ABSTRACTION
In the previous chapters I have been examining the reactions of the
scientific movement upon the deeper issues which have occupied modern
thinkers. No one man, no limited society of men, and no one epoch can
think of everything at once. Accordingly for the sake of eliciting the
various impacts of science upon thought, the topic has been treated
historically. In this retrospect I have kept in mind that the ultimate
issue of the whole story is the patent dissolution of the comfortable
scheme of scientific materialism which has dominated the three centuries
under review. Accordingly various schools of criticism of the dominant
opinions have been stressed; and I have endeavoured to outline an
alternative cosmological doctrine, which shall be wide enough to include
what is fundamental both for science and for its critics. In this
alternative scheme, the notion of material, as fundamental, has been
replaced by that of organic synthesis. But the approach has always been
from the consideration of the actual intricacies of scientific thought,
and of the peculiar perplexities which it suggests.
In the present chapter, and in the immediately succeeding chapter, we
will forget the peculiar problems of modern science, and will put
ourselves at the standpoint of a dispassionate consideration of the
nature of things, antecedently to any special investigation into their
details. Such a standpoint is termed ‘metaphysical.’ Accordingly those
readers who find metaphysics, even in two slight chapters, irksome, will
do well to proceed at once to the Chapter on ‘Religion and Science,’
which resumes the topic of the impact of science on modern thought.
These metaphysical chapters are purely descriptive. Their justification
is to be sought, (i) in our direct knowledge of the actual occasions
which compose our immediate experience, and (ii) in their success as
forming a basis for harmonising our systematised accounts of various
types of experience, and (iii) in their success as providing the
concepts in terms of which an epistemology can be framed. By (iii) I
mean that an account of the general character of what we know must
enable us to frame an account of how knowledge is possible as an adjunct
within things known.
In any occasion of cognition, that which is known is an actual occasion
of experience, as diversified[16] by reference to a realm of entities
which transcend that immediate occasion in that they have analogous or
different connections with other occasions of experience. For example a
definite shade of red may, in the immediate occasion, be implicated with
the shape of sphericity in some definite way. But that shade of red, and
that spherical shape, exhibit themselves as transcending that occasion,
in that either of them has other relationships to other occasions. Also,
apart from the actual occurrence of the same things in other occasions,
every actual occasion is set within a realm of alternative
interconnected entities. This realm is disclosed by all the untrue
propositions which can be predicated significantly of that occasion. It
is the realm of alternative suggestions, whose foothold in actuality
transcends each actual occasion. The real relevance of untrue
propositions for each actual occasion is disclosed by art, romance, and
by criticism in reference to ideals. It is the foundation of the
metaphysical position which I am maintaining that the understanding of
actuality requires a reference to ideality. The two realms are
intrinsically inherent in the total metaphysical situation. The truth
that some proposition respecting an actual occasion is untrue may
express the vital truth as to the aesthetic achievement. It expresses
the ‘great refusal’ which is its primary characteristic. An event is
decisive in proportion to the importance (for it) of its untrue
propositions: their relevance to the event cannot be dissociated from
what the event is in itself by way of achievement. These transcendent
entities have been termed ‘universals.’ I prefer to use the term
‘eternal objects,’ in order to disengage myself from presuppositions
which cling to the former term owing to its prolonged philosophical
history. Eternal objects are thus, in their nature, abstract. By
‘abstract’ I mean that what an eternal object is in itself—that is to
say, its essence—is comprehensible without reference to some one
particular occasion of experience. To be abstract is to transcend
particular concrete occasions of actual happening. But to transcend an
actual occasion does not mean being disconnected from it. On the
contrary, I hold that each eternal object has its own proper connection
with each such occasion, which I term its mode of ingression into that
occasion. Thus an eternal object is to be comprehended by acquaintance
with (i) its particular individuality, (ii) its general relationships to
other eternal objects as apt for realisation in actual occasions, and
(iii) the general principle which expresses its ingression in particular
actual occasions.
Footnote 16:
_Cf._ my _Principles of Natural Knowledge_, Ch. V, Sec. 13.
These three headings express two principles. The first principle is that
each eternal object is an individual which, in its own peculiar fashion,
is what it is. This particular individuality is the individual essence
of the object, and cannot be described otherwise than as being itself.
