask such a question is to
have got too far on, to have assumed something of which we have not
traced the origin. Of these states let us simply say that they occur.
Let us now use the word a “posit” for a phase of consciousness reduced
to its last possible stage of evanescence; let a posit be that phase of
consciousness of which all that can be said is that it occurs.
Let _a_, _b_, _c_, be three such posits. We cannot represent them in
space without placing them in a certain order, as _a_, _b_, _c_. But
Kant distinguishes between the forms of sensibility and the concepts
of reason. A dream in which everything happens at haphazard would be
an experience subject to the form of sensibility and only partially
subject to the concepts of reason. It is partially subject to the
concepts of reason because, although there is no order of sequence,
still at any given time there is order. Perception of a thing as in
space is a form of sensibility, the perception of an order is a concept
of reason.
We must, therefore, in order to get at that process which Kant supposes
to be constitutive of an ordered experience imagine the posits as in
space without order.
As we know them they must be in some order, _abc_, _bca_, _cab_, _acb_,
_cba_, _bac_, one or another.
To represent them as having no order conceive all these different
orders as equally existing. Introduce the conception of
alternativity—let us suppose that the order _abc_, and _bac_, for
example, exist equally, so that we cannot say about _a_ that it comes
before or after _b_. This would correspond to a sudden and arbitrary
change of _a_ into _b_ and _b_ into _a_, so that, to use Kant’s words,
it would be possible to call one thing by one name at one time and at
another time by another name.
In an experience of this kind we have a kind of chaos, in which no
order exists; it is a manifold not subject to the concepts of reason.
Now is there any process by which order can be introduced into such a
manifold—is there any function of consciousness in virtue of which an
ordered experience could arise?
In the precise condition in which the posits are, as described above,
it does not seem to be possible. But if we imagine a duality to exist
in the manifold, a function of consciousness can be easily discovered
which will produce order out of no order.
Let us imagine each posit, then, as having, a dual aspect. Let _a_ be
1_a_ in which the dual aspect is represented by the combination of
symbols. And similarly let _b_ be 2_b_, _c_ be 3_c_, in which 2 and _b_
represent the dual aspects of _b_, 3 and _c_ those of _c_.
Since _a_ can arbitrarily change into _b_, or into _c_, and so on, the
particular combinations written above cannot be kept. We have to assume
the equally possible occurrence of form such as 2_a_, 2_b_, and so on;
and in order to get a representation of all those combinations out of
which any set is alternatively possible, we must take every aspect with
every aspect. We must, that is, have every letter with every number.
Let us now apply the method of space representation.
_Note._—At the beginning of the next chapter the same structures as
those which follow are exhibited in more detail and a reference to
them will remove any obscurity which may be found in the immediately
following passages. They are there carried on to a greater
multiplicity of dimensions, and the significance of the process here
briefly explained becomes more apparent.
[Illustration: Fig. 59.]
Take three mutually rectangular axes in space 1, 2, 3 (fig. 59), and
on each mark three points, the common meeting point being the first on
each axis. Then by means of these three points on each axis we define
27 positions, 27 points in a cubical cluster, shown in fig. 60, the
same method of co-ordination being used as has been described before.
Each of these positions can be named by means of the axes and the
points combined.
[Illustration: Fig. 60.]
Thus, for instance, the one marked by an asterisk can be called 1_c_,
2_b_, 3_c_, because it is opposite to _c_ on 1, to _b_ on 2, to _c_ on
3.
Let us now treat of the states of consciousness corresponding to
these positions. Each point represents a composite of posits, and
the manifold of consciousness corresponding to them is of a certain
complexity.
Suppose now the constituents, the points on the axes, to interchange
arbitrarily, any one to become any other, and also the axes 1, 2, and
3, to interchange amongst themselves, any one to become any other, and
to be subject to no system or law, that is to say, that order does not
exist, and that the points which run _abc_ on each axis may run _bac_,
and so on.
Then any one of the states of consciousness represented by the points
in the cluster can become any other. We have a representation of a
random consciousness of a certain degree of complexity.
Now let us examine carefully one particular case of arbitrary
interchange of the points, _a_, _b_, _c_; as one such case, carefully
considered, makes the whole clear.
[Illustration: Fig. 61.]
Consider the points named in the figure 1_c_, 2_a_, 3_c_; 1_c_, 2_c_,
3_a_; 1_a_, 2_c_, 3_c_, and examine the effect on them when a change of
order takes place. Let us suppose, for instance, that _a_ changes into
_b_, and let us call the two sets of points we get, the one before and
the one after, their change conjugates.
Before the change 1_c_ 2_a_ 3_c_ 1_c_ 2_c_ 3_a_ 1_a_ 2_c_ 3_c_}Conjug-
After the change 1_c_ 2_b_ 3_c_ 1_c_ 2_c_ 3_b_ 1_b_ 2_c_ 3_c_} ates.
The points surrounded by rings represent the conjugate points.
It is evident that as consciousness, represented first by the first
set of points and afterwards by the second set of points, would have
nothing in common in its two phases. It would not be capable of giving
an account of itself. There would be no identity.
