International Society for Philosophers

International Society for Philosophers

Wisdom begins with wonder

PHILOSOPHY PATHWAYS                   ISSN 2043-0728


Issue number 105 20th June 2005


I. 'Interpreting Plato' by D.R. Khashaba

II. 'Mimesis in Aristotle and Pollock' by Andrew Watson

III. 'A Sunday Afternoon with Georges on an Island in the Cosmos' by
    Richard Schain



The nature of metaphysics, the nature of art, the relation between philosophy and science and the philosophies of Plato and Aristotle all feature in this issue.

D.R. Khashaba has kindly allowed us to publish the Introductory chapter from his new book, Plato: An Interpretation where he argues that the study of Plato, and philosophy itself have been seriously hindered by the false assimilation of philosophy to scientific inquiry.

Andrew Watson, a teacher at Loretto School Edinburgh, is currently studying for the Associate Award of the International Society for Philosophers under my mentorship. In a well researched and thought provoking essay, Watson argues for the relevance of Aristotle's theory of art as mimesis to the understanding of the abstract expressionist paintings of Jackson Pollock.

In an imaginary dialogue with the painter Georges Seurat, Richard Schain continues the theme of 'the pointillist canvas of eternity' explored in previous Pathways articles and in his new book, In Love With Eternity.

Geoffrey Klempner



[This is an edited version of the first section of the Introduction to my newly published Plato: An Interpretation.] [1]

Our understanding of Plato and our understanding of the nature of philosophy are two sides of a coin. The dominant academic conception of the nature of philosophical thinking vitiates both our understanding of philosophy and our interpretation of Plato.

The sorry plight into which philosophy has fallen, was the result of philosophy having been expected, and its being deluded into claiming, to serve the same ends as science. It was expected to, and foolishly claimed to, seek true and certain factual knowledge. This is a snare philosophy has to extricate itself from. Unfortunately, this pernicious confusion of philosophy with science has confounded all the terms needed for discussing the question: 'knowledge', 'truth', 'understanding', 'reason', etc., all of these terms suffer ambiguity and can lead to much obfuscation and misunderstanding unless we pay careful attention to the special usage of an individual writer. Because I aim at a radical revision of our understanding of these terms I am painfully aware of the fact that I am especially liable to be misunderstood when using them.

Just as facts about the natural world cannot be quarried from within the human mind, so understanding cannot be found outside of the human mind. If we choose, as is reasonable, to confine the epithet 'truth' to the ascertainment of facts, then since, as Kant saw, no factual knowledge can be derived from pure reasoning, we can say that pure reasoning is not concerned with truth. Our factual knowledge cannot extend beyond our experience, as Locke and Hume rightly insisted. On the other hand all meaning, all intelligibility, we 'find' in the given phenomena of experience, is infused into the phenomena by the mind. It is only then that they turn from blind and brute experiential stuff into ordered, meaningful facts.

Furthermore, the mind not only projects patterns that give meaningfulness and intelligibility to the content of experience, but goes on to create second-order and third-order ideas and ideals that have their whole being in the mind, and have reality (as, in my usage, opposed to existence) in the special sense of constituting a plane of being realized in active, creative intelligence. 'God', 'the soul', moral ideals and values, as creations of the mind, are fictions or myths if you will, but they constitute the reality of the spiritual plane of being that is the peculiar characteristic of humankind.

Religion is wrong when it represents these as facts and houses them in space and time. Science is wrong when it discounts these realities because they fail the criteria of objective verifiability. Philosophy is wrong when it thinks itself obliged to choose between siding with the irrationality of religious faith on the one hand and accepting the reductionist verdict of objective science on the other hand.

Philosophy should see itself as a species of poetry, rational poetry, creatively and coherently dreaming, mythologizing, unfolding the realities of the spiritual life, soberly confessing its outpourings to be dreams, fictions, and myths, but dreams, fictions, and myths that constitute our proper, true, and most precious realities. This, I believe, was the profound insight and vision of Plato, and this, I believe, was the essence of Kant's outlook, though Kant was too much under the influence of the rationalism of his age to give full, clear, and consistent expression to his basically true outlook.

At one point in the Phaedo (84c-88b) both Simmias and Cebes raise objections to Socrates' initial argument for the immortality of the soul. In responding to Cebes, Socrates begins by giving an account of his experience with philosophical thinking, the famous 'autobiography' (96a-101e), which amounts to renouncing not only all objective knowledge but also all demonstration or proof in philosophy. This is what I refer to as the Socratic principle of philosophic ignorance.

In philosophy we do not seek, and can never have, proven conclusions: we seek intelligibility, understanding, a coherent vision. We approach that goal when we have a system or network of concepts, ideals, values, that is internally coherent and harmonious and has the virtue of infusing the various phases and aspects of our life-experience with meaningfulness and value. That is how philosophy, and only philosophy, can take over the role that religion formerly played in human society. As I have been repeatedly saying, a philosophy creates a universe of discourse which brings into being a domain of intelligibility in which the mind can have its proper life as active, creative intelligence.

