The Graphic Figure and the Philosophical Abstraction*

by Ion Banu

The theme of the present study is only one in the vast range of questions which arise in connection with the formation, in the early stages of the history of philosophy, of philosophical abstractions and syntheses, and with the origin of their placement into categories.

The role of poetic metaphor and symbol has often been pointed out in relation to the rendering of philosophical abstractions. This was the time when philosophy when philosophy was still in its primary stage of the abstract universal, which has yet lacked a specifiic conceptual expression and a categorial language.

The first Greek philosophers were poets, not only because this was needed to satisfy the ancient Greeks’ thirst for beauty, but above all because the inherent beauty of the poetic metaphor made the logic clearer, more accessible, enabling them to reach their ideal of philosophical assertion. Though when compared to categorial expression the metaphorical-symbolical one is less accurate, it is nevertheless superior to the former in one way, viz. in its ability to communicate not only to the philosopher, but also to the vast number of non-philosophic minds.

Now all of this is quite well known. What is not similarly known is the part played by the graphic (geometric) figure in the early history of philosophy,

*Article abridged for inclusion in this volume.

[bottom of p. 244]


As in the case of the poetic word, such figures suggest metaphors and symbols (graphic metaphors and symbols), whose comprehensive capacity is often superior.

As a proof of this we shall examine an early moment in the universal-abstract stage of ancient Chinese philosophy. The function of various graphic, geometric designs shall be considered in terms of philosophic abstractions, in distinction from the common sense abstractions usually expressed by ideograms. For example, there is a passage from the Djou-pei-suan-zing treatise of mathematics (written before the 8th century B.C.) which reads:

The square figure stands for the Earth. The round figure, i.e. the circle, stands for the skies (Heaven). . . . The reckonings for the square figure are basic (for those referring to Heaven). It is out of the square that the circle comes. . . Who knows the Earth, possesses knowledge, who knows the Skies possesses supreme knowledge. [1]

Let us now consider the figure in the light of the text, to seize the precise moment when the philosophic thought appears, transcending the pictographic and ideographic meanings. (The representation of the


Earth and the Skies by means of a square and an enscribed circle,* pertains to the pictographic stage. There is yet certainly nothing pertinent to philosophy here.) At the level of the ideographic stage, the figure represents the circle inscribed within the square, a graphic metaphor of the Sky’s dependence upon the Earth. ("it is out of the square that the circle comes"). The philosophic signification of the drawing shows itself in the idea that heavenly or superior knowledge is based on the inferior learning of the Earth. The pure symbol abandons the metaphor.

It could be said that the ideogram was used as a "categoriogram". We distinguish between a figure rendering an object of the surrounding world, chosen to suggest, metaphorically, a philosophic relationship (e.g. a bow and an arrow, possibly drawn on a text of Heraclitus, illustrating things mentioned by him), and a figure making use of signs without an actual model in the external world. In the former case, the philosophical significance is related to the functioning of a bow and an arrow; it is subordinated to the object described and represented. The graphic reproduction itself is incidental and non-significant, for no further, specific philosophic meaning is contributed by the figure. In the other case, the case of the symbol, the situation is different. An example is the graphic, purely

* The turtle’s shell was used for magical purposes in China, due to its allegedly suggestive reference to the universe, with its rather square base (the Earth) and its round carapace (the Sky).


symbolic rendering of the well-known notions of the earliest Chinese philosophy, "yang" and "yin", appearing in the book I Ching (probably previous to the 7th century B.C.); viz., the continuous line for yang (i.e. for the affirmative or the positive), and, the discontinuous line for yin (for negation or the negative). The logic of the discontinuous is the other (alter) of the logic of the continuous; the negative is the other of the positive; the interrupted line of the non-interrupted. These are simple philosophic categories expressed by means of a graphic symbol. Here the philosophical significance is directly connected with the figure, not with another object represented by it.

At this point, we may pause to discuss ideographic writing, so we may better realize the flaws and advantages of graphic representation in general. It is not accidental that the most complex graphic symbols of abstract philosophic meaning are to be met in the Chinese culture, whose language employs a type of ideographic writing. The philosophico-graphic expression is a natural development, apparently, of the functions of ideographic writing. We stress this because ideographic writing has often been unjustly thought of as inferior to the alphabetic, especially as regards to its capacity to provide stimulation to the mind’s attempt to reach philosophical abstraction.

In our opinion, both types of writings have, in this respect, equal qualities, though they express them in different ways.