If, however, we can find any set of points in the cubical cluster,
which, when any arbitrary change takes place in the points on the
axes, or in the axes themselves, repeats itself, is reproduced, then a
consciousness represented by those points would have a permanence. It
would have a principle of identity. Despite the no law, the no order,
of the ultimate constituents, it would have an order, it would form a
system, the condition of a personal identity would be fulfilled.
The question comes to this, then. Can we find a system of points
which is self-conjugate which is such that when any posit on the axes
becomes any other, or when any axis becomes any other, such a set
is transformed into itself, its identity is not submerged, but rises
superior to the chaos of its constituents?
[Illustration: Fig. 62.]
Such a set can be found. Consider the set represented in fig. 62, and
written down in the first of the two lines—
Self- {1_a_ 2_b_ 3_c_ 1_b_ 2_a_ 3_c_ 1_c_ 2_a_ 3_b_
conjugate. {1_c_ 2_b_ 3_a_ 1_b_ 2_c_ 3_a_ 1_a_ 2_c_ 3_b_
Self- {1_c_ 2_b_ 3_a_ 1_b_ 2_c_ 3_a_ 1_a_ 2_c_ 3_b_
conjugate. {1_a_ 2_b_ 3_c_ 1_b_ 2_a_ 3_c_ 1_c_ 2_a_ 3_b_
If now _a_ change into _c_ and _c_ into _a_, we get the set in the
second line, which has the same members as are in the upper line.
Looking at the diagram we see that it would correspond simply to the
turning of the figures as a whole.[2] Any arbitrary change of the
points on the axes, or of the axes themselves, reproduces the same set.
[2] These figures are described more fully, and extended, in the next
chapter.
Thus, a function, by which a random, an unordered, consciousness
could give an ordered and systematic one, can be represented. It
is noteworthy that it is a system of selection. If out of all the
alternative forms that only is attended to which is self-conjugate,
an ordered consciousness is formed. A selection gives a feature of
permanence.
Can we say that the permanent consciousness is this selection?
An analogy between Kant and Darwin comes into light. That which is
swings clear of the fleeting, in virtue of its presenting a feature of
permanence. There is no need to suppose any function of “attending to.”
A consciousness capable of giving an account of itself is one which is
characterised by this combination. All combinations exist—of this kind
is the consciousness which can give an account of itself. And the very
duality which we have presupposed may be regarded as originated by a
process of selection.
Darwin set himself to explain the origin of the fauna and flora of
the world. He denied specific tendencies. He assumed an indefinite
variability—that is, chance—but a chance confined within narrow limits
as regards the magnitude of any consecutive variations. He showed that
organisms possessing features of permanence, if they occurred would be
preserved. So his account of any structure or organised being was that
it possessed features of permanence.
Kant, undertaking not the explanation of any particular phenomena but
of that which we call nature as a whole, had an origin of species
of his own, an account of the flora and fauna of consciousness. He
denied any specific tendency of the elements of consciousness, but
taking our own consciousness, pointed out that in which it resembled
any consciousness which could survive, which could give an account of
itself.
He assumes a chance or random world, and as great and small were not
to him any given notions of which he could make use, he did not limit
the chance, the randomness, in any way. But any consciousness which
is permanent must possess certain features—those attributes namely
which give it permanence. Any consciousness like our own is simply a
consciousness which possesses those attributes. The main thing is that
which he calls the unity of apperception, which we have seen above is
simply the statement that a particular set of phases of consciousness
on the basis of complete randomness will be self-conjugate, and so
permanent.
As with Darwin so with Kant, the reason for existence of any feature
comes to this—show that it tends to the permanence of that which
possesses it.
We can thus regard Kant as the creator of the first of the modern
evolution theories. And, as is so often the case, the first effort was
the most stupendous in its scope. Kant does not investigate the origin
of any special part of the world, such as its organisms, its chemical
elements, its social communities of men. He simply investigates the
origin of the whole—of all that is included in consciousness, the
origin of that “thought thing” whose progressive realisation is the
knowable universe.
This point of view is very different from the ordinary one, in which a
man is supposed to be placed in a world like that which he has come to
think of it, and then to learn what he has found out from this model
which he himself has placed on the scene.
We all know that there are a number of questions in attempting an
answer to which such an assumption is not allowable.
Mill, for instance, explains our notion of “law” by an invariable
sequence in nature. But what we call nature is something given in
thought. So he explains a thought of law and order by a thought of an
invariable sequence. He leaves the problem where he found it.
Kant’s theory is not unique and alone. It is one of a number of
evolution theories. A notion of its import and significance can be
obtained by a comparison of it with other theories.
Thus in Darwin’s theoretical world of natural selection a certain
assumption is made, the assumption of indefinite variability—slight
variability it is true, over any appreciable lapse of time, but
indefinite in the postulated epochs of transformation—and a whole chain
of results is shown to follow.
