J. G. Bennett
In this paper, I shall endeavour to establish the thesis that understanding is possible because there is a world order that is reproduced or reflected in our experience through systems or sets of terms having universal properties. Systematics, or the study of systems, should, according to this thesis, be the appropriate instrument for the development of understanding, as science is the instrument for the development of knowledge.
Understanding is a special relationship between different parts of our experience. There is the general presentation of our senses that we sometimes call the 'world'. There is also an inner awareness that is called thought, or at least includes thought. Apart from these two, there is also an experience of directing, selecting and choosing between the various presentations that we associate with attention or the power of attention. Finally, there is the experience of willing, of initiating action through our own bodies that will change the 'world' or at least some part of our general presentation. Some combination of these four modes of experiencing gives rise to what we call “understanding”.
This understanding differs from sensation and thought by the property of standing astride, as it were, the various parts of the total experience and knitting them together. When we understand, our knowledge is linked to our sensation, but a connection is also made between our inner attention and our outward actions. We cannot simplify this situation by omitting any of the four elements : sensation, thought, attention, action and it seems to follow that understanding itself is not simple, but possibly even more complex than this first analysis suggests. It seems likely, for example, that understanding is progressive. to be approached by stages, but must, in its fullness, always remain beyond our reach.
The impulse to understand, and not merely to know and to act, is an impulse characteristic of man and apparently not shared by other animals. I am not concerned here with the origin and nature of this impulse, but with its implications that there is something to be understood and that understanding is not reducible to knowledge and action. We know facts by way of perception and conception. We act from instinct and desire directed by knowledge. But it also seems that knowledge and action would be mere automatism - indistinguishable from animal behavior or even the work of a machine - if not informed by some kind of understanding.
The assumption that there is something to be understood beyond fact and feeling, means that we suppose that there is some universal order or principles by which both we and our world are regulated. If there were no such order or principles caprice would reign. Anything and everything would be possible and nothing could be known or foreseen. No one doubts that there are possibilities and impossibilities, i.e. that there are universal laws that distinguish what can happen and what cannot happen. Most people would be prepared to admit that there are knowables and unknowables, i.e. that there are limits to what man can know of the totality of which our human experience forms so small a part. It would also probably be agreed that there are predictables and unpredictables. More generally, there are various regularities in our experience that cannot be accounted for solely in terms of the peculiarities and limitations of our human instruments of sensation and thought.
In the present paper, I suggest that these universal regularities are not the result of obscure properties of nature that can only be discovered by centuries of research, but rather modes of connectedness common both to the world and our experience of it. We perceive and understand in certain ways because we and the world are constructed in certain ways. These ways can be described in terms of systems and the study of all the possible forms of connectedness can therefore be called systematics. The word system is commonly used for every kind of group or collection of interacting things or ideas. The meaning common to nearly all uses of the word is that of an inner connectedness that distinguishes what forms part of a system from all that is 'outside' it. I want to define the word system in another more precise way as a set of distinct but mutually relevant terms. This requires clarification. A 'set' means a limited, well defined number, not just an indefinite collectivity. By 'terms' I mean any part of experience that can be identified by some persistent token or recurrent property. A term may be a thing, an idea, a relationship or a complex system of things, ideas and relationships, - provided only we can recognise it. By 'distinct' is meant distinguishable in respect of some property or quality; in other words no two terms of a system can be identical or even nearly so. Finally, there is the condition that the terms are mutually relevant. This means that each of the terms of the system requires all the others in order to be what it is and mean what it means .These definitions may seem so arbitrary and restrictive that we would be unlikely to meet with any set of terms that satisfy them all. In reality we cannot perceive, think, feel, act or understand anything except through. the distinctness and mutual relevance of the objects and ideas that present themselves to our awareness. The properties or attributes of systems are the elements of all possible understanding.
