I have discussed this mindprint thoroughly in a separate essay (Avital, 1997a) and shall therefore content myself with only a brief characterization. The reader should, then, imagine a prehistoric contour drawing of a deer, for example. This drawing does not represent a particular deer, but is a pictorial class-name for all deer which share the visual characteristics denoted by the picture. It is in other words a pictorial universal just like the verbal universal "deer". As such, this picture connects all deer of the particular kind represented by the painting, but at the same time, it separates this class of deer from all other animals and all other entities in the world. In every figurative work there are at one and the same time at least three levels of connectivity: material, perceptual and symbolic. By contrast, in so-called "abstract" art there is only connectivity at the material and perceptual levels, just as with any object and any phenomenal entity, but it never has connectivity at the symbolic level. In the light of this, one should see in the difference in the levels of connectivity a prime difference distinguishing art from pseudo-art.
It has to be emphasized that complementarity is manifested not only in every mindprint but also in the products of culture. Thus for example, it was only in our century that Niels Bohr discovered the tremendous importance for science of the idea of complementarity, but this mindprint was implicit as an necessary condition for the possibility of art from its beginning 40,000 years ago, and it was implicit millions of years before that as a necessary condition for the possibility of reading footprints. In both instances it is impossible to detect the figure on the ground or on the wall without the background which is its complementary aspect. Furthermore, since the symbols in every figurative painting consist in inclusion relations, or in a relation of nesting at various levels, thus in every figurative painting nested levels of complementarity are also present. As against this, in abstract art there is no necessity at all for complementarity between figure and ground, nor for nested levels of complementarity, for here there is the possibility of a uniform background with no figure within it as in monochrome paintings, or paintings in which the surfeit of color causes us to see them as a more or less uniform surface. On the other hand, the very existence of an abstract painting, or any other object, cannot be distinguished without the background in which the painting itself is found, so that complementarity is a necessary condition for perception. Since complementarity is a necessary condition in every figurative painting but not within an abstract painting, it may be that this mindprint can serve as one of the factors that distinguish art from pseudo-art.
The dialectic of Open-endedness - Closed-endedness is the source of all creativity and all metaphorization on the cultural plane; it is the root of existence and evolution in the biological world, and this dialectic can be seen on the cosmological level as well. Thus, the existence of every organism is absolutely finite, but with certain changes it continues its existence in its offspring. Similarly, the duration of the existence of every star is finite, but from the cosmic dust that remains after its disintegration other stars are created. The dialectic of Open-endedness - Closed-endedness also characterizes all types of symbol, whether verbal or pictorial. Symbols are as it might be special vessels, the inner space of which possesses a qualitative and not quantitative character, so that they are thus unlimited in their interior space, but have an outward facing partition. Thus for example the symbol "deer" whether verbal or pictorial, applies to every deer there was in the past, is in the present or will be in the future, and the symbol is thus open-ended. Every symbol has the attribute of extensivity which is a characterization of open-endedness, and therefore the symbol "deer" applies to every deer regardless of its age, size and special characters, unless it is of importance to us to create a sub-class having special characters, in which case a separate symbol is created for it. On the other hand, there has to be a limit to the measure of application of the symbol, for otherwise it will not be efficient for the classification of entities, and this fact indicates its closed-endedness. This dialectical duality of Open-endedness - Closed-endedness is present in every figurative painting without exception, but is not present in so-called "abstract" painting. Paintings of this kind do not include symbols but patches of color and shapes which we may interpret in any way we please as in a Rorschach test, and therefore there is in these works only the dimension of unlimited open-endedness. However, without limitation they have no value from a cultural point of view, for the supreme function of symbols is precisely to create finite coordinates and boundaries within the infinity that enfolds us. By contrast, when the matter of discussion is a non-representational work consisting of some common object taken out of its useful context and transferred to a museum - such as Duchamp’s urinal - there is no open-endedness at all but only closed-endedness; that is, symbols and objects belong to different levels of reality, and symbols are always of a higher level than objects, because symbols are the precondition for the existence and meaning of objects. Hence, the introduction of an object into a museum can never transform it from an object into a symbol. Here again, there is not the complete mindprint, Open-endedness - Closed-endedness, which includes the dialectic of both of them. On the other hand, a so-called abstract painting such as an Yves Klein monochrome has only open-endedness but no closed-endedness, since there are no limitations to its possible interpretations. Since in every figurative work of art there is always the dialectic of Open-endedness - Closed-endedness, and in non-figurative art we find only one of the poles of this mindprint, it seems that Open-endedness - Closed-endedness can be one of the parameters that differentiate between art and non-art.