Thus the individual essence is merely the essence considered in respect
to its uniqueness. Further, the essence of an eternal object is merely
the eternal object considered as adding its own unique contribution to
each actual occasion. This unique contribution is identical for all such
occasions in respect to the fact that the object in all modes of
ingression is just its identical self. But it varies from one occasion
to another in respect to the differences of its modes of ingression.
Thus the metaphysical status of an eternal object is that of a
possibility for an actuality. Every actual occasion is defined as to its
character by how these possibilities are actualised for that occasion.
Thus actualisation is a selection among possibilities. More accurately,
it is a selection issuing in a gradation of possibilities in respect to
their realisation in that occasion. This conclusion brings us to the
second metaphysical principle: An eternal object, considered as an
abstract entity, cannot be divorced from its reference to other eternal
objects, and from its reference to actuality generally; though it is
disconnected from its actual modes of ingression into definitive actual
occasions. This principle is expressed by the statement that each
eternal object has a ‘relational essence.’ This relational essence
determines how it is possible for the object to have ingression into
actual occasions.
In other words: If _A_ be an eternal object, then what _A_ is in itself
involves _A’s_ status in the universe, and _A_ cannot be divorced from
this status. In the essence of _A_ there stands a determinateness as to
the relationships of _A_ to other eternal objects, and an
indeterminateness as to the relationships of _A_ to actual occasions.
Since the relationships of _A_ to other eternal objects stand
determinately in the essence of _A_, it follows that they are internal
relations. I mean by this that these relationships are constitutive of
_A_; for an entity which stands in internal relations has no being as an
entity not in these relations. In other words, once with internal
relations, always with internal relations. The internal relationships of
_A_ conjointly form its significance.
Again an entity cannot stand in external relations unless in its essence
there stands an indeterminateness which is its patience for such
external relations. The meaning of the term ‘possibility’ as applied to
_A_ is simply that there stands in the essence of _A_ a patience for
relationships to actual occasions. The relationships of _A_ to an actual
occasion are simply how the eternal relationships of _A_ to other
eternal objects are graded as to their realisation in that occasion.
Thus the general principle which expresses _A’s_ ingression in the
particular actual occasion α is the indeterminateness which stands in
the essence of _A_ as to its ingression into α, and is the
determinateness which stands in the essence of α as to the ingression of
_Α_ into α. Thus the synthetic prehension, which is α, is the solution
of the indeterminateness of _Α_ into the determinateness of α.
Accordingly the relationship between _Α_ and α is external as regards
_Α_, and is internal as regards α. Every actual occasion α is the
solution of all modalities into actual categorical ingressions: truth
and falsehood take the place of possibility. The complete ingression of
_Α_ into α is expressed by all the true propositions which are about
both _Α_ and α, and also—it may be—about other things.
The determinate relatedness of the eternal object _Α_ to every other
eternal object is how _Α_ is systematically and by the necessity of its
nature related to every other eternal object. Such relatedness
represents a possibility for realisation. But a relationship is a fact
which concerns all the implicated relata, and cannot be isolated as if
involving only one of the relata. Accordingly there is a general fact of
systematic mutual relatedness which is inherent in the character of
possibility. The realm of eternal objects is properly described as a
‘realm,’ because each eternal object has its status in this general
systematic complex of mutual relatedness.
In respect to the ingression of _Α_ into an actual occasion α, the
mutual relationships of _Α_ to other eternal objects, as thus graded in
realisation, require for their expression a reference to the status of
_Α_ and of the other eternal objects in the spatio-temporal
relationship. Also this status is not expressible (for this purpose)
without a reference to the status of α and of other actual occasions in
the same spatio-temporal relationship. Accordingly the spatio-temporal
relationship, in terms of which the actual course of events is to be
expressed, is nothing else than a selective limitation within the
general systematic relationships among eternal objects. By ‘limitation,’
as applied to the spatio-temporal continuum, I mean those matter-of-fact
determinations—such as the three dimensions of space, and the four
dimensions of the spatio-temporal continuum—which are inherent in the
actual course of events, but which present themselves as arbitrary in
respect to a more abstract possibility. The consideration of these
general limitations at the base of actual things, as distinct from the
limitations peculiar to each actual occasion, will be more fully resumed
in the chapter on ‘God.’