This poses a philosophical dilemma. If there can be no finality in philosophical thinking, if no philosophical conclusions can be definitive or certain, how can we avoid thoroughgoing relativism in morals and scepticism in general? At this point in the Phaedo (88c-91c), Socrates warns his audience against losing faith in reason in words that superficially sound like a reversal of the Socratic principle of philosophic ignorance. But only superficially, for Socrates finds assurance in the self-evidence of the intelligible form. In the end, we find the only secure ground in the reality of the active, creative nous; we find that phronesis is the whole of virtue and the whole of reality.

The Socratic principle of philosophic ignorance in Plato develops into the dialectic that destroys its own hypotheses. To overcome Pyrrhonism, ancient and modern, and out-and-out relativism, we need a conception of dynamic rationality, where reason is constantly alive and active and never static. Antisthenes and Wittgenstein equally suffered for want of such a dynamic conception of reason.

The Socratic conception of the intelligible is the foundation of Platonism. The intelligible is born in the mind. No idea comes to us from outside. No sensation is in itself intelligible. The idea of equality is not derived from experience. We might see a million equal things a million times and still not have the idea 'equal' until it flashes in the mind: "Of course, these are equal!" And it is not necessary to see many equal things to form the idea 'equal'; a single pair of equal things seen only once can be the occasion for the creation of the idea. Again, we can have the idea 'equal' and apply it to many equals without having the idea 'equality', which we should not call a higher abstraction but a higher-order idea.

And this is not true only of imperceptible things like the idea 'equal'. We can see trees and have no idea of a tree until we single it out of the nebulous totality of seen things and give it a distinctive character. My seeing a tree is an event. But my calling it a tree, my knowing it for a tree, is a rational act, a creative act of the mind, by which the tree becomes to me, not a given thing, not an impression fed into me from outside, but a meaning. This is the essence of Socrates' distinction between the intelligible and the perceptible.

Socrates, because of his preoccupation with morals, did not speak of the ideas of physical things, but only of ethical notions. But the extension and development of the idea is true to the Socratic insight. Scholars, failing to appreciate the revolutionary originality of Socrates' conception of the intelligible realm and of the creativity of the mind, and seeing the Platonic 'separate forms' and 'separate soul' as novel doctrines without foundation in the Socratic quest, make Socrates into a tame preacher of common morality and Plato into a foolish advocate of indefensible doctrines.

A philosophical problem opens up for human thought a domain for creative conceptual exploration. That is the principal thing that an original thinker contributes to the human cultural heritage. A 'solution' to the problem is a mapping of the domain from a particular perspective. Thales gave us the problem of the universe. Anaximander, Anaxagoras, Leibniz, Schopenhauer, Whitehead (to pick up names at random) gave their various mappings of the Problembereich (to use a happy German word). Socrates gave us the problem of the intelligible realm and the problem of the eternity of the soul (camouflaged in Plato's works as the immortality of the soul). Parmenides gave us the problem of Reality, of which Plato gave the grandest, sublimest mapping in the vision of the Form of the Good. These are all creative conceptions that you cannot find in or derive from anything outside the mind.

I have repeatedly put forward the view that philosophy is a creative endeavour, oracularly proclaiming ideas and ideals that confer meaning and value on the givennesses of experience and on human life. In philosophical thinking we start from a given, more or less chaotic whole, and proceed to a creative, imaginative re-presentation in a more coherent whole. The representation is creative - no formal rules can make it necessarily derivable from the initial whole - and being a representation it is necessarily a falsification. Not being necessarily derivable, the derivation can always be challenged. Being necessarily a falsification, the representation can always be refuted. This is the explanation of the endless controversies of philosophers. However carefully framed the premises, however astutely guarded the derivation, the consequence brings in something that is only there by grace of creativity. It is an impostor, though a divine impostor.

An original philosopher, who will not merely re-state the views of others, finds a new way of looking at things. That philosopher then presents her/his view, expounds it, elucidates it, exemplifies it, sings paeans in its praise. All of that is as it should be. But then s/he goes on to say that all other views are wrong, which is bad enough, but what is worse is that s/he does not stop at that but goes on to 'prove' that all other views are wrong by showing that they fail to reveal what her/his vision reveals, not realizing that the 'truth' thus revealed is the product of the peculiar way of looking at things. This is the source of all philosophical feuds. Philosophers should realize that every philosopher creates - strictly speaking - a whole new intelligible universe that does not negate other intelligible universes.

There are propositions which any human being worth his salt will be willing to fight for and die for, but not - if s/he be a true philosopher - assert as definitively literal truth. In philosophical discussion, a conclusion is only anagkaion ek ton homolegemenon, a phrase we meet with frequently in the dialogues: what is necessary is only necessary as proceeding from what has earlier been agreed; but what has been agreed can always be questioned, and must always be questioned, if we are not to be enslaved by our own creations. In philosophy no statement is ever good for good, simply and without qualification. Plato is never forgetful of this. Those who speak with assurance of Plato'a theory of this and theory of that should remind themselves of this.