Connectivity-Disconnectiviy or Codis is not sufficient for the creation of order, nor is it an ordering principle such as hierarchy, without which there can be no life or intelligence. Basically, hierarchy is recursive or nested Codis. In other words, hierarchy is an embedded oxymoron comprising connections and disconnections (Codis) at various levels of order. That is, hierarchy is connectivity turned upon itself or more precisely; it is connectivity folded upon simpler versions of itself and thereby gradually creating more and more complex versions of itself. In this process the earlier versions are not overruled or canceled, but are preserved and embedded as "intermediate stable stages" (Simon, 1962) or holons (Koestler, 1967, 1978) by their nesting in the new and more complex versions. Through such a process a systemic connection is generated between all stages and levels of the connectivity. However-since there is no connection without separation-simultaneously with the recursion of connections there is also a recursion of separations or disconnectivities, which at a certain limit create disorder or randomness. Thus hierarchy and its opposite and complementary pole-anti-hierarchy or randomness-are the two poles of the same mindprint.
Hierarchy and recursion are inseparable because both are founded on nesting. The more detailed a figurative painting, the deeper is its nesting of symbols or structures within each other; and the deeper its recursive structure. The structure or hierarchic order in a figurative painting is the result of inclusion relationships, nesting, or self-embedding which exist between all the symbols of the painting, all of which are included by its background. That is to say, every figurative painting without exception is a hierarchic system of pictorial symbols. However, different figurative paintings are likely to have completely different levels of stratification. Thus for example, in a typical Vermeer painting there is far greater detail than in a prehistoric painting of a deer, and for this reason the degree of stratification in a Vermeer painting such as "The Milkmaid" is immeasurably more developed, and therefore contains more levels of organization, than any prehistoric painting. By contrast, it can be shown that in non-figurative paintings the degree of stratification is always negligible or extremely small, for, since in this art there is no symbol system, there are inevitably no recursive processes or nesting, but rather repetitions; however this is not enough for the creation of levels of order. Thus for example all monochrome paintings are utterly lacking stratification. Similarly, despite the large difference in the number of colors in minimalist and abstract expressionist paintings, this does not alter the fact that in both the degree of stratification is minute, because the degree of stratification is not determined by the number of elements but rather by the manner of their organization. A further important aspect present here is the fact that in every figurative painting there is always present at the same time a dialectic of hierarchy and randomness. By contrast, in works called "abstract" this dialectic need not necessarily be present at all, and many of these works are quite good examples of random organizations almost entirely devoid of any hierarchical patterning. Another aspect of this matter is the fact that figurative painting has from the beginning and until this day served as a means of presenting the order in the world. This attribute is what makes it above all a branch of culture, for all branches of culture are different ways of expressing the order that is in the world, either as an actual, a hypothetical, or an imaginary phenomenon. This is possible because its hierarchic structure is an ordering relation and it is symmetrical to one degree or another, to the order we see in the phenomenal world. Since non-figurative painting lacks hierarchy it inevitably lacks an ordering relation and cannot therefore represent any extensive order whatsoever. This point may be summed up by arguing that recursiveness, hierarchy and their derivative attributes are factors that distinguish art from pseudo-art.
