Читать книгу The Woods - Vladimir Bibikhin - Страница 17

I am trying to resolve the riddle set by Plato, of having pure geometrical shape in place of matter. We spend a lot of time trying to guess things. Averintsev once said that Russians may not be particularly sharp-witted, but they are good at guessing.

It would be better if I did not try to guess. Without guesswork, of course, it is difficult to know where you should look, and, more importantly, there may just be no point in looking because it is unlikely you are going to find anything. The real problem with guesswork, though, is that you are more likely to start trying to fit your solution to the answer you want to get. My guess is that Plato gives himself over body and soul to the forest: that is, that he ceases to see himself as separate from the forest and intuits that everything, through the air, water, food, the race, is entirely part of everything else. He ceases to ask himself questions about why everything is just as it is, why the sky is above and the earth below, and becomes intoxicated, like the Pythagoreans and Parmenides, with the suchness of everything, that everything is precisely as it is. Everything he sees, everything he thinks, fuses into an ultimate, reassuring experience, an experience of serenity and peace that everything that is, is just as it is, and that everything that has been was just as it was, and that everything that will be, however it turns out, will be just as it will. This experience is at once moral, an acceptance of all that is, and it is mystical, because it opens a channel to ultimate, final, full divine knowledge at the outer limit. When God at the beginning of Genesis says, ‘Let there be light: and there was light. And God saw the light, that it was good,’ and the same is repeated with everything else, that ‘Let there be’ is not design, not engineering. Light is not being given a definition, a specification, a description, to which what appears is to conform. Light already is, since what is said is, ‘Let there be light.’ God himself is taken by the ecstasy of identity.

This merging not only does not lead to any blurring of distinctiveness but, on the contrary, creates a structure of things being identical to themselves, of sameness, of thisness and suchness (immennost’). In other words, we, and we are again guessing here, having been swallowed up by the forest, find ourselves in the realm of logic. But are the foundations of logic identical to those of mathematics? It would be good to find that was the case, but we are suddenly faced with a problem. Wittgenstein warned that there would be difficulties with identity, and the difficulty begins with the trap that there seems to be no problem. I also need to bear in mind the additional problem of how identity relates to unity and unity to number, but when we get down to starting to grapple with this, we find that guesswork is no longer helpful.

Or it is, indeed, distinctly unhelpful in the case of the clue of the Cross. The Cross is the tree. Well, obviously, well-informed people will tell us; indeed, it is also the well-known World Tree of every mythology in the world. So it not only relates to the forest but in fact itself is the forest.

Of all relic discoveries the most impressive was that of the True Cross (the cross upon which Jesus was crucified, found in September 335 or in 326, according to other accounts)…. [Prompted by a dream, Helena, mother of the emperor Constantine, Bibikhin] located the place where the Cross lay buried and had the wood unearthed…. The power of the Cross, the history of the wood, and the story of its discovery became legendary. [In Christian myth this relic of Christ’s death dated back to the mortal origins of humanity. Innumerable cures attested to the authenticity of the Cross, Bibikhin.] Through the symbolism of the Cross early Christian imagery perpetuated, and at the same time transformed, the myths of the World Tree. The sacred drama of Christ’s birth, death, and resurrection participates in the rejuvenating rhythms of the fecund cosmos. Early Christians identified the Cross of Christ as the World Tree, which stood at the centre of cosmic space and stretched from earth to heaven. The Cross was fashioned of wood from the tree of knowledge of Good and Evil which grew in the Garden of Eden. Below the tree lies Adam’s buried skull, baptized in Christ’s blood. The bloodied cross-tree gives forth the oil, wheat, grapes, and herbs used to prepare the materials administered in the sacraments that revitalize a fallen world. The Italian Renaissance painter Piero della Francesca later depicted the myth of the True Cross in his frescoes in Arezzo, Italy. They portray the death of Adam, fallen at the foot of the Tree that provides wood for the crucifix on which Jesus is slain. The wood of the cross becomes the instrument of salvation and the holiest matter in Christendom, and the cross itself became the focus of tales of fantastic historical episodes.¹