It is a paradox of human thought and human communication that we are necessitated to carry out our thinking and our intercourse in ambiguous terms. The Leibnizian dream of a perfect language is a chimera. Except within systems of purely formal, abstract symbols, which, however enormous may be their practical utility, are of strictly restricted applicability, all living thought and discourse, all thought and discourse relating to (I am at a loss for an epithet) 'concrete', 'real', 'organic' situations, can only be carried out in fluid, ambiguous, hazy terms. Otherwise they would fail to be relevant to the ever-changing, never-static, actualities of life.

That is why in poetry and in philosophy at its best, language is most indefinite and most inspirative. When people are oblivious of this, individual thinking is dogmatic, bigoted, intolerant, and conversants throw all kinds of accusations at each other. If and when we are aware of this insight which Socrates and Plato never tired of disseminating, we can humbly and patiently work continually towards more and more clarity in our understanding of ourselves and towards more mutual sympathetic understanding with our fellow-humans.

Plato more than once speaks of giving a logos alethes when he is about to offer a muthos. The two are inseparable: the logos alethes can only be embodied in myth. This is the lesson about the nature of philosophical thinking that we should have learned from Plato, but which we are too clever to grasp.

Plato gave us the profoundest truths about ourselves and about Reality in winged myths - the eternal forms, the immortal soul, anamnesis. Our learned scholars turn the myths into silly dogmata, into transparently erroneous doctrines, and all is lost: the inspirational core, the inspired insight, is dissipated when its housing shell of myth is shattered.

Thus scholars find in Plato's works theories that they proceed to prove untenable, and since those theories are all they see in Plato, or all they are interested in, with their demolition are lost all the insights he clothed in those 'theories' - insights that have enriched humanity, that have in truth translated humanity into a new plane of being. Our life has been so much the poorer because we insist on being so much the cleverer. We have become materialists instead of idealists, and we tell ourselves that it can't be helped, that otherwise we would be fooling ourselves. And why is that so? Only because we have fallen to the scientistic delusion: we think that our philosophy must be true to and of the world. We fail to see that theoretical materialism and theoretical idealism are nothing but ways of looking at things and that it is entirely up to us to adopt this or that view. Our philosophy has nothing to do with the way the world is and has everything to do with what life we choose to live.

It is futile to subject the writings of Plato to the rigour of logical analysis, whether to refute him by showing him to be inconsistent or to vindicate him by discovering consistency underneath the apparent inconsistency. Plato does not give us a neat philosophical system. Plato gives us insight and inspiration that help us look into our own reality to which we may then give expression in philosophical positions of our own making. The harmony and unity in Plato's overall philosophical positions come from the unity of the radical insight into that one reality, our own reality as intelligent beings, which then flows and meanders in many streams that may diverge or criss-cross without disowning their common source.

Scholars torment themselves needlessly in trying to hammer Plato's various views and positions into a well-ordered and consistent system. He was not giving an account of objective actualities but giving mythical expression to ineffable realities, and was at liberty to modify his images and imaginative descriptions. You don't ask a painter who paints several landscapes of a favourite location to make copies of his own work, or one who paints more than one portrait of a single person, even at one and the same period of his subject's life, to produce identical portraits. It is our confusing the nature of philosophy with that of science (which alone is concerned with objective actualities), that is at the root of interminable scholarly controversy and endless futile attempts to force the thought of great creative philosophers into nicely set moulds. Plato only provides the most remarkable illustration of this because he is the most highly creative, but it is true in the case of all great philosophers, the more so the more profound and original a philosopher is.

So, to each her or his own Plato. Accordingly, I present my own Plato. I ask no one to say that I am right, but let no one say that I am wrong. akoue de to emon onar, eite dia keraton eite di' elephantos eleluthen: hear then my dream, be it coming through the horn or through the ivory gate. (Charmides, 173a).


1. Plato: An Interpretation (2005), published by Publishing. See http:---l

(c) D. R. Khashaba 2005


Website: http:---



Metaphors and epiphanies of probable and possible worlds: Aristotle's concept of mimesis and its significance for non-representational 'abstract art', with particular reference to Jackson Pollock

In a recent introduction to Philosophy of Art, it is stated that 'Plato and Aristotle thought that the arts of poetry, painting, sculpture, dance and music shared a common feature: they were all involved in imitation'.[1] It is argued that the theory of art 'presupposed in the writings of Plato and Aristotle' is: 'x is an artwork only if it is imitation'.[2] This theory is then shown to be false or too narrowly restrictive as it cannot accommodate the apparently non-imitative 'pure colour fields' of twentieth-century artists like Mark Rothko or pure instrumental music. In conclusion, what Plato and Aristotle assumed arose as the result of 'what was available to them. It is only through the benefit of hindsight that we can see how far off they were'.[3]

In these terms, Plato and Aristotle seem to have no significance to twentieth-century abstract art. If there is a deeper and more complex relationship between their ideas and paintings produced centuries later, little attempt is made to explore the possibilities. It seems that the superficial label of mimesis keeps them locked in their own culture.

It is the purpose of this article to explore Aristotle's conception of mimesis and its link to nature and to the metaphysical realm, which deserves deeper consideration in relation to our responses to twentieth-century art, particularly that of Jackson Pollock whose work and approach will be discussed.