All kinds of Symmetry-Asymmetry are modes of Connectivity-Disconnectivity, but symmetry also includes other mindprints such as Transformation-Invariance, some kind of recurrence which is a special case of Recursiveness-Singularity, Complementarity-Mutual exclusiveness and perhaps other mindprints as well. It is possible that all kinds of Connectivity-Disconnectivity include, at least in a minimal sense, Symmetry-Asymmetry as well, in the sense that there can be no connectivity without some kind of interface or common denominator, which may be either literal or metaphorical. Nevertheless, symmetry cannot be reduced to connectivity because there are numerous kinds of symmetries besides the one inherent to connectivity. As noted before, the most basic function of symbols is at one and the same time connectivity and differentiation. But symbols of different types serve this function in different ways. This difference is especially noticeable in the special way in which pictorial symbols connect and differentiate the entities they symbolize, in contrast to the way in which verbal and formal symbol systems connect their entities (Avital 1996). The special connectivity of figurative art is based upon maintaining a certain symmetry of a relative nature between the object and the symbol that denotes it. This symmetry is a structural common denominator of the class of entities connected by that symmetry. Thus for example, the contour depicting a deer is the graphical common denominator between all members of the class of deer. In this sense, symmetry is a connecting pattern in art as in science. Therefore the annulment of this symmetry from visual non-representational art, exactly like the annulment of hierarchy or any other mindprint from this art, has far-reaching implications for the cognitive functioning of modern art. This matter is especially relevant to "abstract art", which completely abrogates symmetry or similarity between symbol and symbolized as a principle of representation, thereby losing the cognitive function of Connectivity-Disconnectivity that has been so central to figurative art throughout the whole of its history. The breakdown of symmetry as the connectivity principle of art, is at the very root of the breakdown of art itself in our century, and it can therefore safely be assumed that in the future paradigm of art Symmetry-Asymmetry will be restored, without however reverting to figurative symmetry, but rather to Symmetry-Asymmetry of a much higher level of abstraction. This seems to be inevitable because, like all mindprints, the complementarity of Symmetry-Asymmetry, is one of the most basic means of organization of mind or Being in all of its manifestations: on the material, the biological, and the noetic level, of which art is one sub-aspect.
Transformation is the melody of matter, life and intelligence. It is the magical bridge between Being and Becoming. For Heraclitus change and transformation was the only truth, and invariance was illusory. For Parmenides transformation was sheer illusion and only invariance was the truth. For Plato transformation was the earmark of the phenomenal world, which for him was an intermediate reality between the realm of illusion and the world of Forms or Ideas, which is invariant and the only eternal truth. In Plato’s conception there is thus room for both poles of this mindprint, but he did not see them as complementary opposites. Modern science has clearly opted for the Heraclitean view which perceives reality as dynamic and transformational. However, at the same time, science posits a number of invariants such as levels of organization or hierarchy, symmetry, transformation and others, as well as their complementary opposites. Indeed, the central and as yet unproven supposition of this essay is that the list of mindprints I have indicated is almost certainly a partial inventory of the invariants that are common to all branches of culture, and science among them. There are evidently many kinds of transformation: some are common to all levels of Being, some are unique to each level. The concept of transformation is too wide for discussion here, and I shall therefore focus only upon a few of its aspects that are relevant to symbolization, of which art is a special case.
Transformation-Invariance is not only inherent to all kinds of Symmetry-Asymmetry, but is also the precondition of all perceptual and cognitive activity. The reason for this is, that all mental or cognitive activity involves interpretation, and interpretation involves some kind of coding-decoding, signification or symbolization, which is impossible without transformations of various kinds. While the necessity of transformation is self-evident in the physical and biological domains, it is less apparent in the cognitive context. Thus, the creation of pictorial symbols involves spatial and temporal transformations: from three to two dimensions, and from faster to slower time. The first kind of transformation is self-evident, but the second is less obvious. Time is not a uniform phenomenon but rather is it an immense hierarchy of times which includes within it several hierarchies of kinds of time characterized by different levels of rate of change (Fraser, 1975; Stamps, 1980). Thus for example, the rate of change in the physical world is much faster than in the noetic world. On the other hand, in each of these two domains a hierarchy is present, of rates of difference. By a broadening of this idea, it may be said that in drawing a house, a flower or a horse, the very creation of a symbol for one or all of them together, performs simultaneously two kinds of transformation: on the one hand, the transformation is made of a three-dimensional entity into its two-dimensional image, and furthermore it is removed from physical time to noetic time, which is much slower or characterized by a much lower rate of change. It is as if we had trapped or frozen a bubble from a world in which change takes place at a rapid pace, into a world in which change takes place at a far slower pace. Notwithstanding, despite these two transformations, a drawing representing (for instance) a horse, does not represent a particular horse, but constitutes a pictorial universal that can indicate any horse. This fact indicates the invariant and complementary aspect of transformation. In other words, there is present in figurative art a duality of descriptive vs. described processes, and there is a vast gap between the rates of change and levels of complexity in the two processes. However, the two processes are complementary and are connected by transformation and symmetry. That is, a basic function of pictorial symbolization is the preservation of information by translating or transforming a faster to a slower process, or by creating a slower process which denotes the symbolized process or entity. Thus, information is preserved by increasing connectivity. Connectivity is then in inverse relation to difference, and deceleration in time is a kind of freezing of the object as an image or concept. In most cases (but not always) intelligibility is also achieved by shifts to lower levels of difference, i.e. slower time or higher connectivity. As we shall see in the following, in the case of conceptual and formal symbolization the dynamics of Symbol vs. Symbolized is far more complex.