This element of chance variation is not, however, an ultimate resting
place. It is a preliminary stage. This supposing the all is a
preliminary step towards finding out what is. If every kind of organism
can come into being, those that do survive will present such and such
characteristics. This is the necessary beginning for ascertaining what
kinds of organisms do come into existence. And so Kant’s hypothesis
of a random consciousness is the necessary beginning for the rational
investigation of consciousness as it is. His assumption supplies, as
it were, the space in which we can observe the phenomena. It gives the
general laws constitutive of any experience. If, on the assumption
of absolute randomness in the constituents, such and such would be
characteristic of the experience, then, whatever the constituents,
these characteristics must be universally valid.
We will now proceed to examine more carefully the poiograph,
constructed for the purpose of exhibiting an illustration of Kant’s
unity of apperception.
In order to show the derivation order out of non-order it has been
necessary to assume a principle of duality—we have had the axes and the
posits on the axes—there are two sets of elements, each non-ordered,
and it is in the reciprocal relation of them that the order, the
definite system, originates.
Is there anything in our experience of the nature of a duality?
There certainly are objects in our experience which have order and
those which are incapable of order. The two roots of a quadratic
equation have no order. No one can tell which comes first. If a body
rises vertically and then goes at right angles to its former course,
no one can assign any priority to the direction of the north or to
the east. There is no priority in directions of turning. We associate
turnings with no order progressions in a line with order. But in the
axes and points we have assumed above there is no such distinction.
It is the same, whether we assume an order among the turnings, and no
order among the points on the axes, or, _vice versa_, an order in the
points and no order in the turnings. A being with an infinite number of
axes mutually at right angles, with a definite sequence between them
and no sequence between the points on the axes, would be in a condition
formally indistinguishable from that of a creature who, according to an
assumption more natural to us, had on each axis an infinite number of
ordered points and no order of priority amongst the axes. A being in
such a constituted world would not be able to tell which was turning
and which was length along an axis, in order to distinguish between
them. Thus to take a pertinent illustration, we may be in a world
of an infinite number of dimensions, with three arbitrary points on
each—three points whose order is indifferent, or in a world of three
axes of arbitrary sequence with an infinite number of ordered points on
each. We can’t tell which is which, to distinguish it from the other.
Thus it appears the mode of illustration which we have used is not an
artificial one. There really exists in nature a duality of the kind
which is necessary to explain the origin of order out of no order—the
duality, namely, of dimension and position. Let us use the term group
for that system of points which remains unchanged, whatever arbitrary
change of its constituents takes place. We notice that a group involves
a duality, is inconceivable without a duality.
Thus, according to Kant, the primary element of experience is the
group, and the theory of groups would be the most fundamental branch
of science. Owing to an expression in the critique the authority of
Kant is sometimes adduced against the assumption of more than three
dimensions to space. It seems to me, however, that the whole tendency
of his theory lies in the opposite direction, and points to a perfect
duality between dimension and position in a dimension.
If the order and the law we see is due to the conditions of conscious
experience, we must conceive nature as spontaneous, free, subject to no
predication that we can devise, but, however apprehended, subject to
our logic.
And our logic is simply spatiality in the general sense—that resultant
of a selection of the permanent from the unpermanent, the ordered from
the unordered, by the means of the group and its underlying duality.
We can predicate nothing about nature, only about the way in which
we can apprehend nature. All that we can say is that all that which
experience gives us will be conditioned as spatial, subject to our
logic. Thus, in exploring the facts of geometry from the simplest
logical relations to the properties of space of any number of
dimensions, we are merely observing ourselves, becoming aware of the
conditions under which we must perceive. Do any phenomena present
themselves incapable of explanation under the assumption of the space
we are dealing with, then we must habituate ourselves to the conception
of a higher space, in order that our logic may be equal to the task
before us.
We gain a repetition of the thought that came before, experimentally
suggested. If the laws of the intellectual comprehension of nature are
those derived from considering her as absolute chance, subject to no
law save that derived from a process of selection, then, perhaps, the
order of nature requires different faculties from the intellectual to
apprehend it. The source and origin of ideas may have to be sought
elsewhere than in reasoning.
The total outcome of the critique is to leave the ordinary man just
where he is, justified in his practical attitude towards nature,
liberated from the fetters of his own mental representations.
The truth of a picture lies in its total effect. It is vain to seek
information about the landscape from an examination of the pigments.
And in any method of thought it is the complexity of the whole that
brings us to a knowledge of nature. Dimensions are artificial enough,
but in the multiplicity of them we catch some breath of nature.
We must therefore, and this seems to me the practical conclusion of the
whole matter, proceed to form means of intellectual apprehension of a
greater and greater degree of complexity, both dimensionally and in
extent in any dimension. Such means of representation must always be
artificial, but in the multiplicity of the elements with which we deal,
however incipiently arbitrary, lies our chance of apprehending nature.
And as a concluding chapter to this part of the book, I will extend
the figures, which have been used to represent Kant’s theory, two
steps, so that the reader may have the opportunity of looking at a
four-dimensional figure which can be delineated without any of the
special apparatus, to the consideration of which I shall subsequently
pass on.