Whenever we say “this is a. . . ” we are pointing to a one-term system. Whenever we say “A is composed of B and C” we refer to a two-term system or dyad. Whenever we speak of connections or relatedness we affirm the reality of a three-term system: for if A and B are connected there must be another term C to connect them. A, B and C must be distinct and the fact that they need one another to exemplify connectedness means that they satisfy our definition of a system.
By systematics I mean the study of systems and their application to the problem of understanding ourselves and the world. It is possible to distinguish four branches of systematics.
1. Formal Systematics which studies the properties of systems without reference to the nature of the terms. It consists mainly of the investigation of possible modes of connectedness which evidently can be very complex for systems with more than three or four terms.
2. Pure Systematics which seeks to identify and describe the universal properties or attributes common to all systems. I shall give later a few examples of the results obtainable through the study of pure systematics
3. Applied Systematics This is the study of systems occurring in our experience and is chiefly directed to the identification of the terms and their characteristics.
4. Practical systematics as the name implies is the application of the understanding gained through the study of systems to the problems that arise in all departments of life.
Systems can be of three kinds: determinate, indeterminate and infinite. The number of terms gives the order of the system. We shall mainly be concerned with determinate systems in which the number of terms is known and less than twelve. Indeterminate systems can also be called societies: they are composed of a relatively large number of terms making it impossible to specify all the connections or even the main groups of connections. The infinite system is the complete expression of all possible modes of connectedness without limit to the number and variety of terms.
The independence of the terms of a system is expressed by saying that every term has a character. The combination of characters gives the system an attribute that will depend upon the way in which the terms are connected and interact. For example, the two-term system man-woman has the characters of masculinity and femininity. These may be combined to. produce harmony, mutual completion and fecundity, or they may result in opposition, conflict and mutual destruction. Nevertheless, there is for all the systems of a given order a certain similarity or analogy in their total quality. This observation leads to the basic postulate of pure systematics, namely:
All the systems of a given order participate more or less in a common property called the systemic attribute. The systemic attributes are the source of the basic regularities that we discover in our experience and the key to understanding ourselves and the world.
We shall examine now some of the simpler systems with a view to elucidating their systemic attributes.
The first point to be noted is that the attribute of a system depends upon its order, i.e. upon the number of its terms. All systems with only one term, i.e. monads are characterised by wholeness without inner distinctions. A whole may be diversified, but the diversity has not developed into distinctions so that all the system remains monadic. The total content of a moment of awareness is such a one-term system. The whole universe regarded as the totality that presents itself to our experience is a monad. The combination of wholeness and diversity is expressed by the word universality and we can readily see that every one-term system shares the common attribute of universality. Moreover this attribute can have no meaning except in a monad. This will be apparent if we reflect that we should never say that a pair of objects or ideas is an universe.
The only exception to this proposition that every whole combines unity and diversity is the hypothetical true atom. It is of considerable importance to philosophy that physical science tends to regard even the so-called ultimate particle as composite and indeed as an universe. The nearest notion to that of ultimate indivisibility is that of Planck's quantum of action. As Bohm has shown , there are grounds for supposing that sub quantum levels exist. The notion of hyle developed in the first volume of my Dramatic Universe suggests that universality characterises the ground state of matter no less than the totality of all its parts.
Here 1 should reply to the objection that a 'diversity in unity' is a dualistic notion inapplicable to the monad. This objection is due to a defect of language. Unity in diversity is in reality a simple, indivisible idea that should be conveyed by the word 'universality'.
In Bacon's Advancement of Learning, he uses the word to mean the unification of knowledge, the Philosophia Prima which seeks the 'unity in diversity' of all the particular arts and sciences .
We should, however, think of it as the immediate and simplest delivery of our experience : the “here and now” of the present moment is both one and diverse and there is no question of separating the unity and diversity into distinct concepts until we distinguish them and that means to go from the monad to the dyad. The view that universality is a simple notion - indeed the simplest possible notion because the most immediate is confirmed by Piaget's studies of the development of intelligence in the child.