As already stated, when we construct a representation of a phenomenon it is necessary to move to a slower time than that of the symbolized phenomenon. But when attempting to represent a totally conceptual and highly abstract entity, such as "God" for example, it may be that we then pass to a level of change much more rapid than that of the matter symbolized since according to the monotheistic view, for instance, God does not exist in time and in any case has no variance! On the other hand, our concept of God, however abstract this may be, will include some measure of difference since we are unable to think otherwise. A less extreme case would be when we try to represent a mindprint like Symmetry-Asymmetry. For this we shall have to pass from the low level of difference at which the meta-patterns of the mind exist, to a higher level of difference, in order that the concept shall have sense within our conceptual system. Two more examples: A close childhood friend whom I have not seen for many years has remained in my imagination in the same state, a kind of freezing in time of the image, and if I were to meet him in the street I might very well not recognize him. By contrast, when I draw a circle, there is no passage into a slower time than that in which geometrical ideas exist, but on the contrary: we pass from a low level of difference in which these ideas are present in our thought, to a much higher level of difference in order that the concept of the circle should receive actuality in the phenomenal world. The conclusion to be drawn from all that has been said is, that our consciousness exists only within a certain range of levels of difference. That is to say, in order that we may be able to function cognitively we move, in certain cases, into a time that is slower than that of the subject of symbolization, while in other cases we move into a more rapid time.
Unlike the case of figurative art, in abstract art there is no symbolization and therefore no transformation-neither spatial nor temporal. There are neither descriptive nor described processes. The work in this case is time-dependent only in a physical sense, as with any perceptual object. There are no shifts or transformations up or down the hierarchy of time and there is therefore no symbolization, no preservation of information and no intelligibility. It has also no invariant aspect, because one may interpret it in any way desired. In the light of these profound differences between figurative art and abstract art, it is reasonable to suppose that Transformation-Invariance, like the other mindprints, is one of the parameters that may distinguish art from pseudo-art.
Determinism in its classic formulation, as with Laplace and others, assumed a total causal connectivity between all events at all levels of Being, and therefore saw in selection and in free choice only illusion. Spinoza, Hume, Darwin and others saw in the assumption of the existence of chance an admission of our ignorance with regard to the causality of things. In a less extreme formulation, as with Descartes, absolute determinism exists only in the material world but not in the spiritual world, and not with regard to God. Modern physics learned to understand what had already been understood thousands of years earlier in the mythologies of Egypt, Greece, Iran and India: that there is no complete determinism, but two opposed tendencies of order and disorder. The difference is that modern physics, like Daoism, sees in these two tendencies opposed but complementary tendencies, whereas the mythologies saw in them opposed forces that were not dependent upon one another. In complete opposition to the mechanistic view which is fundamentally classical determinism, Prigogine argues that matter is not passive but is characterized by spontaneous activity (Prigogine, 1984, p.9). This means, that the physical world is an open-ended process and that therefore in principle our knowledge regarding material reality discloses only a probabilistic situation, and not an absolute one. From this follows the profound connection between Open-endedness-Closed-endedness and between Determinism-Indeterminism. The fallacy of determinism is in the end the assumption that in Being there is absolute connectivity without the opposite pole of disconnectivity. In other words, determinism is an expression of connectivity and closed-endedness, and indeterminism is an expression of disconnectivity and open-endedness. And indeed, as there is no absolute connectivity and no absolute diffusion as permanent states but rather for very brief durations as a stage within a broader process in which they change, so too there is no determinism or its opposite as absolute states, but rather only intermediate states of connections of different strengths. Moreover, creativity is one of the salient expressions of Open-endedness - Closed-endedness, and the fact that there exists continuous becoming and creativity in all aspects and at all levels of being is perhaps the best refutation of the deterministic view.