Let us continue this brief excursion into the World Tree, a myth of primaeval humanity, and since we are not primaeval but have progressed, we can accordingly look down condescendingly on the forest and the World Tree. We note from the heights of our scientific understanding that there are two types of World Tree, one vertical, the other horizontal. Admittedly, the distinction is more for convenience of description and classification, and in the World Tree the horizontal and vertical are interwoven and merge. In Genesis, we find both trees: the Tree of Knowledge is vertical and enables contact with the gods, its sanctity impugned only by a taboo, a moral nuance optional in the mythology. What the Ophites, serpent-worshippers, did was simply to remove the moral veneer, the tinge of transgression, from the biblical story and restore the vertical tree to its eternal role of linking the earth below with the divine world above, of ascending to ultimate knowledge and wisdom, the knowledge of good and evil. The horizontal tree is the heavenly tree of life, the source of fertility. It, too, has a taboo attached: it may not be cut down if procreation and abundance are not to end. A fairly recent television interview with one of the few remaining primaeval sages indicated that for him Europeans, with all their pretensions, their manners and clothing, were no longer people of the forest; as far as he was concerned, they were the dead and the harbingers of death.

In Norse mythology, Yggdrasil (in old Norse, they said mimameidr), the giant rowan tree, sank its roots down into three worlds: Niflheim, the lower world of darkness; Jotunheim, the world of giants; and Asgard, the city of the Æsir gods.² Similarly, there are three keys by the roots of the World Rowan Tree: Urðarbrunnr is the key of prediction; Mimisbrunnr is the key of wisdom; and Hvergelmir is the key of passion. The Boiling Cauldron is where a monster, Níðhöggr, resides which is engaged in gnawing at a root of the World Tree. Applying our basic classification, this is, of course, a vertical tree. As in the Bible, there are the Norns, who live by Yggdrasil near Urðarbrunnr, and they are associated with good and evil. As in Socrates, they assist at childbirth.

When the world comes to an end with Ragnarök, the gods, too, may die, as in Wagner’s Götterdämmerung, but the World Tree, the tree of the cosmos, although damaged, will remain and will give birth to two beings, Líf (life) and Lífþrasir (lover of life), from whom humankind will be reborn. The tree is more enduring than the gods. As in the Ophite reading of the Bible, God creates only the horizontal tree of matter, while the vertical tree that hints at limits of the divine is not and could not be revealed by God.

Traditionally, the tree pierces and simultaneously links different tiers of life. In Siberian religions in the Altai Mountains, a tree is installed in the hole in the roof of the tent. It is beneath the roof in the human world, but above the roof in the cosmic and divine world; smoke from the stove inside, entwining the tree, rises to the upper tiers. The shaman himself then climbs the tree in the direction indicated by the smoke, ascending to the higher world up the World Tree. By doing so, he is of course also taking the risk of dying on the tree for humankind.

The shaman clings to the tree, merges with it, or, we might say, is crucified on it, because he is taking a terrible physical and spiritual risk. This cleaving of the shaman to the tree brings to mind the relationship of the Crucified to the wood of the Cross. The wood raises him and they become one. Rather than repudiate the Cross as an instrument of execution, Christ clings to and connects with it. This theme of merging, even of identification of Christ with the Cross, is evident in an unusual 1939 sculpture in elm by Ossip Zadkine.³ Born in 1890 in Smolensk, he died in Paris in 1967 and is best known for his 1951 sculpture The Destroyed City in Rotterdam, which depicts a broken human figure with arms outstretched in horror. Zadkine’s elm Christ appears to be convulsed, but his arms are like bare tree branches. This merging with the Cross is more evident in the earliest extant crucifixes, in which Christ does not have his eyes lowered in mortal anguish but is alive, with his eyes wide open. The Cross seems more the place where his divinity is made manifest, and he seems to be reaching out with his arms intentionally.

This corresponds to something about the Cross which is now almost overlooked and which Pavel Florensky (1882–1937) in his thinking about the divinity of the Cross needed to reconstruct: the wood of the Cross itself has features of divinity.⁴ It is life-giving. That is, the Cross itself is a tree, like the body of the god. The Cross was absolutely the most important of all the relics of Christianity as a result of the awareness of this fusion of the deity with his tree.