Unlike Plato, who, in his fixation with eternal forms, viewed the natural world as an illusory realm, Aristotle sought to give a satisfactory account of nature, studying material things, natural phenomena and general aspects of nature in a systematic manner. Aristotle argued that the ideal or the universal can be found in the particulars and this became the cornerstone of his metaphysics of nature. This is generally recognised to be the most fundamental difference between Aristotle and his master, Plato.

It is true, as Aristotle states quite clearly in the Poetics, that 'Epic and tragic poetry, as well as comedy, dithyramb, and most music for aulos and lyre, are all, taken as a whole, kinds of mimesis' (1447a).[4] But Aristotle made a distinction between useful crafts and fine arts. He said that 'Art [techne] either brings to an end [it realises and fulfils] what nature cannot achieve, or it mimesises nature' (Physics 199a). To understand Aristotle's use of the word 'mimesise' is an important first step in the process of freeing oneself from the biased overtones of the verb 'to imitate'.

At 1448b of the Poetics Aristotle states what he feels to be the core of art and poetry. 'It is clear' he begins, 'that the general origin of poetry was due to two causes, each of them part of human nature'. The first is that 'imitation is natural to man from childhood' and that 'man learns first by imitation'; the second is that 'it is also natural for all to delight in works of imitation'. Aristotle thus initially uses the term mimesis to connote the duplication of sounds in a straightforward sense. But this mimesis also serves as a vehicle through which learning can be expressed and conveyed. It is also asserted at 1448b that the 'delight in seeing a picture is that one is at the same time learning, gathering the meaning of things'.

One of the most important additions to these passages is when Aristotle develops another strand of meaning from mimesis to show that it is not solely located in elementary perception of objects, but that it 'involves the formal properties of the mimetic object'.[5] If one has not seen the thing in a picture that is being represented, one's 'pleasure will not be in the picture as an imitation of it, but will be due to the execution or colouring or some similar cause' (Poetics 1448b) - or in other words, the work's formal properties.

It is the objects of mimesis that have been claimed to reveal the 'full character of Aristotelian mimesis' of which nature (physis) and action (praxis) are the two core objects.[6] Nature is discussed in the Physics and contains Aristotle's celebrated claim he techne mimeitai ten physin, usually translated as 'Art imitates nature'. Bredin/ Santoro-Brienza's analysis of this statement is important and worth citing in full as it clears away the misleading nature of the above translation. They emphasise that:

     Aristotle does not say that art mimesises natural objects,
     but that it mimesises nature - that is, nature itself, the
     universal immanent process of self-unfolding, the internal
     principle that produces and manifests itself in natural
     beings. Nature, understood in this way, is not a thing or
     an object, nor a set of things or objects. It is not an
     empirically observable object or phenomenon at all, nor any
     kind of datum or given. And nature in this sense cannot be
     copied or imitated or represented by any kind of concrete
     image... what art 'imitates' is, rather, the teleological
     dynamic of nature[7]

Aristotle explains that 'Nature is the end for the sake of which. For if a thing undergoes a continual change toward some end, that last stage is actually that
for the sake of which'. This also applies to the arts as they also 'make their material' and 'we use everything as if it were there for our sake. For we also are in a sense an end' (Physics 194a). So nature has its end in itself, and art has man as its aim, as art is the result of an idea or plan in the creator's mind. As Bredin/ Santoro-Brienza sum up, a proper translation of he techne mimeitai ten physin would be 'Art produces extrinsically as nature unfolds immanently'.[8] In other words, art is an emergent process and nature is an emergent process.

The second division of nature into praxis also benefits from elucidation. Action might be seen to stand for concrete behavioural things like talking and moving but Aristotle is speaking about one single action. The multiplicity of actions and things that are shown by, and happen to characters in plays cannot be unified, as some of these, such as the hero of the Odyssey getting wounded at Parnassus and his feigning of madness 'had no necessary or probable connection with one another' (Poetics 1451a). Homer made no attempt to unify actions understood in the behavioural sense because these types of things that are unconnected cannot be unified. Instead Homer's subject was an 'action with a unity' (Poetics 1451a) of a different kind: a single spiritual occurrence whose inherent creative principle unfolds to reveal one essential plot. Aristotle further confirms his position by comparing poetry with history.

Like Plato, Aristotle also realised that the poet does not always write about particular events or facts. Aristotle states that 'the poet's task is to describe, not the thing that has happened, but a kind of thing that might happen, that is, what is possible as being probable or necessary' (Poetics 1451a-b). He explains that the historian 'describes the thing that has been', and the poet 'a kind of thing that might be', concluding that poetry is something more philosophical and of graver importance than history, since its statements are of the nature rather of universals, whereas those of history are singulars' (Poetics 1451a-b). Although not made explicit in the passage just cited, Aristotle's conception of mimesis is implicit in it. Things that are possible and probable cannot be detected through empirical observations and cannot be copied in a representational way.