Notions of one as the unit of counting, of homogeneity, continuity, undivided unity are all derivative and far more complicated than at first appears.
I shall make the assumption that all the properties common to all systems of a given order can be expressed as their systemic attribute. There should be one and only one attribute for each order, but in order to express this attribute it may be necessary to put together many partial or incomplete descriptions. We have our first systemic attribute in the universality of all monads.
The next step comes when we introduce a distinction valid for the whole monad. We now have two parts that satisfy the conditions of independence and mutuality. This is exemplified in the account of creation in Genesis and the Babylonian tablets. 'Light' is the undivided awareness of what is. It corresponds to the moment of consciousness in our current experience. Its only attribute is universality. The second step is separation of light and darkness or of the upper and lower regions. That which was .,one is now two but the two comprise the one and their separation is an enrichment - a creative act.
It is not hard to see that the systemic attribute of the dyad is complementarity. Light and darkness are not opposites but complementarities. In the story of the creation, light first appears alone - revealing the universe - but not revealing distinction. When light and darkness are separated all other dyads are revealed. Nothing can be known except by light and shade, i.e. by contrast.
The notion of complementarity is of unlimited generality. It has in recent years played a great part in the development of physical theory thanks to the work of Niels Bohr, Max Born and others. It implies acceptance of the irreducible character of the dyad. We encounter many complementary dyads in philosophy, science and human affairs. The Cartesian doctrine of two substances is derived from the dyad, mind-brain. The dyad man-woman is the foundation of human society. In every case, the systemic attribute of complementarity gives us the key to understanding the situation. We gain nothing by seeking to reduce the dyad to the monad, but we feel nevertheless, that complementarity does not exhaust the attributes of systems. As we found it necessary to go from the monad to the dyad, so we must seek in a third term for the resolution of the enigma of complementarity. The enigma can be stated thus : if a monad X is divided into two mutually exclusive P and Q, how is a link between P and Q to be found without reverting to the universality of X? The link must clearly be different from P, Q or X itself. We must then postulate a triad ABC such that
A+B+C P+Q X
where the symbol H does not mean equal or identical, but 'referring to the same situation'. For example we can have
X = man
P+Q = male and female
A+B+C = parents and child.
P and Q in becoming A and B have changed character : they are no longer a complementary dyad but two terms in a triad. P and Q are both human beings i.e. both belong to the one-term system MAN=X.
Another example can be taken from physical science
X = electron as electric charge
P + Q = electron as particle and wave
A + B + C = electron as particle in three aspects: electron-positron-neutrino.
In each case we have a transition from complementarity to a completely new situation in which the terms, though individually the same, have acquired quite new characters from their relationship to the others. It is not hard to recognise that the new systemic attribute is akin to relatedness; but it is a dynamic relatedness that can be understood only if it is associated with notions of will and freedom. I have already discussed very fully the connection between relatedness, will, freedom and the triad in the Dramatic Universe 5 and shall not attempt here to cover the same ground. The only point that need be made is to draw attention to the immense enrichment of our understanding that comes from understanding the systemic attribute of relatedness. Whereas neither universality nor complementarity are such as to allow for connection between systems, relatedness establishes a nexus of connections that extends through all possible worlds. The reason for this is that a term A of a triad X can also be a term of another triad Y thus linking X and Y together. It is also possible for X to be a term in a superordinate system Z. Thus triadic relatedness can comprise co-ordination, subordination and superordination.
For example we have A as husband and father in system X but son in system Y of the preceding generation. In Y, A fulfills the role of C, the child in X. The family (ABC) = X is a term in the system Z consisting of the three generations: grand parents D, parents E and children F. In this way, X fulfills the same role as the link between D and F, as the child C fulfills as the link between A and B.
Evidently, the network of triads can be extended in all directions of space, time and number. It can also be shown that any set of relations however complex can be reduced to a nexus of triads. It follows that as relatedness is the systemic attribute of the triad so also conversely all cases of relatedness can be expressed as systems of the third order, i.e. triads.