In the Cross, people see both trees, and often refer to its horizontal as representing the human world and the vertical as humanity standing before God, which is not apart from but rises above the horizontal. A variety of pious and pleasing interpretations are possible. Out of this range of interpretations, meditations, mythologems, and other kinds of mystical understanding, what matters for us, what we are reaching for, is just one thing: the Cross unexpectedly points in the same direction as Plato with his tetrahedron in place of the first element of matter, fire. The Cross is wood, it is the World Tree, and it is geometric. An easy and rather widespread notion is that the wood is matter and the Cross is form brought to and superimposed on matter. If we settle for that, we will have got one problem out of the way and can move expeditiously on to the next. The trouble is that, having adopted that approach, we can no less expeditiously deal with any other difficulty and will end up in the unenviable position of the cultural historian, a historian of thought whose sole mission is to ‘assimilate and present’ his or her material. Well, who cares anyway that, if we stubbornly refuse to acknowledge the dualism of matter and form, we will have to wave goodbye to all traditional history of philosophy and culture? Away with them! So we’ll be empty-handed. Sooner that than find ourselves with a museum on our hands and playing the part of museum attendants. We’re better off out in the open and empty-handed.

Well, actually, no. We are not going to make the obvious mistake of thinking that Plato chose one pole on the materialism–idealism spectrum and then made sure everything he said conformed to it. The materialism–idealism divide dates from long after Plato, and is a great deal shallower than his profundity. His conundrum that matter is pure geometry exactly reflects the mystery of the Cross. The Cross is not a philosophical construct, a primitive representation or abstraction of the World Tree: the Cross is the forest. It is not the Cross that needs to be explained in terms of the World Tree but, on the contrary, if we are to understand anything about the World Tree at all, the only possibility is by way of the Cross.

So, it will be better if we again mill around on the spot where we stumbled. The dark, primaeval forest, the later forest of the megapolises, tobacco, alcohol, and drugs, all liberate us from metric space. In the forest, you are disorientated. The forest is in the Cross just as pure geo-metry is in the tetrahedron. We find our way through by distinguishing number from number, ontological number from arithmetical number. It transpires that mathematics does not know what number is and surrenders it to philosophy. So much the better; that only makes things easier for us. It means we now have to construct a theory of number. The commonsense theory is clear: the generalizations derive from experience. We supposedly count our fingers, or sheep, then look away from our fingers, or the sheep, and arrive at pure numbers. Let us discard that out of hand as a piece of nonsense that can only trip us up. In the first place, before we can start counting fingers or sheep we need to standardize them: that is, they need to have been strong-armed into the realm of arithmetic. Abstract counting, then, was there first, before specific counting. Secondly, if counting were an abstraction from specific counting, where did the infinite set of natural numbers come from?

After all, in practice no one has ever counted up to infinity, and the total number of objects in the entire world is most probably finite, so that in practice we have no grounds at all to believe in an infinite set of numbers. It has come from a different source, which we started thinking about last time.

We talked about the alluring, attractive power of the whole: it wants to be named, enumerated, although we know in advance that it cannot be exhausted through enumeration. We can sense enumeration’s inadequacy in the face of the whole at every step. For example, there are so many members in a collective. We immediately add that, of course, the team is more than the mechanical sum of its members: it has an extra quality. Has this quality been added because quantity has been transformed into quality? This is a bad law of dialectical materialism that results from poor eyesight: the new quality derives not from some quantitative addition but because the set under consideration has, barely perceptibly, unexpectedly, been drawn towards unity. The whole is beginning to shine in it more strongly.

It would be more precise to say that the way of viewing it has switched; there has been a change of viewpoint from one unity to a different one. The inclusive, attractive power of unity cannot be encapsulated by enumerating its components. The universe is a heap, and no matter how many components you throw on to it, there will still be room for more. And that is true of virtually any unity. Behind the family, we detect the genus, and here is where we need to seek the cause of the inexhaustible bounty of nature. We cannot construct a cell from its constituents because it is a unity. Why it is a unity is a separate matter, and it is as difficult to find an answer to that as it is impossible to create a unity, a wholeness: it has to be found, intuited; it has to give itself away. It is impossible to detect elementary particles, neutrinos or quarks; it is impossible because of the ‘natural’ method of physics. The reason it is called natural science is because it is unable, is not supposed to, has never learned how to, deal with anything that is not a whole. Any whole, any unity, cannot by definition be mechanically assembled from parts. That is a peculiarity of the structure of any unity in nature.