Further, the status of all possibility in reference to actuality
requires a reference to this spatio-temporal continuum. In any
particular consideration of a possibility we may conceive this continuum
to be transcended. But in so far as there is any definite reference to
actuality, the definite _how_ of transcendence of that spatio-temporal
continuum is required. Thus primarily the spatio-temporal continuum is a
locus of relational possibility, selected from the more general realm of
systematic relationship. This limited locus of relational possibility
expresses one limitation of possibility inherent in the general system
of the process of realisation. Whatever possibility is generally
coherent with that system falls within this limitation. Also whatever is
abstractedly possible in relation to the general course of events—as
distinct from the particular limitations introduced by particular
occasions—pervades the spatio-temporal continuum in every alternative
spatial situation and at all alternative times.
Fundamentally, the spatio-temporal continuum is the general system of
relatedness of all possibilities, in so far as that system is limited by
its relevance to the general fact of actuality. Also it is inherent in
the nature of possibility that it should include this relevance to
actuality. For possibility is that in which there stands achievability,
abstracted from achievement.
It has already been emphasised that an actual occasion is to be
conceived as a limitation; and that this process of limitation can be
still further characterised as a gradation. This characteristic of an
actual occasion (α, say) requires further elucidation: An
indeterminateness stands in the essence of any eternal object (_Α_,
say). The actual occasion α synthesises in itself every eternal object;
and, in so doing, it includes the _complete_ determinate relatedness of
_Α_ to every other eternal object, or set of eternal objects. This
synthesis is a limitation of realisation but _not_ of content. Each
relationship preserves its inherent self-identity. But grades of entry
into this synthesis are inherent in each actual occasion, such as α.
These grades can be expressed only as relevance of value. This relevance
of value varies—as comparing different occasions—in grade from the
inclusion of the individual essence of _Α_ as an element in the
aesthetic synthesis (in some grade of inclusion) to the lowest grade
which is the exclusion of the individual essence of _Α_ as an element in
the aesthetic synthesis. In so far as it stands in this lowest grade,
every determinate relationship of _Α_ is merely ingredient in the
occasion in respect to the determinate _how_ this relationship is an
unfulfilled alternative, not contributing any aesthetic value, except as
forming an element in the systematic substratum of unfulfilled content.
In a higher grade, it may remain unfulfilled, but be aesthetically
relevant.
Thus _A_, conceived merely in respect to its relationships to other
eternal objects, is ‘_A_ conceived as _not-being_’; where ‘not-being’
means ‘abstracted from the determinate fact of inclusions in, and
exclusions from, actual events.’ Also ‘_A_ as _not-being_ in respect to
a definite occasion α’ means that _A_ in all its determinate
relationships is excluded from α. Again ‘_A_ as _being_ in respect to α’
means that _A_ in some of its determinate relationships is included in
α. But there can be no occasion which includes _A_ in all its
determinate relationships; for some of these relationships are
contraries. Thus, in regard to excluded relationships, _A_ will be
_not-being_ in α, even when in regard to other relationships _A_ will be
_being_ in α. In this sense, every occasion is a synthesis of _being_
and _not-being_. Furthermore, though some eternal objects are
synthesised in an occasion α merely _quâ not-being_, each eternal object
which is synthesised _quâ being_ is also synthesised _quâ not-being_.
‘_Being_’ here means ‘individually effective in the aesthetic
synthesis.’ Also the ‘aesthetic synthesis’ is the ‘experient synthesis’
viewed as self-creative, under the limitations laid upon it by its
internal relatedness to all other actual occasions. We thus
conclude—what has already been stated above—that the general fact of the
synthetic prehension of all eternal objects into every occasion wears
the double aspect of the indeterminate relatedness of each eternal
object to occasions generally, and of its determinate relatedness to
each particular occasion. This statement summarises the account of how
external relations are possible. But the account depends upon
disengaging the spatio-temporal continuum from its mere implication in
actual occasions—according to the usual explanation—and upon exhibiting
it in its origin from the general nature of abstract possibility, as
limited by the general character of the actual course of events.
The difficulty which arises in respect to internal relations is to
explain how any particular truth is possible. In so far as there are
internal relations, everything must depend upon everything else. But if
this be the case, we cannot know about anything till we equally know
everything else. Apparently, therefore, we are under the necessity of
saying everything at once. This supposed necessity is palpably untrue.
