Science and the Modern World/Chapter 10

by Alfred North Whitehead

CHAPTER X

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 In this alternative scheme, the notion of material, as fundamental, has been replaced by that of organic synthesis.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^[1] 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.

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 definite 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 A into α. Thus the synthetic prehension, which is α, is the solution of the indeterminateness of A into the determinateness of α. Accordingly the relationship between A and α is external as regards A, 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 A into α is expressed by all the true propositions which are about both A and α, and also — it may be — about other things.

The determinate relatedness of the eternal object A to every other eternal object is how A 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 A into an actual occasion α, the mutual relationships of A to other eternal objects, as thus graded in realisation, require for their expression a reference to the status of A 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 (A, say). The actual occasion a synthesises in itself every eternal object; and, in so doing, it includes the complete determinate relatedness of A 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 A 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 A as an element in the aesthetic synthesis. In so far as it stands in this lowest grade, every determinate relationship of A 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 a. 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, . . . X_n, 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 ὓλη — which is common to all actual occasions; and the synthetic activity which prebends 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, . . . D_n), the eternal objects D₁, . . . D_n, whose individual essences are constitutive of the individual essence of S(D₁, . . . D_n), are called the components of S(D₁, . . . D_n). It is obvious that the grade of complexity to be ascribed to S(D₁ . . . D_n) 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 individlial 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.

Notes

1. Cf. my Principles of Natural Knowledge, Ch. V, Sec. 13.