Later in the Poetics at 1460b Aristotle specifies that the poet is a 'mimetist' and 'must of necessity mimesise one of three objects: things as they were or are, things as they are said or thought to be, or things as they ought to be'. Obviously, to use the last category as an example, 'things as they ought to be' are not actual objects that can be imitated. This clearly differs considerably from Plato's idea of art as generating inferior copies of real objects. Aristotle believed that artists deal with truth by looking at possibilities and probabilities 'with the imaginative, creative, fictional constructions of symbolic and ideal worlds'.[9] He argued that 'it may be impossible that there should be men such as Zeuxis painted. "Yes", we say, "but the impossible is the better thing; for the paradigm or ideal type must go beyond [reality]"' (Poetics 1461b).

So, art, in Aristotle's terms, consists not in imitating an ideal form but rather in composing an ideal form. Verisimilitude in art means that it conforms to laws of 'ideal probability and necessity' as it is through art that 'we encounter metaphors and epiphanies of probable and possible worlds'.[10]

It is therefore apparent that Aristotle could not have meant that artists should slavishly copy nature in order to achieve an elementary verisimilitude in their works. This is to simplify what is obviously a much more intricate matter and is too restrictive in its analysis: the very thing of which Aristotle often stands accused. Bredin/ Santoro-Brienza's sensitive, sophisticated account realises that in Aristotelian terms, works of art are 'co-realities or verisimilitudes of reality'.[11]

There have been many twentieth-century artists who have sought to paint 'reality'. Georgio Morandi and Piet Mondrian did so cerebrally, Jackson Pollock, instinctively.[12] To use Pollock as an example, it is worthwhile considering his work and his approach in light of Aristotle's conception of mimesis.

Pollock's alignment with nature was finely tuned. His connection with nature's intrinsic patterns, rhythms and structures gave rise to a process in the artist that inspired him to produce dynamic, yet carefully wrought images full of the 'epiphanies' that Bredin/ Santoro-Brienza speak of. The artist gives us insights with things on various levels, producing layers of meaning that we can compare with those that we recognise in the physical world such as the structures of trees, for example. The artist, however, has penetrated further, giving us a new world to consider, transcending the stuff of paint and its physical properties towards a universal fractal structure that cannot be empirically observed.[13] An understanding of the principle of such structures, not only allows a deeper insight into Pollock's work, but also throws light on Aristotle's concept of mimesis, especially in connection with the aesthetics of music, which many philosophers, like Carroll, feel mimetic theory cannot account for.

When we look at clouds, coastlines or trees, we experience on one level an immediate response to their intrinsic beauty, and this familiarity seems to be a shared human experience. But what most observers of nature do not realise is that a fractal, a mathematical principle of self-similarity, lies behind the patterns that we see on a daily basis, and is a principle of profound mathematical and scientific importance - an invisible yet tangible universal that beats at the heart of the universe. This principle is also found in what we hear. 1/f noise, its origins still a mystery to science, has been found in various physical systems like sounds from air and water movement, and in music, covering a vast range from medieval to the Beatles.[14]

What links our experience of 1/f noise with other natural phenomena or music with painted images is that, 'aesthetically, our visual and auditory senses are "tuned" to the borderland between regularity and irregularity, the detail of which is captured simply by the notion of statistical self-similarity and fractal dimension',[15] which in the case of clouds, for example, is connected with spatial dimensions, and in the case of 1/f noise, with time. Thus, for a truly engaging structure to emerge in a painting, the application of paint has to be formed in a way that lies on the edge of randomness. If the paint is too uniform, the images lose power, if it is too chaotic, it is not possible for a structure to emerge. Similarly, fractal generated music demonstrated three different types of noise, the first of which, so called 'white' music, is too random, and virtually unbearable to listen to, 'Brown' music or 1/f2 is too synchronized, whereas 1/f noise is closest to real music and the most pleasing to the ear. It has been claimed that these 'measurements show that music is imitating the characteristic way our world changes in time',[16] and at the same time, transcending it. This suggests an answer to a concern that many philosophers have had, and which was first voiced by Plato, namely that in music without words it is 'extraordinarily difficult to know what the rhythm and harmony without speech are supposed to signify and what worthwhile object they imitate and represent' (Laws II, 669e).[17]

Jackson Pollock's Lavender Mist, widely recognised to be one of his most beautiful and harmonious paintings, has a fractal dimension of approximately 1.67, which accords with the Golden Mean, a principle of proportion that the Greeks first recognised as being present in nature.[18] Now for Pollock to have arrived at this conclusion without using any traditional mathematical formulas, or painting techniques, suggests that the artist's emotional alignment with the natural world was so sensitively attuned that he was able to unlock a universal in a highly original way. Thus Pollock anticipated Benoit Mandelbrot's proof of the universal's existence in nature by twenty five years, his now celebrated Mandelbrot Set, which was itself visually released from a formula that had existed for some time.[19]

But if one accepts that art and music mimesise the 'teleological dynamic of nature', how exactly do they do this? If 'art is the result of an idea or a plan in the creator's mind' what form does this artistic plan take? Klempner has wondered if Pollock has 'a plan in his mind' at all or is it rather that the painting follows its own intrinsic laws which 'the painter has no choice but to follow?'[20]

It has been shown that Pollock's crucial anchor layer of paint with which he began his drip paintings was completed in under a minute, an extremely short period of time given the large-scale of the canvas. This is all the more astounding because the patterns created were 'complex and intricate'.[21] It has been speculated that once the process of dripping paint had begun, this '''triggered" an implicit or instinctive recognition of the fractal geometry pouring onto his canvas'.[22] The conclusion drawn from this is that 'Pollock's actions weren't driven purely by conscious deliberation'[23] and his appreciation of nature was therefore instinctive or in Pirsigian terms, pre-intellectual.