If we contemplate the scheme so far developed of universality, complementarity and relatedness, we can have no doubt that we have not exhausted the attributes either of the world or of our own nature. There is a certain rigidity in the net-work of triads which must be relaxed if we are to find place for creative activity. Moreover, no principle of order and hence of continuity can be derived from the first three systems. It has been shown by Russell that mathematical order can be defined only by reference to four independent terms. This agrees with the view that the triad is not capable of supporting a principle of order.
In the Dramatic Universe, I associated the tetrad with Being and Creativity', but neither with order nor continuity, except in so far as it became clear that the notion of being itself requires to be understood relatively and so implies both order and continuity.
We can approach the systemic attribute of the tetrad if we recall that freedom is the quintessence of relatedness. Freedom to be realised, must be exercised and we can ask the question how and in what medium is freedom exercised. The answer must surely be that the exercise of freedom is creative activity and its medium is being. Now creativity is the dynamic aspect of being reciprocal to order as its passive aspect. We can reasonably conclude that reciprocity is the systemic attribute of the tetrad providing we understand the word rightly. It is not capricious, arbitrary or transcendental, but the regulated orderly activity whereby the world undergoes progressive enrichment of its content and quality. Herein lies the reciprocity of the tetrad.
The wealth of possible connections between four independent terms: K, L, M, N - there are twenty-four primary arrangements - entitles us to suppose that reciprocity has many forms.
The entire process of existence in space and time is a form of creativity. The act of freedom whereby entirely new factors enter the process is another form. There is casual and there is non-casual reciprocity. There is absolute and there is relative reciprocity. To understand all the forms, we need to recognise the characters common to the four terms of any and every tetrad. These we can deduce from our intuition of the nature of any creative activity. There must be:
First term K : A motive force or source of the action Second term L: A medium or field in which the action proceeds Third term M: A character which represents the state of the system
Fourth term N: A character which corresponds to the new element introduced by the creative action.
Figuratively one could speak of K and L as “above and below” and M and N as “within and without”. Creativity in all its forms involves an interplay of the four factors of such a kind as to transform and to enrich the situation.
It is worth noting that the four factors K, L, M, N can be used to define order which needs the concepts of 'extremes' and 'betweens'.
In order to illustrate the tetrad, I shall take an example recently studied by the Integral Science Education Research Group of the Institute. The scientific activity of man is directed towards knowing, doing and understanding. It is evidently creative in character and should therefore best be exemplified in a tetrad. We can, in fact, recognise four independent factors.
K. Understanding as the source of creative activity and also its goal.
L. Insight into Nature as the field of scientific work.
M. The whole body of scientific knowledge representing the state of the system.
N. Experimentation, observation and technical progress as the new element introduced by the creative action.
All scientific work requires, though in varying proportions, all four elements. The scientist must first of all make contact with his material. His insight into what lies before him enables him to bring to bear both his knowledge and his experimental skill. As new data are discovered he has to reconcile them with existing theories and for this he must formulate a hypothesis which requires a creative act of the understanding. As the hypothesis is tested and verified it gradually enters into man's total understanding of nature. Thus there is a flux and reflux of creative activity in which all the factors play a part.
The four elements correspond to four abilities or skills which the accomplished scientist displays.
Insight - the ability to recognise significant characteristics in the subject matter of the research. The feeling or flair for natural phenomena.
Experimental skill - instrumentation and the conduct of
experiments. Power of observation.
Theoretical ability - analysis of results. Empirical generalisation.
Knowledge and memory.
Synthetic understanding - hypothesis formation. Devising of crucial tests. Integration of new ideas into existing body of theory and practice. True creativity in science.