Accordingly it is incumbent on us to explain how there can be internal
relations, seeing that we admit finite truths.
Since actual occasions are selections from the realm of possibilities,
the ultimate explanation of how actual occasions have the general
character which they do have, must lie in an analysis of the general
character of the realm of possibility.
The _analytical character_ of the realm of eternal objects is the
primary metaphysical truth concerning it. By this character it is meant
that the status of any eternal object _A_ in this realm is capable of
analysis into an indefinite number of subordinate relationships of
limited scope. For example if _B_ and _C_ are two other eternal objects,
then there is some perfectly definite relationship _R(A, B, C)_ which
involves _A, B, C_ only, as to require the mention of no other definite
eternal objects in the capacity of relata. Of course, the relationship
_R(A, B, C)_ may involve subordinate relationships which are themselves
eternal objects, and _R(A, B, C)_ is also itself an eternal object. Also
there will be other relationships which in the same sense involve only
_A, B, C_. We have now to examine how, having regard to the internal
relatedness of eternal objects, this limited relationship _R(A, B, C)_
is possible.
The reason for the existence of finite relationships in the realm of
eternal objects is that relationships of these objects among themselves
are entirely unselective, and are systematically complete. We are
discussing possibility; so that every relationship which is possible is
thereby in the realm of possibility. Every such relationship of each
eternal object is founded upon the perfectly definite status of that
object as a relatum in the general scheme of relationships. This
definite status is what I have termed the ‘relational essence’ of the
object. This relational essence is determinable by reference to that
object alone, and does not require reference to any other objects,
except those which are specifically involved in its individual essence
when that essence is complex (as will be explained immediately). The
meaning of the words ‘any’ and ‘some’ springs from this principle—that
is to say, the meaning of the ‘variable’ in logic. The whole principle
is that a particular determination can be made of the _how_ of some
definite relationship of a definite eternal object _A_ to a definite
finite number _n_ of other eternal objects, _without_ any determination
of the other _n_ objects, X1, X2, ... Xn, except that they have, each of
them, the requisite status to play their respective parts in that
multiple relationship. This principle depends on the fact that the
relational essence of an eternal object is not unique to that object.
The mere relational essence of each eternal object determines the
complete uniform scheme of relational essences, since each object stands
internally in all its possible relationships. Thus the realm of
possibility provides a uniform scheme of relationships among finite sets
of eternal objects; and all eternal objects stand in all such
relationships, so far as the status of each permits.
Accordingly the relationships (as in possibility) do not involve the
individual essences of the eternal objects; they involve _any_ eternal
objects as relata, subject to the proviso that these relata have the
requisite relational essences. [It is this proviso which, automatically
and by the nature of the case, limits the ‘any’ of the phrase ‘any
eternal objects.’] This principle is the principle of the _Isolation of
Eternal Objects_ in the realm of possibility. The eternal objects are
isolated, because their relationships as possibilities are expressible
without reference to their respective individual essences. In contrast
to the realm of possibility, the inclusion of eternal objects within an
actual occasion means that in respect to some of their possible
relationships there is a togetherness of their individual essences. This
realised togetherness is the achievement of an emergent value
defined—or, shaped—by the definite eternal relatedness in respect to
which the real togetherness is achieved. Thus the eternal relatedness is
the form—the εἶδος—; the emergent actual occasion is the _superject_ of
informed value; value, as abstracted from any particular superject, is
the abstract matter—the ὕλη—which is common to all actual occasions; and
the synthetic activity which prehends valueless possibility into
superjicient informed value is the substantial activity. This
substantial activity is that which is omitted in any analysis of the
static factors in the metaphysical situation. The analysed elements of
the situation are the attributes of the substantial activity.
The difficulty inherent in the concept of finite internal relations
among eternal objects is thus evaded by two metaphysical principles, (i)
that the relationships of any eternal object _A_, considered as
constitutive of _A_, merely involve other eternal objects as bare relata
without reference to their individual essences, and (ii) that the
divisibility of the general relationship of _A_ into a multiplicity of
finite relationships of _A_ stands therefore in the essence of that
eternal object. The second principle obviously depends upon the first.