For the defining principle of the whole work to emerge so fluently and purely at the outset of the artistic process is surely significant. This emergence seemed to have happened at a pre-intellectual level, and once registered, first emotionally and then intellectually by the artist, he seems to have experienced a type of magnetic pull to fractal patterns, fascinated by what he was recognising intuitively and visually, which he assembled, broke up and re-assembled into layer upon layer of complex harmonies, a dynamic process of emergence and reductionism, until a greater whole emerged. Is this whole something as it 'ought to be', the 'ideal type that goes beyond'?

Pollock's richly textured canvases continue to captivate large numbers of people who view them. The works exude a still, resonating force, and allow the viewer to step into the same world that Pollock found so arresting. This can work on two levels: in the recognition of nature's harmony; and in the recognition of a transcendent harmony for which the colours and patterns act as trigger.[24] Above the painting's colour and texture, which on one level can produce a pleasurable response, lies the work's underlying fractal forms conforming to laws that are 'ideal probable and possible', creating in us not only deeper understanding, but also many other feelings like joy or wonder. This might partly answer the question that one philosopher has asked, namely 'what it is about [mimetic] art that enables it to represent its (ideal, typical) subjects in a way that is aesthetically rewarding'.[25]

The core of this universal wonder is no doubt the same one that Plato believes the poet arrives at through divine inspiration. Aristotle too points to the non-material aspect of 'reality itself' but has followed a different path from that taken by Plato, one involving reflection and analysis of matter in the ephemeral realm. It is a wonderful thought to consider mathematicians, scientists and artists 'composing' ideal forms because in Aristotelian terms, this is what happens when true engagement with nature has taken place. To merely copy nature or dryly analyse it, is not to create at all. To mimesise nature is to create through 'action with a unity', like a single pulse that stilly and quietly unfolds itself, like a cloud in wind whose shape changes almost imperceptibly into myriad fractal forms, each one equally as harmonious and beautiful as the last, but the cloud nevertheless remaining one form.

Aristotle may not then have been as surprised as some might think if he had been presented with an image of the type that Pollock produced. Pollock, like many artists before him, knew that his art could not in its essence, 'better' nature. Aristotle recognised this too. In his Politics he mentions that 'the eye of one person' taken in isolation, 'would be fairer' than the one 'in the picture' (1291b). If the artist only copied a pattern in nature then Plato would have been right to condemn it. But Pollock has not done this. He told us something more about nature, more about the universe, by recognising that the goal orientated extrinsic process he was involved in as an artist was analogous with the intrinsic progression of nature.

Science has shown that Pollock did not 'mimic what patterns in Nature looked like' but 'instead used Nature's motion - chaos - in his painting technique and hence generated pure Nature in his paintings'.[26] This calls into question the accuracy of describing Pollock as an Abstract Expressionist as his 'patterns are far from abstract'.[27] This then gives rise to the need to re-assess the relevance of Aristotle's concept of mimesis in relation to so called abstract art. As highlighted in this article, a more sensitive reading of what Aristotle says would still allow for a connection to be made between his ideas and the 'pure colour fields' of artists like Mark Rothko, because Aristotle realised that pleasure could be taken from a painting based purely on the work's formal properties. With the benefit of scientific analysis of Pollock's work, the connection between Aristotle and twentieth-century art is further strengthened. In fact, there could hardly be an artist who more aptly fits an Aristotelian based theory than Pollock because the artist has made manifest in physical form, an ideal, without copying anything: he has instead 'combined' the 'scattered elements' (Politics 1291b) and truly mimesised nature.


1. Noel Carroll, Philosophy of Art A contemporary introduction, London, 1999, p.21.

2. Ibid., p.21.

3. Ibid., p.22.

4. All passages that quote Aristotle are taken from Jonathan Barnes, ed., The Complete Works of Aristotle, 2 vols., Princeton (New Jersey), 1999.

5. Hugh Bredin and Liberato Santoro-Brienza, Philosophies of Art and Beauty Introducing Aesthetics, Edinburgh, 2000, p.37.

6. Ibid., p.38.

7. Ibid., p.38.

8. Ibid., p.38.

9. Ibid. p.40.

10. Ibid. p.40.

11. Ibid., p.42.

12. The exhibition catalogue of Pollock's work that has been used in the formation of this article is Kirk Varnedoe and Pepe Karmel, eds., Jackson Pollock New Approaches, The Museum of Modern Art, New York , 1999.

13. For a fractal analysis of Pollock's work see Richard P. Taylor, Adam P. Micolich, David Jonas, 'Using Science to Investigate Jackson Pollock's Drip Paintings', Journal of Consciousness Studies, 7 no. 8-9, 2000, pp.137-50.

