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 In this alternative scheme, the notion of material, as fundamental, has been replaced by that of organic synthesis.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 previous chapters, I have examined how the scientific movement has affected the deeper issues that have occupied modern thinkers. No one person, small group, or single age can think of everything at once. So, to bring out the various effects of science on thought, I have treated the subject historically. In looking back, I have kept in mind the ultimate issue of the whole story. The familiar framework of scientific materialism is clearly falling apart. It dominated the three centuries I have examined. I have therefore emphasized various schools of criticism of the dominant views. I have also tried to outline an alternative view of the universe. It must be broad enough to include what is fundamental to both science and its critics. In this alternative view, organic synthesis replaces matter as the fundamental concept. But I have always approached the subject by considering the actual complexities of scientific thought and the particular puzzles it raises.

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.

In this chapter and the next, we will set aside the particular problems of modern science. Instead, we will consider the nature of things objectively, before examining their details. This approach is called ‘metaphysical.’ Readers who find metaphysics tiresome, even in two brief chapters, may prefer to skip straight to the chapter on ‘Religion and Science.’ That chapter returns to 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.

These metaphysical chapters are purely descriptive. They are justified on three grounds: (i) our direct knowledge of the actual occasions that make up our immediate experience, (ii) their success in providing a basis for bringing our systematic accounts of different kinds of experience into harmony, and (iii) their success in providing the concepts needed to develop an epistemology, or account of knowledge. By (iii), I mean that an account of the general character of what we know must do something more. It must enable us to explain how knowledge is possible as something that exists within the things known.

In any occasion of cognition, that which is known is an actual occasion of experience, as diversified¹⁶ 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.

In any occasion of cognition, what is known is an actual occasion of experience. It is diversified¹⁶ by reference to a realm of entities that transcend that immediate occasion. These entities have similar or different connections with other occasions of experience. For example, a definite shade of red may be linked with a spherical shape in a definite way in the immediate occasion. But that shade of red and that spherical shape show that they transcend that occasion. Each has other relationships to other occasions. Also, even apart from the actual occurrence of the same things in other occasions, every actual occasion is set within a realm of interconnected alternatives. This realm is revealed by all the untrue propositions that can meaningfully be stated about that occasion. It is the realm of alternative suggestions, whose foothold in actuality transcends each actual occasion. Art, romance, and criticism with reference to ideals reveal how untrue propositions are truly relevant to each actual occasion. This relevance is the foundation of the metaphysical position I maintain: understanding actuality requires reference to ideality. Both realms are intrinsically present in the total metaphysical situation. The fact that a proposition about an actual occasion is untrue may express a vital truth about its aesthetic achievement. It expresses the ‘great refusal’ that is the primary characteristic of that achievement. An event is decisive to the extent that its untrue propositions are important to it. Their relevance to the event cannot be separated from what the event itself is as an achievement. These transcendent entities have been called ‘universals.’ I prefer the term ‘eternal objects.’ It frees me from assumptions that cling to the former term because of its long philosophical history. Eternal objects are therefore abstract by nature. By ‘abstract’ I mean that an eternal object’s essence, what it is in itself, can be understood without reference to any 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. I call this connection its mode of ingression into that occasion. Thus, to understand an eternal object, we must know (i) its particular individuality, (ii) its general relationships to other eternal objects as capable of being realised in actual occasions, and (iii) the general principle that expresses its ingression into 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 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.

These three headings express two principles. The first is that each eternal object is an individual, which is what it is in its own particular way. This individuality is the object’s individual essence. It cannot be described except as itself. Thus, individual essence is simply essence considered in terms of its uniqueness. Further, the essence of an eternal object is simply the object considered as making its own unique contribution to each actual occasion. This contribution is the same for all such occasions in one respect. In every mode of ingression, the object is its identical self. But the contribution varies from one occasion to another because its modes of ingression differ. Thus, the metaphysical status of an eternal object is that of a possibility for an actuality. The character of every actual occasion is defined by how these possibilities are actualized in it. Thus, actualization is a selection among possibilities. More accurately, it is a selection that results in possibilities being realized to different degrees in that occasion. This conclusion brings us to the second metaphysical principle. An eternal object, considered as an abstract entity, cannot be separated from its reference to other eternal objects or to actuality in general. It is, though, disconnected from its actual modes of ingression into specific actual occasions. This principle is expressed by the statement that each eternal object has a ‘relational essence.’ This relational essence determines how the object can 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.