A thorough examination of the tetrad will reveal the immense significance of the systemic requirements of independence and mutual relevance. The'scientific tetrad' is applicable to the work of the individual, to team work, to the advance of a particular branch of science and to the scientific activity of mankind as a whole: thus exemplifying the extreme generality of the systemic attribute of reciprocity and the power of the tetrad as an instrument of understanding.
Nevertheless, the first four systems by no means exhaust the modes of understanding open to us. The tetrad is the field of creativity: but it does not provide for non-creativity ' . It comprises all that becomes real but it does not allow for non-realisation. Because of this lack, it has no central point from which alternative paths can bifurcate. In the Dramatic Universe, I connected the five-term system with potentiality and the quality that I called 'spiritualisation'. We can also look upon it as the focus of the creative agent. Referring back to the diagram, we might say that the tetrad needs to be completed by installing in the centre, the scientist himself.
Yet another way of looking at the transition from tetrad to pentad is to notice that whereas the triad is too rigid, the tetrad is too lifeless to give an adequate representation of reality. To bring the tetrad to life we must go forward and add a fifth term.
In Volume I of the Dramatic Universe I showed how potential energy can be represented by adding the fifth dimension of eternity to the four dimensions of space-time.
In theoretical physics, it has not been found possible to formulate a theory of potential energy fields without adding an independent parameter to the four coordinates of space-time. Looking more closely into the meaning of potentiality we can see that it is the field of creativity just as is the field of freedom. It seems then that in order to express the systemic attribute of the five-term system we must find a word that will convey the notion of open potentiality within which creative action can be accomplished and attach this notion to that of the creative agent. The word spirituality conveys some part of what we require, but it would certainly be confusing to the reader who was not aware of the way we have reached it. It seems better therefore to keep to the word potentiality making it clear that this is to be taken subjectively as referring to the agent as well as objectively as applied to the field.
Potentiality thus generalised, is a notion of far-reaching significance. It is closely associated with the idea of life itself - for life is both the creative agent and the field of creative action. In psychology, the fifth term is the “I” or self that exercises the powers or functions of the psyche - the latter according to Dr. C.G Jung consisting of four independent factors: sensation, intuition, thought and feeling.
In attempting to assess the importance of understanding the pentad, we must remember that a system is a set of terms significantly connected. There are very many ways in which five terms can be interconnected and this suggests that potentiality is a richer notion than is commonly supposed. We tend to see it in terms of temporal successiveness, but there are probably more important forms of potentiality that lie outside the fields of sense perception and mental constructs. Much that is mysterious and unaccountable, the immense field of non-casual phenomena, probably refers to five-term systems which we incorrectly interpret as dyads and so miss their true meaning.
We must not pause to discuss examples, but go forward to reach for the field in which potentiality is realised. This is clearly the act itself whereby creativity is accomplished. The additional term is that which gives concreteness and uniqueness to the creative act.
The nature of the hexad is to provide the conditions for free and independent self-realisation. This can also be regarded as a complete event standing out of the undifferentiated goings-on of the existing world.
In the Dramatic Universe, the hexad is associated with recurrence and the sixth dimension I have called hyparxis. This introduces a new depth and wealth of meaning for it allows that which already is what it is to become what it is. Self-realisation in this sense does not mean transformation into something different, but to become in reality what one was only in potentiality.
It is easy to see the connection between these notions and the Thomist doctrine of actus whereby the world becomes real. There are the further notions of the self-contained field and of the completed Being who can not only create, but does so within a world that is wholly his own. For reasons that cannot be fully discussed here, I propose to use the word significance to designate the systemic attribute of the hexad. We sometimes make the mistake of supposing that abstractions like 'things', 'ideas' or 'people' can be significant. Significance can be ascribed only to the concrete event which stands out from the general stream of happenings. Even an idea can be at the heart of an event. “Universal suffrage” is an idea, which only became significant in the context of the Reform which was an event. Without events neither people nor ideas can rightly be called either significant or insignificant. Only events - or as Whitehead called them actual occasions can be said to exist concretely. I must, however, sound a note of warning. An event, to deserve the name, is not matter in motion within a limited region of space and time. It has a pattern and it has something more than that which, in the Dramatic Universe, is called ableness-to-be. The event asserts itself, it reverberates through time and space. As it recurs it gains in concreteness. Starting as potentia it becomes actus. In passing from the pentad to the hexad it acquires just that significance that I have taken to be the systemic attribute.