Moreover, it is true that writing is only able to bring out favorably the existence and. free movement of abstractions when these graphic signs become


conventional, i.e. when they escape the concrete. This condition is met by both types of writing. Alphabetic writing achieved it by the capacity of its letters, they themselves having evolved from former pictograms, by acquiring full neutrality in regard to nature’s appearances and shapes. They were thus freed from any type of qualitative subordination. Thanks to their complete independence from sensorial images, they provide an urge for reason to escape the empirical, thus opening up the way for essentiality, enabling reason to achieve its work of conceptual abstraction and synthesis.

The ideogram can yield a similar result, only this is achieved in another way, due to the specific character of the ideogram’s peculiar kind of simplification. Let us start by considering one of the older Chinese signs for wood., viz. [Chinese ideogram]. The sign obviously refers to trees, ignoring the variety of individual or incidental phenomena, rendering what is common to all the trees from an illustrative, visual perspective. Naturally the phenomenal common character is far from being identical with the general and the essential; however, much like the generality of the essence, the phenomenal common character overlooks and goes beyond sensorial variety—by abstracting that which is principal, it simplifies and thus facilitates access to essence. During their evolution ideograms have gradually, but fully, lost their figurative resemblance to the signified. One could imagine an ideogram teaching us as students of it: "If you really have the desire to find the general, the essence, beyond the shapes of things, beyond


the phenomenality suggested by my graphic character; then consider the phenomenon all the way through, by all means leaving it behind."

Using such a strategy, one can more comfortably pass beyond visual phenomenality, coming to the "pure" ideogram, covering the road to the philosophic abstraction.

From the point of view of the object, the essence is instantaneously given in the substratum of the individual. Since they are discursive, alphabetic speech and writing can only refer to the essence unfolded in time; thus the instantaneous character of the essence is impaired. When one says, philosophically, that something is "difficult to understand", he is precisely attempting to recognize this lack of parity. Meanwhile, the graphic representation appears, like essence itself, to the observor as instantaneous; it is by means of the contiguity of the lines, their various modes of association and dissociation, the mutual attraction and contrast of light and shadow, that the typical relations of the essence can be graphically rendered, while one is observing their concomitance. Tsong Ping, a painter and theorizer who lived in the 4th century A.D., drew the analogy between the instantaneous way of grasping tao by intuition and the instantaneous way of grasping the essence by means of plastic form. In this he is referring to the qualities of graphic representations, about whose flaws, as compared to speech and discursive expression, we shall address ourselves later.

Similar attributes, similar patterns of evolution,


can be met with in cuneiforms* and hieroglyphs. Regarding the entirely disparate development of philosophical thinking of various peoples using either an alphabetic, or a hieroglyphic, or a cuneiform or ideographic writing; it can be accounted for by the fact that, complex social, historical, and gnosiological reasons other than the nature of the writing itself, made the peoples differently use the philosophical potentialities inherent in the various types of writing. For example, the philosophical potential of alphabetic writing was not universally actualized. The Phoenicians who created the alphabet had a negligible role in the history of philosophy.

As far as China is concerned, one notices an efficient use of the philosophical potentialities of ideographic writing.

We have already in another study [2] referred to various types of geometric, graphic symbols used in ancient China to express philosophic abstractions. In our study we had presented eight trigrams of the I Ching, standing for the eight alleged substances,

* Yvonne Rosengarten mentions that at a certain moment in the history of cuneiform writing, which itself had been initially pictographic, a turn occurred due to the deliberate desire to obscure the initial image, to make writing a mere convention. Cf. "La civilisation sumérienne de Lagash au IIIe millénaire," Rev. philos. de la France et de l'etranger, nr. 1, 1967, p. 2.


i.e. forces of nature thought to be the essence of everything in the universe. We had also reproduced the complex geometrical drawing, termed the "Yellow River" and the "Lao River", which graphically symbolized the whole philosophic content of the Hong-fan text in the book Shu King. To repeat what we said then: Ancient Chinese commentators explained the meaning of the figure in the following way:

—the dark part of the circle stands for Yin, the white for Yang, as the negative is dark and the positive clear. The moment when one part reaches its climax (the convexity), the other, at its inferior limit, already almost invisibly begins to replace it (the thinner part). Both of them contain the germ of their contrary, as suggested the inside spot of a contrary color. Moreover, the 28th hexagram of the I Ching points to the circle as being the Universe or "tai-tsi" and as being halved (as suggested by the ying-yang opposition). The circle as a whole is infinitely moving round and turning.