In other words: If A is an eternal object, then what A is in itself involves A’s status in the universe. A cannot be separated from that status. The essence of A determines its relationships to other eternal objects. But it leaves its relationships to actual occasions undetermined. Because A’s relationships to other eternal objects are determined by its essence, those relationships are internal relations. By this I mean that these relationships are part of what makes A what it is. An entity with internal relations cannot exist as an entity without those relations. In other words, once an entity has internal relations, it always has them. Together, the internal relationships of A 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.

Again, an entity cannot have external relations unless its essence has an openness to them. This openness is an indeterminateness in the entity’s essence. The term ‘possibility’ as applied to A simply means that A has an essential openness to relationships with actual occasions. The relationships between A and an actual occasion are simply the different degrees to which A’s eternal relationships with other eternal objects are realized 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.

Thus, the general principle expressing A’s ingression into the particular actual occasion α has two sides. In the essence of A, its ingression into α is indeterminate. In the essence of α, the ingression of Α into α is determinate. Thus, α, a synthetic prehension, resolves the indeterminateness of Α into the determinateness of α. Accordingly, the relationship between Α and α is external to Α but internal to α. Every actual occasion α resolves all modalities into actual categorical ingressions. Truth and falsehood take the place of possibility. All true propositions about both Α and α express the complete ingression of Α into α. These propositions may also 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.

The definite relationship of the eternal object Α to every other eternal object follows necessarily and systematically from its nature. This relationship represents a possibility for realization. But a relationship is a fact that concerns all the things related. It cannot be treated as if it involved only one of them. So systematic mutual relatedness is a general fact inherent in the nature of possibility. The realm of eternal objects is properly called a ‘realm’ because each eternal object has its place in this general, systematic network of mutual relationships.

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.’

Consider the ingression of Α into an actual occasion α. The relationships between Α and other eternal objects are graded according to their realization. To express these relationships, we must refer to the status of Α and the other eternal objects in the spatio-temporal relationship. For this purpose, we cannot express that status without also referring to the status of α and other actual occasions in the same spatio-temporal relationship. Accordingly, the spatio-temporal relationship expresses the actual course of events. It is nothing more than a selective limitation within the general systematic relationships among eternal objects. By ‘limitation,’ as applied to the spatio-temporal continuum, I mean certain factual determinations. These include the three dimensions of space and the four dimensions of the spatio-temporal continuum. Such determinations are inherent in the actual course of events, but appear arbitrary when considered in relation to a more abstract possibility. These general limitations underlie actual things, unlike the limitations peculiar to each actual occasion. I will return to these general limitations more fully 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.

Further, understanding how all possibility relates to actuality requires reference to this space-time continuum. When considering a particular possibility, we may imagine going beyond the continuum. But insofar as there is any definite reference to actuality, we must specify how the continuum is transcended. The space-time continuum is therefore primarily a domain of possible relationships, selected from the broader realm of systematic relationships. This limited domain expresses one limit on possibility inherent in the general system of realization. Any possibility generally consistent with that system falls within this limit. Also, some things are possible in the abstract in relation to the general course of events. This is distinct from the particular limits introduced by particular occasions. Whatever is possible in this abstract sense extends throughout the space-time continuum, at every possible place and time.

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.

Fundamentally, the spatio-temporal continuum is the general system connecting all possibilities. This system is limited to what is relevant to the general fact of actuality. Possibility itself necessarily includes this relevance to actuality. For possibility is what can be achieved, considered apart from its actual 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.