14. See Heinz-Otto Peitgen, Dietmar Saupe, eds., The Science of Fractal Images, New York, 1980, pp.39-44. I am most grateful to my colleague Dr. Martin Baker for drawing this book to my attention and also for being so generous in sharing his ideas with me.

15. Extract taken from correspondence with Dr. Martin Baker.

16. Heinz-Otto Peitgen, Dietmar Saupe, op. cit., (note 14), p.42.

17. John M. Cooper, ed., Plato Complete Works, Indianapolis, 1997.

18. Note taken from a lecture on the connection between maths and art given by Dr Martin Baker at Loretto School, 2002.

19. The formula was Z n+1 = Zn2 + C. Mandelbrot's 'Set' was printed in colour from a computer. I am grateful to Dr Martin Baker for drawing my attention to this.

20. Extracts taken from correspondence with Dr. Geoffrey Klempner.

21. Richard P. Taylor et al, op. cit. (note 13) p. 146.

22. Ibid., p. 148.

23. Ibid., p.148.

24. See Robert Pirsig, Zen and the Art of Motorcycle Maintenance, An Inquiry into Values, London, 1999, especially chapters 19 and 20.

25. The neurobiologist, Semir Zeki, has shown in his stimulating and important book, Inner Vision An Exploration of Art and the Brain, Oxford, 1999, that the neurological response of the observer of a piece of art is homeomorphic (ie. mimesises) the neurological state of the artist that conceived the work, a significant claim that deserves deeper consideration with regard to aesthetics, and especially to Aristotle's conception of mimesis. 'Aristotle's use of the concept of mimesis is similar to the mathematical concept of "homeomorphism" where the intrinsic properties of one mathematical object are compared to the intrinsic properties of another, apparently different system'. Extract from correspondence with Dr Martin Baker.

26. Sebastian Gardner, 'Aesthetics', in A. C.Grayling, ed., Philosophy 1 a guide through the subject, Oxford, 1995.

27. Richard P. Taylor et al, op. cit. (note 13) p.149.

(c) Andrew Watson 2005




  "Any individual who does not live poetically or religiously is a fool."
  Kierkegaard Concluding Unscientific Postscript Existential Pathos, 2

GEORGES[1] I am surprised, Richard, that you have found my theory about pointillism to be of value in understanding the cosmos.

RICHARD It is not at all surprising, Georges, because the thought of an individual always reflects the entire universe. You have hit upon something of profound metaphysical significance - without realizing it yourself.

GEORGES Please, I brought optical science to the art of composition of a painting. Do not confuse my work with metaphysics!

RICHARD You may have brought optical science to painting, but all science is founded on metaphysical suppositions. Most scientists keep them in the shadows. However, my thoughts on the subject are rational and greatly rely on science for their legitimacy. Let me tell you how.

The contribution that modern physics has brought to philosophy is very significant. It has exploded the notion that the past no longer exists. And I don't mean that it exists in the collective memory of Homo sapiens or as antecedents to present events or as great accomplishments that persist. No, the study of time has revealed that there is no difference between the past, the present or the future. It is a human illusion that they are different. The only reality is space-time existing as a seamless whole.

GEORGES That sounds ridiculous to me. Of course, I have a past, an all too short one but one of which I am proud. Unfortunately I no longer have a future, yet others do. Here now is the present in which we are conversing.

RICHARD My thoughts sound ridiculous to you only because of your habits of thinking. If you had studied Kant instead of optical science, you would know what I mean. Your ideas about time stem entirely from your own brain and not from reality. They are a useful shorthand for getting on in the world but of no value in understanding its nature. Now that physics has finally caught up with Kant, perhaps his ideas will have more currency in our society. The prestige of science does wonders for neglected ideas.

But it is not my intent to elucidate the relativity theories of Einstein and his epigones - I don't have the ability or the desire to do so. What interests me are the radical metaphysical implications that they bring to light. Suddenly the question of death and immortality are seen in a new way.

GEORGES What has all this got to do with my theory of pointillism in art?

RICHARD Patience, Georges, patience. One must proceed slowly in metaphysical matters.

The special problem of every individual is the apparent transitoriness of his life. All of his other concerns are minor compared to this one. Death means oblivion; he could tolerate all manner of ills if oblivion were not the inevitable specter at the end of his efforts. This is why the promises of Christianity are so appealing to him. Christianity promises him immortality if he subscribes to its tenets. Never mind that these promises have been long recognized to be ill-founded. They meet an essential need of his nature. Human beings, to use Spinoza's phrase, wish to persist in their being, which means to live on indefinitely.

GEORGES I never expected to live forever, no matter what the priests told me. I resigned myself to my mortality - as does any intelligent person.

RICHARD Yes, but in the depths of your soul you were unhappy about it. As well you should be, since it would be a tragedy that a man of your intellect and achievements should suddenly vanish from existence. But this was not the case: what happened was that a limit was placed on the temporal dimension of your being as it is on every living thing. You still exist in the space-time continuum of the cosmos. You yourself are a vibrant brush stroke on the pointillist canvas of eternity.