To understand _A_ is to understand the _how_ of a general scheme of
relationship. This scheme of relationship does not require the
individual uniqueness of the other relata for its comprehension. This
scheme also discloses itself as being analysable into a multiplicity of
limited relationships which have their own individuality and yet at the
same time presupposes the total relationship within possibility. In
respect to actuality there is first the general limitation of
relationships, which reduces this general unlimited scheme to the four
dimensional spatio-temporal scheme. This spatio-temporal scheme is, so
to speak, the greatest common measure of the schemes of relationship (as
limited by actuality) inherent in all the eternal objects. By this it is
meant that, _how_ select relationships of an eternal object (_A_) are
realised in any actual occasion, is always explicable by expressing the
status of _A_ in respect to this spatio-temporal scheme, and by
expressing in this scheme the relationship of the actual occasion to
other actual occasions. A definite finite relationship involving the
definite eternal objects of a limited set of such objects is itself an
eternal object: it is those eternal objects as in that relationship. I
will call such an eternal object ‘complex.’ The eternal objects which
are the relata in a complex eternal object will be called the
‘components’ of that eternal object. Also if any of these relata are
themselves complex, their components will be called ‘derivative
components’ of the original complex object. Also the components of
derivative components will also be called derivative components of the
original object. Thus the complexity of an eternal object means its
analysability into a relationship of component eternal objects. Also the
analysis of the general scheme of relatedness of eternal objects means
its exhibition as a multiplicity of complex eternal objects. An eternal
object, such as a definite shade of green, which cannot be analysed into
a relationship of components, will be called ‘simple.’
We can now explain how the analytical character of the realm of eternal
objects allows of an analysis of that realm into grades.
In the lowest grade of eternal objects are to be placed those objects
whose individual essences are simple. This is the grade of zero
complexity. Next consider any set of such objects, finite or infinite as
to the number of its members. For example, consider the set of three
eternal objects _A, B, C_, of which none is complex. Let us write _R(A,
B, C)_ for some definite possible relatedness of _A, B, C_. To take a
simple example, _A, B, C_ may be three definite colours with the
spatio-temporal relatedness to each other of three faces of a regular
tetrahedron, anywhere at any time. Then _R(A, B, C)_ is another eternal
object of the lowest complex grade. Analogously there are eternal
objects of successively higher grades. In respect to any complex eternal
object, _S(D1, D2, ... Dn)_, the eternal objects _D1, ... Dn_, whose
individual essences are constitutive of the individual essence of _S(D1,
... Dn)_, are called the components of _S(D1, ... Dn)_. It is obvious
that the grade of complexity to be ascribed to _S(D1, ... Dn)_ is to be
taken as one above the highest grade of complexity to be found among its
components.
There is thus an analysis of the realm of possibility into simple
eternal objects, and into various grades of complex eternal objects. A
complex eternal object is an abstract situation. There is a double sense
of ‘abstraction,’ in regard to the abstraction of _definite_ eternal
objects, _i.e._, non-mathematical abstraction. There is abstraction from
actuality, and abstraction from possibility. For example, _A_ and _R(A,
B, C)_ are both abstractions from the realm of possibility. Note that
_A_ must mean _A_ in all its possible relationships, and among them
_R(A, B, C)_. Also _R(A, B, C)_ means _R(A, B, C)_ in all its
relationships. But this meaning of _R(A, B, C)_ excludes other
relationships into which _A_ can enter. Hence _A_ as in _R(A, B, C)_ is
more abstract than _A simpliciter_. Thus as we pass from the grade of
simple eternal objects to higher and higher grades of complexity, we are
indulging in higher grades of abstraction from the realm of possibility.
We can now conceive the successive stages of a definite progress towards
some assigned mode of abstraction from the realm of possibility,
involving a progress (in thought) through successive grades of
increasing complexity. I will call any such route of progress ‘an
abstractive hierarchy.’ Any abstractive hierarchy, finite or infinite,
is based upon some definite group of simple eternal objects. This group
will be called the ‘base’ of the hierarchy. Thus the base of an
abstractive hierarchy is a set of objects of zero complexity. The formal
definition of an abstractive hierarchy is as follows:
An ‘abstractive hierarchy based upon _g_,’ where _g_ is a group of
simple eternal objects, is a set of eternal objects which satisfy the
following conditions,
(i) the members of _g_ belong to it, and are the only simple eternal
objects in the hierarchy,
(ii) the components of any complex eternal object in the hierarchy are
also members of the hierarchy, and
(iii) any set of eternal objects belonging to the hierarchy, whether all
of the same grade or whether differing among themselves as to grade, are
jointly among the components or derivative components of at least one
eternal object which also belongs to the hierarchy.