In culture, as in the physical and biological worlds, there are constraints of different kinds which constitute the deterministic aspect of the products of culture; but along with these constraints there are also indeterminism, open-endedness or one measure or another of degrees of freedom. The deterministic aspects are the factor making the products of culture inter-subjective; otherwise they would have no cultural value. On the other hand, along with these constraints there are also anti-deterministic factors such as the idiosyncrasy, talent and the special point of view of the creators. Similarly, another contribution to this matter is the uniqueness of the consumers of culture and other factors such as arbitrariness and randomality, which are a dimension that accompanies every creative process and every interpretation of it. Basically the indeterministic aspect, which is largely subjective, becomes in particularly successful cases public property. However, in less successful cases it remains the property of the subject, and therefore irrelevant to culture. Thus for example the basic structure of all languages is hierarchical, but different languages interpret and map reality in different ways; the speakers of every language use it in different ways to one extent or another, and in every language different combinations of phonemes are used in order to denote the same things. Moreover poets, philosophers and scientists try persistently to extend language and renew it so as to match an existing or hypothetical reality. Similarly, every figurative painting is a hierarchical symbol system depicting real or fictitious entities by means of a specific symmetry that enables us to identify the painted object. However, in every such painting there are, alongside structural, syntactic, material and other constraints, also not a few factors which contribute to the open-endedness both of painting as an artistic domain, and to the open-endedness of the painting as a specific work. Thus for instance the special use that, throughout the history of painting, every artist makes of colors and shapes; shades and configurations that occur by chance alongside those that are planned; the special interpretation which he gives to the symbols and to divergences of one kind or another from the figurative syntax; all of these and others contribute to the creativity, originality, renewal and richness of the art of painting. In abstract painting there is by contrast only an indeterministic, subjective or idiosyncratic element, but no deterministic inter-subjective element at all, so that it is very doubtful whether it is art. It may thus be said in conclusion that Determinism-Indeterminism is a mindprint in art and in every other area, and can therefore serve as one of the parameters for distinguishing between art and pseudo-art.
Negation-Affirmation (or double negation) would appear to be the most basic mindprint, since negation is immanent in every mindprint in the sense that it is the necessary condition for the generation of complementarity in all mindprints. In other words, negation is what creates otherness, and in this case the reciprocal connection and opposition between the poles that form each of the mindprints. From a psychological viewpoint, we tend to think that affirmation is more basic than negation. But from a logical point of view, negation is more primary, for negation cannot be derived from affirmation, whereas affirmation can be derived from negation by means of double negation. At the same time, affirmation has no meaning without negation, and not the contrary, for the one always assumes the other and they are therefore complementary. Thus for instance, in a proposition such as: "This table is made of wood", we explicitly affirm that the table is made of wood but we implicitly deny the possibility that it is made of some other material. Such as iron, for example. As against this, when we maintain that: "This table is not made of iron", we explicitly deny the possibility that the table is made of iron, but we implicitly affirm that there are other materials of which it may be made, such as wood or stone, for example.