GEORGES You are telling me the same kind of fairy tale that the priests did! This makes no sense to me, it could not be true.

RICHARD I won't dwell further on how it can be true. In my view, it has been established beyond a shadow of a doubt. You would have to read the popularizers of Einstein to learn for yourself how it can be. You would have to suspend your intuitive common sense and plunge into the language of physics and mathematics. This is difficult for anyone accustomed to his life-long perceptual intuitions about time. You must trust the reliability of physics in its own domain without necessarily limiting your mind to its discoveries.

The implications of Einstein's demonstrations go beyond physics. Here we enter into the province of philosophy. Before we talk of pointillism, I want to tell you of a vision that came to me one night in a half-waking, half-dreamlike state. I don't claim that it is an exact depiction of existence. That would be too much to ask of anyone trying to discern ultimate realities. I am convinced, however, that something like it is true. Furthermore, in my judgement, it is a picture worthy of the critical faculties of homo sapiens and one that does not violate his intellectual conscience.

I became aware that the existence of a first principle, an ultimate reality, or if I may use the term without offense, a Deity that underlies existence, is such a compelling thought and its rejection is so absurd that no thinking person, other than a few fanatics of materialism, could deny its truth. This Deity "expresses" his nature in manifold ways; thus the cosmos with all its ramifications has appeared. Initially, matter was spread out in the vastness of intergalactic time and space. Although its dimensions were enormous, they lacked the necessary subtlety to do justice to his nature. Matter followed exact laws laid down by him, which gradually became repetitive and monotonous. Deity's plastic powers looked for new directions for its expression.

Then, in a distant corner of the universe, he produced a new form of existence we call life. This new creation existed in an infinitesimally small part of the space-time continuum, but this smallness was compensated for by its qualities of spontaneity and development. Its compression into minute dimensions permitted a vitality that was impossible for sidereal matter. Still, it was only a crude expression of Deity. The tree of life bloomed, but still did not satisfy his creative desires.

At last, however, life was endowed with a new property called thought, which by its nature must be free. Suddenly (cosmically speaking) all things became possible for this life form. Homo sapiens could remember, plan, create, form abstractions and generate consciousness. In its creativity, it began to resemble Deity although I consider it exaggerated to say this form was created in his image since all life forms, including homo sapiens, have a limited time dimension. They are mortal. This seemingly gives a tragic quality to the otherwise deity-like aspects of a person possessing thought.

It is essential to remember, though, that for Deity there is no such thing as transitoriness because he is not limited to the time dimension imposed on the perceptions of living creatures. There is no past or future for the perceptions of Deity; all realities are eternal for him. No individual "brush stroke" of being ever disappears from his gaze. Thus we come to the pointillist canvas of eternity.

GEORGES I was wondering if you would ever get to that point - no pun intended.

RICHARD Your patience is finally rewarded. You discovered a new art form resulting from the application of individual brush strokes. It is applicable not only for canvases appearing in the exhibition halls of the world, but also for the totality of individual human beings endowed with thought. Each human life is like a luminous brush stroke applied upon an eternal cosmic canvas. To the extent that it develops its unique individuality, each human life enhances the canvas. The event of death for a human is not his end in the eyes of Deity who experiences all space-time as the continuous whole of mathematical physics. The result is an eternal pointillist canvas endowed with qualities that no individual point in it could ever possess. Thus human life is not transitory but has its eternal existence on the cosmic canvas.

Now one day even this cosmic canvas must be delimited within time and the human race will have fulfilled its destiny. I doubt that this canvas can be Deity's final expression. You must remember I defined Deity as the ultimate principle of being without further specification - a negative theology. There may be other forms of being in universes spatially or temporally distant from ours. There are even other dimensions known to theoretical physics that are unknown to human perceptions. Perhaps there are parallel universes present at this very point in space and time containing more adequate expressions of Deity. Here one approaches impenetrable cosmic mists beyond which, as Aristotle says in his Metaphysics, human thought should not extend.

Of course, there are those whose soul has not been touched by an ultimate reality and they will dismiss my report as a myth, not understanding that the meaning missing from science can be found in myths. They provide their own explanation of the phenomenon of man. They say he is a statistical aberration in the flow of entropy, a quirk occurring in an infinite time span. They do not recognize any meaning to the human condition and refuse to accept any form of knowledge other than that provided by their laboratory instruments. Experimental verification to them is the hallmark of truth; without this imprimatur, they deny the possibility of knowledge. They reach heights of insufferable arrogance by confining truth exclusively to their methods of natural science.

You, Monsieur Seurat, should feel privileged that in your brief life you hit upon a fundamental feature of the cosmos, albeit you had a different goal in mind. So did Columbus when he discovered America for the Europeans. Even if the cognoscenti of the art world had never valued your canvases, you yourself would have a prominent place in the vastly more important pointillist canvas of eternity.

GEORGES You seem to have much enlarged my concept of depicting nature by points and dabs. Tell me more about this artist-Deity who uses my technique.

RICHARD There is no more that I know. My report is finished.

(c) Richard Schain 2005


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1. Georges Seurat French Pointillist Painter, 1859-1891

© Geoffrey Klempner 2002–2020