It can do this only if there is a certain correspondence between its own character and the character of the historical environment. Failing this an event, however remarkable in its own right fails to play its part in history. Such abortive events do indeed frequently occur upon all scales and their occurrence is evidence of the real distinction between hexad and heptad. The charge of the Light Brigade at Balcaclava reverberates as an event, but it failed to become part of history. Indeed, the same can be said of the Crimean War as a whole. The death of Nicholas II deprived the event of its final act and with, the treaty of Paris, history slipped back to the status quo of 1848. The distinction between abortive and integrative events throws much light upon the nature of the heptad; but we must know more of the character of the seven terms if we are to find the right word to express the systemic attribute.
Now it is well known that the number seven has had a special, even sacred, character for both the Aryan and the Semitic cultures. It predominates in the Vedic and Avestan mythology and in the Hebrew and other Semitic traditions and rituals. The belief that there are seven primary qualities that attach to every important group of entities or powers is almost universal ; seven colours, seven metals, seven planets, seven Pleiades, seven Maruts, seven virtues, and seven sins, and very significantly, seven tones in the musical scale.
Throughout all the septenaries there are also notions of an inner structure : primary and secondary colours, half- and full-tone intervals, major and minor planets, beneficent and harmful metals, and so on. A recent, very interesting study of the septenary is Alice Bailey's Treatise on the Seven Rays. Here there is a clear statement that the qualities of the septenary correspond to the seven main types of historical activities divided into three primary and four secondary characters.
A different approach is that of Gurdjieff who combines the notion of seven qualities with that of a seven-fold progression from the event in posse to the event in actu as characteristic of all true history.
There is another feature of the seven-term system, namely its connection with structure. Traditionally, men have believed that every harmonious structure has seven coordinated segments. Representations of the human body as a septenary are to be found in almost all the traditional systems. These often depict the proportions and also the arrangement required in order to achieve harmony. Innumerable representations of the human body in art and in literature depict man as a septenary structure. No doubt much of fantasy and misunderstanding mars these schemes and the closely allied notion of microcosm and macrocosm linked by a common seven-fold structure; nevertheless, it is probable that behind it all are genuine insights that could be brought into focus if we had the key to the systemic attribute of the heptad.
The only sound approach to the question is to see if there are any notions that cannot be expressed adequately with less than seven independent terms. It is known from mechanical science that a completely stable structure requires seven independent supports. It has also been shown in our preceding analysis that the sequence : Universality, Complementarity, Relatedness, Reciprocity, Potentiality and Significance takes us to a concrete situation where we can describe events in all the wealth of
Triad Relatedness Receptivity
Tetrad Reciprocity Quantity
Pentad Potentiality Higher
lieptad Integrality Completeness
Octad Individuality Transcendence
The First Eight Systems
I shall not carry the present discussion further. It will be elaborated as fully as I am able in the 38th Chapter of Vol.111 of the Dramatic Universe. Meanwhile my purpose is to introduce Systematics as a new fundamental discipline of thought and action and the key to an informed understanding of many problems that at present issue in contradiction and confusion. Systematics can be looked upon as the complete development and generalisation of the doctrine of the “principle of formal purposiveness” first proposed by Kant in the Critique of Judgment. This principle means that there is something to be understood - as I said at the beginning of this paper - and further that understanding itself is capable of unlimited progress, because there is no limit to the series of systemic attributes, each of which penetrates more deeply into the reality than its predecessors. The idea of the correspondence between systems in nature and in thought is well expressed by Cassirer. “We find that nature 'favours' the effort of our faculty of judgment to discover a systematic order among her separate forms, and, so to speak, meets it half way”“. It seems to me that once we have grasped the notion of systems and have seen that every system constitutes a legitimate way of looking at the world and even of understanding it, the further development will come spontaneously by reflecting upon every kind of situation that can arise in our experience.