It has already been emphasized that an actual occasion should be understood as a limitation. This process of limitation can be described further as a gradation. This feature of an actual occasion, which we may call α, needs further explanation. Indeterminateness is part of the essence of any eternal object, which we may call Α. The actual occasion α brings every eternal object together within itself. In doing so, α includes the complete determinate relationship of Α to every other eternal object or set of eternal objects. This synthesis limits what is realized, but not its content. Each relationship preserves its inherent identity. But each actual occasion, such as α, has inherent grades of entry into this synthesis. These grades can be expressed only as relevance of value. The relevance of value varies in grade between different occasions. At one end of the range, the individual essence of Α is included as an element in the aesthetic synthesis, to some degree. At the lowest grade, the individual essence of Α is excluded as an element in the aesthetic synthesis. In this lowest grade, every determinate relationship of Α is part of the occasion only as a particular unfulfilled alternative. It contributes no aesthetic value, except as an element in the systematic substratum of unfulfilled content. At a higher grade, a relationship may remain unfulfilled but still 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.

Thus, when A is considered only in relation to other eternal objects, it is ‘A conceived as not-being.’ Here ‘not-being’ means ‘considered apart from the definite fact that it is included in or excluded from actual events.’ Also, ‘A as not-being in respect to a definite occasion α’ means that A is excluded from α in all its definite relationships. Again, ‘A as being in respect to α’ means that A is included in α in some of its definite relationships. But no occasion can include A in all its definite relationships, because some of those relationships are opposites. Thus, in its excluded relationships, A will be not-being in α. This is so even when, in other relationships, A will be being in α. In this sense, every occasion is a synthesis of being and not-being. Furthermore, some eternal objects are synthesized in an occasion α merely quâ not-being. But every eternal object synthesized quâ being is also synthesized quâ not-being. Here ‘Being’ means ‘individually effective in the aesthetic synthesis.’ Also, the ‘aesthetic synthesis’ is the ‘experient synthesis’ viewed as self-creative. Its self-creation is limited by its internal relatedness to all other actual occasions. We thus reach a conclusion already stated above. Every occasion synthetically prehends all eternal objects. This general fact has two aspects: each eternal object is indeterminately related to occasions in general, and determinately related to each particular occasion. This statement summarizes the account of how external relations are possible. But the account depends on separating the spatio-temporal continuum from its mere implication in actual occasions, as usually explained. It also depends on showing that the continuum originates in 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.

The difficulty with internal relations is explaining how any particular truth is possible. To the extent that there are internal relations, everything must depend on everything else. But if everything depends on everything else, we cannot know anything until we know everything else equally well. Apparently, then, we must say everything at once. This supposed necessity is plainly untrue. So we must explain how internal relations can exist, given that we accept the existence of 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.

Actual occasions are selections from the realm of possibilities. Therefore, the ultimate explanation of their general character must come from an analysis of the realm of possibilities itself.

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 analytical character of the realm of eternal objects is the primary metaphysical truth about it. This means that the status of any eternal object A in this realm can be analyzed into an indefinite number of subordinate relationships, each limited in scope. For example, suppose B and C are two other eternal objects. Then there is a perfectly definite relationship R(A, B, C) involving only A, B, C. No other definite eternal objects need to be mentioned as things related by R(A, B, C). Of course, the relationship R(A, B, C) may involve subordinate relationships that are themselves eternal objects. The relationship R(A, B, C) is also itself an eternal object. There will also be other relationships that involve only A, B, C in the same sense. We must now examine how this limited relationship R(A, B, C) is possible, given the internal relatedness of eternal objects.

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.

Finite relationships exist in the realm of eternal objects for a reason. The relationships among these objects are entirely unselective and systematically complete. We are discussing possibility, so every possible relationship belongs to the realm of possibility. Each such relationship of an eternal object is based on that object’s perfectly definite status as a relatum in the general scheme of relationships. I have called this definite status the ‘relational essence’ of the object. An object’s relational essence can be determined by reference to that object alone. It does not require reference to any other objects, except those specifically involved in its individual essence when that essence is complex (as will be explained immediately). The meaning of the words ‘any’ and ‘some’ comes from this principle. So does the meaning of the ‘variable’ in logic. The whole principle is this: we can determine exactly how a definite eternal object A relates to a definite finite number n of other eternal objects. We can do this without determining anything about the other n objects, X₁, X₂, ... Xₙ, except that each has the status needed to play its respective part 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 relational essence alone of each eternal object determines the complete uniform scheme of relational essences. This is because 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. All eternal objects stand in all such relationships, as 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.