It is to be noticed that the components of an eternal object are
necessarily of a lower grade of complexity than itself. Accordingly any
member of such a hierarchy, which is of the first grade of complexity,
can have as components only members of the group _g_; and any member of
the second grade can have as components only members of the first grade,
and members of _g_; and so on for the higher grades.
The third condition to be satisfied by an abstractive hierarchy will be
called the condition of connexity. Thus an abstractive hierarchy springs
from its base; it includes every successive grade from its base either
indefinitely onwards, or to its maximum grade; and it is ‘connected’ by
the reappearance (in a higher grade) of any set of its members belonging
to lower grades, in the function of a set of components or derivative
components of at least one member of the hierarchy.
An abstractive hierarchy is called ‘finite’ if it stops at a finite
grade of complexity. It is called ‘infinite’ if it includes members
belonging respectively to all degrees of complexity.
It is to be noted that the base of an abstractive hierarchy may contain
any number of members, finite or infinite. Further, the infinity of the
number of the members of the base has nothing to do with the question as
to whether the hierarchy be finite or infinite.
A finite abstractive hierarchy will, by definition, possess a grade of
maximum complexity. It is characteristic of this grade that a member of
it is a component of no other eternal object belonging to any grade of
the hierarchy. Also it is evident that this grade of maximum complexity
must possess only one member; for otherwise the condition of connexity
would not be satisfied. Conversely any complex eternal object defines a
finite abstractive hierarchy to be discovered by a process of analysis.
This complex eternal object from which we start will be called the
‘vertex’ of the abstractive hierarchy: it is the sole member of the
grade of maximum complexity. In the first stage of the analysis we
obtain the components of the vertex. These components may be of varying
complexity; but there must be among them at least one member whose
complexity is of a grade one lower than that of the vertex. A grade
which is one lower than that of a given eternal object will be called
the ‘proximate grade’ for that object. We take then those components of
the vertex which belong to its proximate grade; and as the second stage
we analyse them into their components. Among these components there must
be some belonging to the proximate grade for the objects thus analysed.
Add to them the components of the vertex which also belong to this grade
of ‘second proximation’ from the vertex; and, at the third stage analyse
as before. We thus find objects belonging to the grade of third
proximation from the vertex; and we add to them the components belonging
to this grade, which have been left over from the preceding stages of
the analysis. We proceed in this way through successive stages, till we
reach the grade of simple objects. This grade forms the base of the
hierarchy.
It is to be noted that in dealing with hierarchies we are entirely
within the realm of possibility. Accordingly the eternal objects are
devoid of real togetherness: they remain within their ‘isolation.’
The logical instrument which Aristotle used for the analysis of actual
fact into more abstract elements was that of classification into species
and genera. This instrument has its overwhelmingly important application
for science in its preparatory stages. But its use in metaphysical
description distorts the true vision of the metaphysical situation. The
use of the term ‘universal’ is intimately connected with this
Aristotelian analysis: the term has been broadened of late; but still it
suggests that classificatory analysis. For this reason I have avoided
it.
In any actual occasion α, there will be a group _g_ of simple eternal
objects which are ingredient in that group in the most concrete mode.
This complete ingredience in an occasion, so as to yield the most
complete fusion of individual essence with other eternal objects in the
formation of the individual emergent occasion, is evidently of its own
kind and cannot be defined in terms of anything else. But it has a
peculiar characteristic which necessarily attaches to it. This
characteristic is that there is an _infinite_ abstractive hierarchy
based upon _g_ which is such that all its members are equally involved
in this complete inclusion in α.
The existence of such an infinite abstractive hierarchy is what is meant
by the statement that it is impossible to complete the description of an
actual occasion by means of concepts. I will call this infinite
abstractive hierarchy which is associated with α ‘the associated
hierarchy of α.’ It is also what is meant by the notion of the
connectedness of an actual occasion. This connectedness of an occasion
is necessary for its synthetic unity and for its intelligibility. There
is a connected hierarchy of concepts applicable to the occasion,
including concepts of all degrees of complexity. Also in the actual
occasion, the individual essences of the eternal objects involved in
these complex concepts achieve an aesthetic synthesis, productive of the
occasion as an experience for its own sake. This associated hierarchy is
the shape, or pattern, or form, of the occasion in so far as the
occasion is constituted of what enters into its full realisation.