Systematics is not a science, if by this we mean, the study of a group of natural phenomena; it is rather an instrument applicable to all problems. It is nearer to mathematics than to any other discipline. Indeed, it may be possible to show that mathematics is that branch of general systematics which deals solely with one- two- and three-term systems. Universality, Complementarity and Relatedness are probably all the a priori notions required for deriving all the postulates and operations of mathematics.
Systematics is applicable to Art by adding the systemic attribute of reciprocity, to psychology, by invoking the notions of field and potentiality. It is the instrument required for historical criticism and can help us even to understand more of the subtle yet concrete dogmas of religion.
In this paper, I have not touched upon practical systematics: but I have verified in my own experience that light is thrown, by applying the systemic attributes, upon many of the apparent contradictions of our daily lives.
If systems are constituents of Reality and if we can, by research and experiment, come to understand them better, then systematics will prove to be an instrument of great importance for testing the validity of theories, for discovering hitherto unsuspected regularities in nature and for the better ordering of our affairs.
There is no standing still in systematics, but an inherent dynamism that leads on from system to system and yet leaves nothing behind. As a system takes shape for our understanding and begins to disclose its systemic attribute, it also compels us to look beyond itself to a fuller, richer and above all more concrete expression of the Reality in which we all share.
“Es so]] sich regen, schaffend handeln,
Erst sich gestalten, dann verwandeln;
Nur scheinbar steht's Momente still,
Das Ewige regt sich fort in allem:
Denn alles muss in Nichts zerfallen
Wenn es im Sein beharren will.”
GOETHE Gedichte Eins und A lles.
There must be a dynamic self-creative preparation for further transformations, each moment of which is only seemingly motionless. The dynamism of Reality pervades all and whatever seeks fixation in static being is condemned to disintegration and nothingness.
I . This last condition distinguishes systems as here understood from those of say Camap's Logical Syntax. The recognition of a term can be made with the help of elementary predicates, but the point is that each term of a system differs in respect of some elementary predicate from all the rest. Cf. H.
B. Curry Outlines of a Formalist Philosophy of mathematics p.28.
2, D. Botim Causality and Chance in Modern Physicv. Roudedge and Kegan Paul pp. 104-128.
3. F. Bacon. Advancement oflearning 1605. Book I v.art. 5 and 6
4. The monad here is merely a one-term system and as such no more “real” than two- three- or multiterm systems. Nevertheless it is worth noting that the monadology of Leibnitz is distinguished from atoniism precisely by the property of monads of being universal. For Leibnitz, 'each nionad contains the whole infinity ofexistence within itselfand is thus a concentrated imiverse.” Cf. Leibnitz Letterv to Bouquet and Bayle, and also Monadology (I 714 Vienna) p.706.
5. Vol II Chapter 27 - 31
6. Vol 11 Chapter 32 - 34
7. 'Ibis was a favourite notion of Herbert Spencer who took it as the further stage beyond coordination. It we take ro-ordination as the juxtaposition of two triads, and therefore a hexed, integration is the binding together of two acts of will and hcnce a beptad,
8. Cf. Dramatic Universe Vol. I pp. 34, 45-46.
9- Cf. 1. Kant Critique of Judgment Werke Vol. 5. Introduction. Translation J. H. Bernard 1892 pp.24-27.
10. Ibid. p.26. 'ne judgment has in itself a principle a priori of the possibility of nature … which … it assumes on behalf of a natural order cogidsable by our understanding.'
11. E. Cassirer The Problem of Knowledge Yale 1950 p. 1 26.
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See also Emergence from Chaos