Accordingly, relationships as possibilities do not involve the individual essences of eternal objects. They involve any eternal objects as relata, provided the relata have the required relational essences. [This condition automatically limits the “any” in the phrase “any eternal objects,” simply by its nature.] This is the principle of the Isolation of Eternal Objects in the realm of possibility. Eternal objects are isolated because their relationships as possibilities can be expressed without reference to their individual essences. The realm of actuality is different from the realm of possibility. When eternal objects are included in an actual occasion, their individual essences are together in some of their possible relationships. This realized togetherness produces an emergent value. The value is defined, or shaped, by the definite eternal relatedness in 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, considered apart from any particular superject, is the abstract matter, the ὕλη, common to all actual occasions. The synthetic activity that prehends valueless possibility into superjicient informed value is the substantial activity. This substantial activity is omitted from any analysis of the static factors in the metaphysical situation. The elements identified by such an analysis are 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.’

The difficulty inherent in the concept of finite internal relations among eternal objects is thus avoided by two metaphysical principles. (i) The relations that constitute any eternal object A involve other eternal objects merely as things related to A. They do not refer to the individual essences of those other objects. (ii) The general relationship of A can therefore be divided into many finite relationships of A. This divisibility is part of the essence of that eternal object. The second principle obviously depends on the first. To understand A is to understand the how of a general scheme of relationship. Understanding this scheme does not require knowing the individual uniqueness of the other things related to A. The scheme can also be analyzed into many limited relationships, each with its own individuality. Yet these relationships also presuppose the total relationship within possibility. In actuality, there is first a general limitation of relationships. This limitation reduces the general unlimited scheme to the four-dimensional spatio-temporal scheme. The spatio-temporal scheme is, so to speak, the greatest common measure of the schemes of relationship inherent in all eternal objects, as limited by actuality. In other words, the how of the realization of selected relationships of an eternal object (A) in any actual occasion can always be explained. It can be explained by expressing the status of A in relation to the spatio-temporal scheme. It also requires expressing, within that scheme, the relationship of the actual occasion to other actual occasions. A definite finite relationship involving the definite eternal objects of a limited set is itself an eternal object. It is those eternal objects as they stand in that relationship. I will call such an eternal object ‘complex.’ The eternal objects related within a complex eternal object will be called its ‘components.’ If any of these related objects are themselves complex, their components will be called ‘derivative components’ of the original complex object. The components of derivative components will also be called derivative components of the original object. Thus, the complexity of an eternal object means that it can be analyzed into a relationship of component eternal objects. Similarly, analyzing the general scheme of relatedness of eternal objects means showing it as a multiplicity of complex eternal objects. An eternal object that cannot be analyzed into a relationship of components will be called ‘simple.’ A definite shade of green is an example.

We can now explain how the analytical character of the realm of eternal objects allows of an analysis of that realm into grades.

We can now explain how the analytical nature of the realm of eternal objects allows us to divide it 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.

The lowest grade of eternal objects contains those whose individual essences are simple. This is the grade of zero complexity. Next, consider any set of such objects, whether it has a finite or infinite number of members. For example, consider a set of three eternal objects, A, B, C, none of which is complex. Let us write R(A, B, C) for a definite possible relation among A, B, C. For a simple example, A, B, C may be three definite colours. Their relation in space and time may be that of three faces of a regular tetrahedron, anywhere at any time. Then R(A, B, C) is another eternal object, belonging to the lowest complex grade. In the same way, there are eternal objects of successively higher grades. Consider any complex eternal object, S(D₁, D₂, ... Dₙ). The eternal objects D₁, ... Dₙ are called the components of S(D₁, ... Dₙ). Their individual essences make up the individual essence of S(D₁, ... Dₙ). Clearly, the grade of complexity assigned to S(D₁, ... Dₙ) is one above the highest grade of complexity 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 therefore analyze the realm of possibility into simple eternal objects and various grades of complex eternal objects. A complex eternal object is an abstract situation. There are two senses of ‘abstraction’ when we abstract definite eternal objects, i.e., when the abstraction is not mathematical. 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, including R(A, B, C). Similarly, R(A, B, C) means R(A, B, C) in all its relationships. But this meaning of R(A, B, C) excludes other relationships that A can enter. Therefore, A as it appears in R(A, B, C) is more abstract than A simpliciter. Thus, as we move from simple eternal objects to increasingly complex grades, we abstract more 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:

We can now imagine the stages of a definite progression toward a particular way of abstracting from the realm of possibility. In thought, this progression moves through levels of increasing complexity. I will call any such path ‘an abstractive hierarchy.’ Every abstractive hierarchy, whether finite or infinite, is based on a particular group of simple eternal objects. I will call this group the ‘base’ of the hierarchy. Thus, the base of an abstractive hierarchy is a set of objects with 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,

An ‘abstractive hierarchy based upon g’ is a set of eternal objects that meet the following conditions, where g is a group of simple eternal objects:

(i) the members of g belong to it, and are the only simple eternal objects in the hierarchy,

(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

(ii) the parts 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.

(iii) Any set of eternal objects in the hierarchy may consist of objects of the same grade or of different grades. Together, the objects in the set are components or derivative components of at least one eternal object in 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 components of an eternal object must be less complex than the object itself. So any member of such a hierarchy at the first grade of complexity can have only members of group g as components. Any member of the second grade can have only members of the first grade and members of g as components. The same pattern applies to 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.

The third condition an abstractive hierarchy must satisfy is called the condition of connexity. An abstractive hierarchy begins with its base. It includes every successive grade from that base, either indefinitely or up to its maximum grade. The hierarchy is ‘connected’ in the following way. Any set of its members from lower grades reappears in a higher grade as 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.

An abstractive hierarchy is called ‘finite’ if it stops at a finite level of complexity. It is called ‘infinite’ if it includes members at every level 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.

The base of an abstractive hierarchy can have any number of members, finite or infinite. An infinite number of members in the base does not determine whether the hierarchy itself is 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.

A finite abstractive hierarchy, by definition, has a grade of maximum complexity. No member of this grade is a component of another eternal object in any grade of the hierarchy. This grade must also have only one member. Otherwise, the condition of connexity would not be satisfied. Conversely, any complex eternal object defines a finite abstractive hierarchy that can be discovered through analysis. We will call the complex eternal object we start with the ‘vertex’ of the abstractive hierarchy. It is the only member of the grade of maximum complexity. In the first stage of analysis, we identify the components of the vertex. These components may vary in complexity. But at least one component must belong to the grade one level below the vertex. We will call the grade one level below a given eternal object the ‘proximate grade’ for that object. We then take the components of the vertex that belong to its proximate grade. In the second stage, we analyse those components into their own components. Some of these must belong to the proximate grade for the objects we have just analysed. We add to them any components of the vertex that also belong to this grade of ‘second proximation’ from the vertex. In the third stage, we analyse them as before. This gives us objects belonging to the grade of third proximation from the vertex. We add to them any components from earlier stages of the analysis that belong to this grade. We continue through successive stages in this way until 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.’

When we deal with hierarchies, we are entirely within the realm of possibility. Therefore, eternal objects have no real togetherness. They remain in ‘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.

Aristotle used classification into species and genera as a logical tool. He used it to analyze actual facts by breaking them down into more abstract elements. This tool is overwhelmingly important in the early stages of science. But when used in metaphysical description, it distorts our true view of the metaphysical situation. The term ‘universal’ is closely connected with this Aristotelian analysis. The term has recently taken on a broader meaning, but it still suggests classification. 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.

In any actual occasion α, there will be a group g of simple eternal objects. These objects are ingredients in that group in the most concrete way. In this complete inclusion in an occasion, individual essence fuses as fully as possible with other eternal objects. Together, they form the individual occasion as it emerges. This complete inclusion is evidently unique and cannot be defined in terms of anything else. But it necessarily has one distinctive characteristic. There is an infinite abstractive hierarchy based on g. All members of this hierarchy are equally involved in the 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.