The circle’s turning round suggests the dialectical conception of the infinite passage of an entity into its contrary. Let us suppose the white (representing


an entity) is swelling. It will only give way when it has reached maximum swelling, i.e. convexity; or to put it another way, the developing element only dies after having exhausted its entire capacity for growth. This means the closer it is to its apex, the closer it is to decline. That idea is suggested by the penetration, hardly noticeable initially, of the darkly colored thread into the substratum of the white convexity at its maximum. The insidious thread is amplifying, while flowing into its contrary, the dark spot. But the evolution of either entity is bound to engender simultaneously what is opposed to itself; its conversion into its other would be impossible, unless something of this other had not previously appeared within the self-same former entity (this is the dark spot inside the white convexity, as a seed of the future development of the black). Extreme affirmation leads to negation, culmination to decline. These things already explicitly appear in the book Tao-Te Ching, which appears after the I Ching and whose* philosophical character is universally acknowledged.

The case we have thus far presented also relies on the fact that, within the intellectual life of ancient China, the capacity of a geometric figure to reveal essential reality was not an isolated mental act, but rather a particular example of a more general attitude. What we have in mind is the general use of the figurative. In our opinion, the ancient Chinese used geometric figures in order to connect them to essence, since they believed that figurative representations in general had such

* That is, Tao-Te Ching.


capabilities, geometric figures for them being but a special case of the figurative. Our point is more conclusively made when we consider the other species of the genre "figure".

The other species we have in mind come from the fine arts and horticulture. An old Chinese belief, undoubtedly of magical origin, asserts that the plastic image has the capacity of rendering the hidden essence of an object in the work of art. Much later, the Taoist peisagist painter Tsong Ping (373-443 A.D.) put that old belief theoretically, by writing what, while the wise man addressed tao (envisaged here as the magical, mysterious essence of things) with his mind, the painter was able to reach the same result through the "landscape and its plastic forms." [3] The picture, the landscape, acquires the magical force of including, within a limited frame, the immensities of nature.

The essential potentialities thus attached to painting are manifold. The plastic reproduction is not only capable of rendering the essence, but it also has the ability to ensure a magical fraternization with the essence by the painter.

Furthermore, the painter Wen Tong (fl. 9th century A.D.) was said. "to lose self-consciousness when painting bamboo, to identify with bamboo," thus enabling his painting to live the life of the trees. In this way the pictorial image fulfills its function of comprehending essence to such a degree that it enables the painter to experience it, to identify with it, in a magical way. It is also worthwhile to cite the idea of N. Vendier Nicolas, an historian of Chinese art, that the intuitive act mentioned above, though originating from a mystic


impulse, as a consequence acquires a rational character; the magical experience is an instrument meant to stimulate the effort of reason. The result of this same effort is the cognition of the thing’s essence. [4]

In this connection we must consider the role of another type of figurative representation, viz., that embodied by horticulture. The garden arranged in such a way as to be a miniature, an artistic suggestion of nature (mountains, valleys, rivers), will, in the Chinese view, enable the passer-by to come in touch with the very essence of nature portrayed by the tiny relief of the garden. The Sinologist, J. Gernet, observes that this is the "same magical principle" met with in landscape painting. [5]

All of that belongs to magic. The magic mentality pervades the plastic horticultural speculation already described. In fact, the geometrical figures we have analyzed previously are, without exception, also associated with magical activities. Where, then, does their philosophical significance arise?

Magic is a mystic doctrine imaginatively making use of the actual features of geometric figures. The figures upon which magic speculates are those which we shall examine, figures which are multi-purposive.

We thus encounter one of the modalities of magic, expressing the conviction of the magician that, the figure is identical with the object of the figure itself considered in its secret, hidden nature; that, imitating or graphically symbolizing natural objects and phenomena through figures, he could communicate with all of the object, including its inherent, invisible force: he could master the object. Consequently he


makes use of the imitative figures—geometric, pictorial, or horticultural. But let us translate this magical language into gnosiological terms. The "phenomenality" (instead of the "figure") of an object is an expression of that very object and its essence simultaneously. The essence is non-apparent, non-phenomenal (instead of "hidden"); in other words, the phenomenal aspect facilitates access (instead of "communication") to the entire object, its non-apparent essence (instead of "hidden force") included. A cognitive approach to the object thus becomes possible (instead of "gaining mastery" of the object). For the magician, who attached magical virtues not only to the figure but also to its possession and to the thing represented, he who possessed the figure, could implicitly possess the object. The realistic philosopher would say, he who comprehends the phenomenon attains access to its essence; and his assertion is quite accurate.