Without negation no kind of thought is possible in any area, nor the most basic laws of thought such as the law of contradiction, and the law of the excluded middle, already formulated for the first time in the sixth century B.C., by Parmenides. In a wider sense, without negation no noetic activity would be possible-whether perceptual, instinctive, symbolic or emotional. Negation and double negation accompany all processes of thought at all levels, and every comparison and every state of consciousness. For there is no awareness without consciousness of difference, and there is no difference without negation. Explicitly or implicitly, negation and affirmation are inseparable from every proposition, judgment and predication. Without negation and double negation there is no meaning to truth and falsehood, and evidently no logic; there is no possibility of verification and refutation in any domain; there is no certainty and no uncertainty, and there can be no order, organization or orientation of any kind. Not only is epistemology impossible without negation and double negation, but neither is ontology possible without this mindprint. That is to say, there is no Being at all levels without its complementary opposite, nonbeing or nothingness. In both cases, in the noetic world and also in the material world, negation creates otherness: it splits unity and simplicity and thus creates diversity and complexity. Negation creates the complementary classes: thus the class of "not-blue cars" is the complementary class of the class of cars which are blue. Without negation there can be no inclusion-exclusion relations, classification, differentiation of any kind or individuation; there will be no process or entropy, no evolution or negentropy and no variance or time. However, without these there can be no intelligibility or coherent view of mind or reality. In short, eventually, negation grants the emergence of mind and reality.
The wonder of Creation is perhaps the wonder of the creation of negation. Everything else is derived from it. The first verses of Genesis describe the first distinctions that God made, which are also the creation of the first complementary pairs: heaven-earth, light-darkness, etc., but no distinction is possible without negation, and negation and double negation therefore preceded all distinctions that followed. For the same reason complementarity too, which was generated by negation, preceded the complementary pairs that were created. Actually, the first Asymmetry, which according to the Big Bang theory is the moment of creation, could not be without negation. In a humorous vein, one might suggest a different opening for the first chapter of the Bible: In the beginning God was very bored amidst Perfect Symmetry, in which absolutely nothing happened. Then accidentally He sighed, "Oh No!" This created the first Asymmetry, which brought into being the other mindprints... and the rest is History. In other words, there is no symmetry without asymmetry, and there is no asymmetry without negation, therefore negation is a precondition for Symmetry-Asymmetry, and the same can be shown with regard to all the other mindprints. In a final regression, the negation of negation is perhaps what created Being, and this is perhaps the significance of the proposition that Being was created from nothingness. There is nothing new about this, since the idea already arose in the creation myths and in philosophy, in Western and Eastern cultures, and also in modern physics.
It is doubtful whether there has in the history of philosophy been an issue whose implications for the history of Western thought have been so decisive as in the case of the concept of negation, and mention should therefore be made in this case, of the context within which this issue first arose. It is perhaps not by chance that Heraclitus and Parmenides, who largely established the main channels of the development of Western philosophy, presented in a polarized manner two opposing world views, the essential difference between which was a different view of negation. Heraclitus does not appear to have discussed explicitly the problem of negation, but since the world view that he presented is constructed upon principles of transformation and complementarity, then implicitly negation and affirmation, and also being and non-being, must be two opposing but complementary aspects, as with all the other opposites. By contrast, in the view of Parmenides, opposites and complementarity are only an illusion connected to the Way of Seeming and not to the Way of Truth, whereas the problem of negation was the main axis in his philosophy, and his conclusions had a decisive influence upon the subsequent development of Greek philosophy.
For Parmenides there was no clear distinction between subject and predicate, and no distinction between negation and nonbeing, and therefore the negation in ‘what is not’ is not the negation of a specific attribute of the subject, but rather the negation of the existence of the subject. Another assumption of his, was that there exists an identity between the content of thought and the reality of the object of thought: "...for it is the same thing that can be thought and can be" (fr.3), and it is therefore impossible to think about ‘what is not’, or what does not exist. Thus in his explanation of the impossibility of the becoming of the One or of ‘what is’, out of what is not, he argues: " I shall not allow thee to say or think ‘from what is not’, for it is not to be said or thought that ‘it is not’. (fr 8.6; the fragments are from Guthrie, 1965, p.14, 26.) But as a result of the identity between negation and non-being, and because of the absence of the distinction between predicate and subject, for Parmenides a double paradox was created: on the one hand he argued that it was impossible to think of ‘what is not’, but the greater part of his philosophy deals with thinking about the negation of the possibility of thought regarding what, according to his conception, it is impossible to think about. On the other hand, in his opinion it is possible to think only about ‘what is’. However, it is not possible to think anything regarding that utterly undifferentiated transcendent Unity, without introducing a multiplicity of words and predicates-something that is opposed to his own view. And indeed he too is obliged to characterize this unity mainly by way of negation, with the aid of a few predicates, for otherwise he could not have said or thought anything regarding that unity. Parmenides was aware of the fact that because of our essential need for names and words, which for him were only conventions that did not necessarily describe a true reality, it is then possible in actuality to think only about contents or subjects which he considered it impossible to think, and impossible to think about what he considered it possible to think.