Some confusion of thought has been caused by the fact that abstraction
from possibility runs in the opposite direction to an abstraction from
actuality, so far as degree of abstractness is concerned. For evidently
in describing an actual occasion α, we are nearer to the total concrete
fact when we describe α by predicating of it some member of its
associated hierarchy, which is of a high grade of complexity. We have
then said more about α. Thus, with a high grade of complexity we gain in
approach to the full concreteness of α, and with a low grade we lose in
this approach. Accordingly the simple eternal objects represent the
extreme of abstraction from an actual occasion; whereas simple eternal
objects represent the minimum of abstraction from the realm of
possibility. It will, I think, be found that, when a high degree of
abstraction is spoken of, abstraction from the realm of possibility is
what is usually meant—in other words, an elaborate logical construction.
So far I have merely been considering an actual occasion on the side of
its full concreteness. It is this side of the occasion in virtue of
which it is an event in nature. But a natural event, in this sense of
the term, is only an abstraction from a complete actual occasion. A
complete occasion includes that which in cognitive experience takes the
form of memory, anticipation, imagination, and thought. These elements
in an experient occasion are also modes of inclusion of complex eternal
objects in the synthetic prehension, as elements in the emergent value.
They differ from the concreteness of full inclusion. In a sense this
difference is inexplicable; for each mode of inclusion is of its own
kind, not to be explained in terms of anything else. But there is a
common difference which discriminates these modes of inclusion from the
full concrete ingression which has been discussed. This _differentia_ is
_abruptness_. By ‘abruptness’ I mean that what is remembered, or
anticipated, or imagined, or thought, is exhausted by a finite complex
concept. In each case there is one finite eternal object prehended
within the occasion as the vertex of a finite hierarchy. This breaking
off from an actual illimitability is what in any occasion marks off that
which is termed mental from that which belongs to the physical event to
which the mental functioning is referred.
In general there seems to be some loss of vividness in the apprehension
of the eternal objects concerned: for example, Hume speaks of ‘faint
copies.’ But this faintness seems to be a very unsafe ground for
differentiation. Often things realised in thought are more vivid than
the same things in inattentive physical experience. But the things
apprehended as mental are always subject to the condition that we come
to a stop when we attempt to explore ever higher grades of complexity in
their realised relationships. We always find that we have thought of
just this—whatever it may be—and of no more. There is a limitation which
breaks off the finite concept from the higher grades of illimitable
complexity.
Thus an actual occasion is a prehension of one infinite hierarchy (its
associated hierarchy) together with various finite hierarchies. The
synthesis into the occasion of the infinite hierarchy is according to
its specific mode of realisation, and that of the finite hierarchies is
according to various other specific modes of realisation. There is one
metaphysical principle which is essential for the rational coherence of
this account of the general character of an experient occasion. I call
this principle, ‘The Translucency of Realisation.’ By this I mean that
any eternal object is just itself in whatever mode of realisation it is
involved. There can be no distortion of the individual essence without
thereby producing a different eternal object. In the essence of each
eternal object there stands an indeterminateness which expresses its
indifferent patience for any mode of ingression into any actual
occasion. Thus in cognitive experience, there can be the cognition of
the same eternal object as in the same occasion having ingression with
implication in more than one grade of realisation. Thus the translucency
of realisation, and the possible multiplicity of modes of ingression
into the same occasion, together form the foundation for the
correspondence theory of truth.
In this account of an actual occasion in terms of its connection with
the realm of eternal objects, we have gone back to the train of thought
in our second chapter, where the nature of mathematics was discussed.
The idea, ascribed to Pythagoras, has been amplified, and put forward as
the first chapter in metaphysics. The next chapter is concerned with the
puzzling fact that there is an actual course of events which is in
itself a limited fact, in that metaphysically speaking it might have
been otherwise. But other metaphysical investigations are omitted; for
example, epistemology, and the classification of some elements in the
unfathomable wealth of the field of possibility. This last topic brings
metaphysics in sight of the special topics of the various sciences.