The existence of such an infinite abstractive hierarchy means that concepts cannot fully describe an actual occasion. I will call the infinite abstractive hierarchy associated with α ‘the associated hierarchy of α.’ This hierarchy is also what is meant by the connectedness of an actual occasion. This connectedness is necessary for the occasion’s synthetic unity and for it to be intelligible. A connected hierarchy of concepts applies to the occasion. It includes concepts of all degrees of complexity. In the actual occasion, the individual essences of the eternal objects involved in these complex concepts come together in an aesthetic synthesis. This synthesis produces the occasion as an experience for its own sake. The associated hierarchy is the shape, pattern, or form of the occasion, insofar as the occasion is made up of what enters into its full realization.

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.

Some confusion has arisen because abstraction from possibility works in the opposite direction from abstraction from actuality, in terms of how abstract each is. When we describe an actual occasion α, we come closer to the complete concrete fact by attributing a highly complex member of its associated hierarchy to α. We have then said more about α. Thus, greater complexity brings us closer to the full concreteness of α, while less complexity takes us farther away. Simple eternal objects therefore represent the greatest degree of abstraction from an actual occasion. But they represent the least degree of abstraction from the realm of possibility. I think that when people speak of a high degree of abstraction, they usually mean abstraction from the realm of possibility. In other words, they mean 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.

So far I have considered an actual occasion only in its full concreteness. It is in this respect that the occasion is an event in nature. But a natural event, in this sense, is only an abstraction from a complete actual occasion. A complete occasion includes what takes the form of memory, anticipation, imagination, and thought in cognitive experience. These elements of an experiencing occasion are also ways in which complex eternal objects are included in the synthetic prehension. They are included as elements in the emerging value. They differ from the concreteness of full inclusion. In a sense, this difference cannot be explained. Each mode of inclusion is of its own kind and cannot be explained in terms of anything else. But these modes of inclusion have a common feature that distinguishes them from the full concrete ingression discussed above. This differentia is abruptness. By ‘abruptness’ I mean that a finite complex concept fully captures what is remembered, anticipated, imagined, or thought. In each case, one finite eternal object is prehended within the occasion as the highest point of a finite hierarchy. This breaking off from an actual boundlessness distinguishes the mental in any occasion from what belongs to the physical event to which the mental functioning refers.

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.

In general, we seem to perceive the eternal objects involved less vividly. For example, Hume speaks of ‘faint copies.’ But this faintness seems a very unreliable basis for distinguishing them. Often, things we picture in thought are more vivid than the same things in inattentive physical experience. But there is always a limit to what we perceive mentally. When we try to explore ever more complex relationships among these things, we reach a stopping point. We always find that we have thought of just this, whatever it may be, and nothing more. This limit cuts off the finite concept from higher levels of boundless 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.

Thus, an actual occasion is a prehension of one infinite hierarchy (its associated hierarchy) along with various finite hierarchies. The infinite hierarchy is brought into the occasion according to its specific mode of realisation. The finite hierarchies are brought in according to various other specific modes of realisation. One metaphysical principle is essential to 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 remains itself, whatever mode of realisation it is involved in. Any distortion of its individual essence produces a different eternal object. The essence of each eternal object contains an indeterminateness. This indeterminateness expresses its equal readiness for any mode of ingression into any actual occasion. Thus, in cognitive experience, the same eternal object can be recognized as having ingression into the same occasion. Its ingression can have implications in more than one grade of realisation. Together, the translucency of realisation and the possible multiplicity of modes of ingression into the same occasion 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.

In describing an actual occasion through its connection with the realm of eternal objects, we have returned to the ideas in our second chapter. There we discussed the nature of mathematics. We have expanded the idea attributed to Pythagoras and presented it as the first chapter of metaphysics. The next chapter concerns a puzzling fact. There is an actual course of events, but it is limited in itself, because, metaphysically speaking, it might have been otherwise. But other metaphysical inquiries are left out. These include epistemology and the classification of some elements in the unfathomably rich field of possibility. This last topic brings metaphysics close to the particular subjects of the various sciences.