The polar opposition between Heraclitus and Parmenides is not only with regard to negation, but also in that they emphasized in their philosophies the different poles of another mindprint: Complementarity-Mutual exclusiveness. Heraclitus emphasized complementarity and ignored the other pole, which is mutual exclusiveness, whereas Parmenides denied complementarity and emphasized only mutual exclusiveness. For this reason there can also be for him only total negation or only total affirmation of the content of consciousness, which is for him identical with the object of thought: that is, for Parmenides there can be only absolute negation with regard to the perceptual world, or absolute affirmation with regard to the One, and there is no possibility of his affirming one aspect and denying another aspect in one of these two worlds (Scolnicov, 1988, p.151.)
The conclusions of Parmenides concerning negation led for the first time to a distinction between phenomenal reality as an illusory reality, and transcendent reality which is true, but with no possibility of bridging the gap between the two. Indeed, the chief life work of Plato was the attempt to forge a compromise between the opposed world views of Heraclitus and Parmenides, and in particular to bridge the abyss created by Parmenides. The key to his solution lay in showing that negation does not relate to a thing, but to characteristics or predicates which can be related to a thing, so that there is no problem of negative things (Plato. Sophist, 257-258.) Aristotle agreed with his opinion in the matter of the nature of negation, but he rejected the rest of the implications of the Platonic solution which created three worlds, of which he attributed to the phenomenal world an intermediate status of between ‘what is’ and ‘what is not’: between the true world of Ideas whose attributes are similar to those of the Parmenidean One, and the world of illusion. On the one hand Plato’s solution introduced multiplicity or negation into the world of unity of Parmenides, through the plurality of ideas, and on the other hand introduced unity into the world of diversity, since the objects in the world owe their existence to the fact that they partake of the Ideas or imitate them. Plato anchored the Ideas or Forms in the transcendent level, whereas Aristotle considered that they were immanent to the things themselves. This was the central point of disagreement between these two giants, and the subsequent history of philosophy up to Kant is to a great extent the continuation of the argument between them. The problem of negation in its wide sense was the point of departure for Parmenides, but the discussion of it and its derivatives laid the foundations for epistemology and ontology, metaphysics and logic; the complete separation of the perceptual and the conceptual and their relation to the possibility of knowledge; the assumption of rationality as the point of departure for philosophical method and as a criterion for reality itself, and other issues. Here it can be seen to what extent the problem of negation indeed determined the character of Western philosophy for more than two thousand years. (Scolnicov, 1988, p.162.)
On a superficial view it is hard to see in what way the Negation-Affirmation mindprint could have importance in relation to the problem of demarcation lines between art and non-art. However, on deeper inspection its importance is revealed at two levels: firstly, with regard to figurative art it is very easy to establish whether some thing belongs to figurative art or not. By contrast, in non-representational or abstract art, there is no way of denying some thing its inclusion in this art, and thus in principle any thing can be accepted as a work of art of this type. In other words, modern art is not skeptical, as many try to present it, but rather is it nihilistic and therefore in the end also self-nullifying: it negated figurative art but it has no alternative of equal value, let alone a better one. Secondly, one of the functions of negation is the creation of differentiation on different planes. Thus for example there is always in figurative art a differentiation between figure and ground, and likewise a rich and well distinguished system of symbols each of which serves as a pictorial class-name for certain entities. As against this, in abstract art negation is not necessary at all: there is no necessity at all for a distinction between figure and ground, and a picture may well contain only unity, with no differentiation at all, as occurs in monochrome paintings. In the light of all this, it is clear that the Negation-Affirmation mindprint may be one of the parameters for the distinction between art and pseudo-art.