This "translation of terms" is possible because magic is, in fact, a fantastic, distorted transmutation of actual relations, relations unknown to the magician who nevertheless has an intuition of them in his own way, since the magician unwittingly relies on daily practice (which is actually based on the experience of the layman, though this experience is often turned into crazy statements). Practice shows us that all things possess something beyond their appearances: a butterfly, though it look like a leaf is none the less something other than a leaf. The magician was not a philosopher, but unconsciously and unwittingly he turned towards essence, the object of philosophy. Temporally, the act of the magician is prior to that of the first philosopher, but we are aware of the


fact that thousands of years elapsed before the act of this kind of abstractive awareness was accomplished and recognized. Ours has not been an attempt to rationalize magic, but to draw attention to the actual relations among and within objects implied by magical statements, relationships which the magic vision distorts. We have tried to exhibit the possible service made in the formation of actual gnosiology by the magical grasp of these relations when this has been liberated from its magical shell and examined in a different manner.

No matter how much the representation through graphic or oral images stimulated the formation of categories, or suggested through symbols the marks, structure, and essential character of things; a major distinction still existed between the figurative and the conceptual. The graphic figure, contrasted with other elements of the sensible sphere to which it belongs, is homogeneous and simple, thus possessing a capacity towards a qualitatively different plane discriminating essence from the richness, the heterogeneity of phenomenality. This quality exhibits the catalytic, gnosiological function of the geometric figure.

There are facts of history that show that the "Chinese phenomenon" is less Chinese than would appear, due to the universal ontological and gnosiological relations upon which it is based. Universality aroused echoes and was implied by partly similar philosophies in different parts of the world; for instance, we can point to the Platonic view of geometric figures. In this case, the graphic is posterior to the categorial, the graphic being a mere auxiliary serving didactic and illustrative purposes. But the


very fact that such illustration is possible testifies to the qualities of graphic representations analyzed above.

We have praised the figural element; it is now time to expose its philosophical deficiencies. Philosophic language is categorial; it is speech inseparable from thinking. When the graphic figure aims at being more than the representation of a category (attempting to symbolize judgments and reasonings), more than a mere "categoriogram," it gets "blurred", equivocal, likely to be given various meanings. Secondly, its static character conflicts with the dynamism of essence. What is gained in suggestiveness and instantaneousness, it loses in precision and mobility, especially when one compares it to speech and thought, which are discursive.* The discursiveness of thought

* In this respect, the poetic metaphor is superior to the graphic one, To Piet Mondrian in the definite modality of non-figurative painting there is to be found "the expression of the real abstraction." This connection appears to exist when the composition endeavors to render plastically the intelligible by means other than objective ones. We have in mind those cases when the non-figurative painting embarks upon the road of abstraction; in such cases it addresses reason through an artistic emotion manifested by non-objective plastic works. It aims at suggesting to us a way towards abstractions which are either common or philosophical. It thus endeavors to play a catalytic role between concept and essence. It can take advantage of its instantaneousness, while it suffers little from such a limitation; since it does not claim logical precision, nor does it try to escape from a [continued on next page]


is a kind of bondage, but this is its unique modality. Thinking expresses essential relations, relations considered in their complexity, their mutual action and dynamism, relations to be rendered discursively only. Due to their discursive nature, thinking and speech cannot be required to express everything at once; on the contrary, they are required to be inexhaustible, in harmony with the inexhaustiveness of essence. Thus graphism, a contributor to the edifice of the history of philosophy, has remained, once the building arose, a decorative auxiliary.

[footnote continued from previous page] variegation of meaning, but includes all these. If it is unable to reproduce the dynamism of things, it is still capable of touching our fantasy, making up for its inaptitude by means of its own kind of dynamism. Poetry endeavors to communicate essence, not to clarify it; but, through this communication, it may be said to be our clarification when catharsis is understood as a kind of clarification.



1. Tcheou-pei-souan-king, trans. by E. Bijot. Journal asiatique, Paris, 1841, T. XI, p. 602. [-> main text]

2. I. Banu, Sensuri universale si diferente specifice


in filozofia Orientului Antic. Bucarest, 1967, ed. Stiintifica. [-> main text]

3. Tchang Yen-yuan, Li Tai ming houa ki (The History of Painting in the History of the Dynasties, ch. 6), after N. Vendier Nicolas, in his "L’homme et le monde dans la peinture chinoise", in Rev. Phil. de la France et de l’etranger, No. 3, 1964, p. 303. [-> main text]

4. N. Vendier Nicolas, op. cit., p. 318. [-> main text]

5. Cf. J. Gernet, La vie quotitienne en Chine, à la veille de l’invasion mongole. Paris, Hachette, 1959, p. 128. [-> main text]

SOURCE: Banu, Ion. "The Graphic Figure and the Philosophical Abstraction", in: Contemporary East European Philosophy, Vol. III, edited by Edward D'Angelo, David H. DeGrood, Dale Riepe (Bridgeport, CT: Spartacus Books, 1971), pp. 244-259.

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