I have some doubt as to whether Comparison-Imparison is indeed a mindprint in its own right, or whether it is not an internal organization, or nested mindprint of other mindprints such as Negation-Affirmation. For, at least in the area of predication, propositions and judgments, no negation or affirmation is possible without comparison between at least two states of affairs regarding the extent of difference, resemblance or identity of the attribute or attributes one is attempting to negate or affirm in relation to some subject. Thus for example, according to the law of contradiction a proposition cannot be true and false at the same time. Or, two propositions, p and not-p, cannot both together be true. However, the law of contradiction is not meaningful without an explicit or implicit comparison between p and not-p. Negation and affirmation are, then, not possible without comparison between two opposing possibilities regarding the same matter and the rejection of one of these possibilities. Thus for instance, for a person to be able to maintain rightly or wrongly: "This painting is not by Vermeer", he must compare the observed characteristics of the given picture with the totality of characteristics that there would be in an authentic painting by Vermeer. In the light of the difference between the characteristics of the given painting and those of a typical Vermeer, he rejects the possibility that the given painting is indeed a painting by Vermeer. By contrast, when a person maintains: "This painting is by Vermeer", he compares the characteristics observed in the given painting with the totality of characteristics that there would be in a typical painting by Vermeer, and in the light of the great similarity or identity of the two classes of characteristics he rejects the possibility that the given painting is not by Vermeer. That is to say, he affirms that the given picture is indeed a painting by Vermeer. We have seen, then, that at least within certain areas there is no negation without comparison. But comparison is not possible without negation, in the sense that there is no comparison without the perception of variance or duality between things or between two appearances of the same thing. Similarly, there is no point in the act of comparison if it is not accompanied by an affirmative, negative, or dubious decision regarding the degree of variance, the similarity or identity of the characteristic considered in the objects of the comparison. It would seem that in the epistemological realm at least, negation and double negation are conclusions from comparison. However, I am by no means certain that this is so in all domains. In this, as in other matters connected with mindprints, I am still groping in the dark, and hope to understand them better in the future.
To summarize:In order to understand art as a product of the mind, it is necessary to understand the structural patterns or mindprints that the mind stamps upon all phases of Being: in the physical, the biological, and the noetic world, of which art is one aspect. Seen in this light, human culture, including art, is not antithetic to nature, as suggested by some anthropologists, but is in a profound sense the latest phase in the evolution of nature itself. In this phase, the main product is not matter or life, but the unfolding of intelligence itself and its structures, which are implicit in nature from its beginning. An adequate theory of the origins of art must therefore indicate at least the linkage of art with the tremendous process of the emergence of intelligence. Seen in this way the characterization of art cannot be another particular theoretical caprice to be lightly accepted or rejected. Rather such a characterization of art is needed that anchors it in the broadest possible context - to cosmology itself, which is the grand objectivation of mindprints. In fact, a characterization of art in this way is to my mind a direct derivative of the most sublime principle that science has yet discovered: the anthropic cosmological principle (Barrow and Tipler, 1986) according to which many of the extraordinary properties of the universe constitute a necessary condition for the existence of life and of an intelligent observer of that universe. Intelligence is according to this view a purpose of the universe, and on our tiny planet this purpose began to materialize explicitly through culture and the stages which preceded it: footprints literacy at least four million years ago; tool making some two and a half million years ago; through image making or prehistoric art some 40,000 years ago; and through language and all of its products, which crystallized at some time between the emerging of tool making and image making, and has been to this day the main bearer and propellant of cultural evolution. If the mindprints are indeed basic structures of the mind as argued here, then the real test of this idea will be whether people from domains different from art will also identify the mindprints that have been indicated here as meta-structures in their domains as well. If this in fact happens, then the mindprints theory may indeed be able to serve as the structural basis for a transdisciplinary view of culture, or as the basis for a philosophy of culture. It can be seen from this essay that Symmetry-Asymmetry is only one out of nine or ten other mindprints, and not the most essential of them. In the light of this, I hope that the Society for the Interdisciplinary Study of Symmetry (ISIS-Symmetry) will widen its platform to include the rest of the mindprints as well, or the general investigation of the basic patterns of the mind and the mutual relations between them.