The issue of the elusiveness of wholeness in nature is different from the issue of wholeness in technology, where, for example, there is no difficulty in enumerating how many parts a wheel consists of, and I cannot raise it here. Some other time.

For now, let us hold on to our thread of how and why the forest proves to be geometry. It is so tempting to try to fill up unity with quantity, because we feel the need to respond to it in some way. It challenges us, but perhaps the purest way to redeem thought is to leave unity alone.

So leave it alone we shall, but whether we worry at it or leave it alone and in peace, it remains unassailable. Nevertheless, we understand the origin of numbers and their strength: their infinite reserves. We know negatively and not necessarily consciously, perhaps intuitively, that mere enumeration will never exhaust the power of unity. So let us rest assured that there will be no end to our enumeration.

The origin of number is, then, negative. Numbers with their infinite counting have as their base the hidden intuition that it is possible to carry on safely enumerating till the end of time: unity is strong enough to cope with any amount of enumeration. We have enumerated all the constituent parts and capabilities of the cell, but that is not the end: there are more fragmentary parts, newly discovered, unresearched. We encountered something similar in the computation of mechanical time. Its boundlessness is explained by our ineradicably late arrival in the occurrence of the world. No matter how many years we add to ourselves or to humankind, we can do so secure in the knowledge that, precisely because of our secret awareness that we know nothing of its origin, the event that is the world will be sufficient for us to draw on it indefinitely. The steady movement of unified or official time is reliably ensured, again negatively, by our late arrival, by the fact that the world was already there when we arrived. It can never come to an end.

Just as, separate from the official, standardized time of negative origin there is positive being-time, so, separate from the negatively founded unit of counting, there is the unity of the whole. To use Wittgenstein’s expression, any unit of counting is a test or a measure of the unassailable whole. We approach it this way and that, calling it our experimental number. The more we operate with these measures, these tests of unity, the more the experience of unity recedes into the unfamiliar, something we do not know how to deal with. Plato needs to remind us that the experience of number affects us more directly and fully than, say, the experience of our encounter with the donkey. The latter concerns, let us say, the living, the vegetative in us, and even then not always; while the experience of unity affects us always and completely. The experience of unity is at the same time both very rare and definitive, like the full stops we put at the end of every sentence. We can put them anywhere and everywhere, but do not even notice the charge of a full stop, the experience of concentration, because we have become completely used to operating with them. Prayer as the exposing of everything to what is nothing out of everything is something we undertake very rarely; we are usually busy with something else. In reality, though, we are showing ourselves constantly, always posturing, only we have become confused about who we are, and who it is that we are posing in front of. For a child, for example, the face of the person to whom it tells everything and before whom it poses, until emancipated from the family, is identified with the face of the parent, simply because the parent is constantly imposing a particular agenda. God does not impose himself.

So, number is a measure of unity as a whole, and not the other way round. Unity is not the measure of number. The dimensional number comes from a different, negative, space than unity. The shadow takes its orientation from the tree and not vice versa. But, even while recognizing this, we do not see for the present how all-embracing unity can move, or count, give form to order, a series. For now all we see is one unity, and yet the Pythagoreans and Plato speak of substantial numbers, not only about a substantial unit. I understand one wholeness. Two wholenesses, however, by virtue of there being two of them, will immediately cease to be joint or separate wholeness. Or am I wrong?

Substantial numbers are a difficult issue, and I have no confidence at all we will be able to resolve it; there may not be enough mindfulness, our attention may stray to other matters. It is tempting to say that there simply are no such numbers. The main problem is that we have no idea how to set about resolving this issue. For the time being, therefore, I will skirt round it. Actually, I do have a negative hypothesis, so here it is. Aristotle says clearly and distinctly that number is matter: ἀριθμὁν … ὓλην τοῖς όὔσι (986a, 16–17), but in the context of criticizing the Pythagoreans and Plato. Number and eidos seem to be the same thing for him and he uses the terms interchangeably in Metaphysics A6 and elsewhere.⁵ Or so, at least, people say. It is said that if we listen attentively, as we did, to Plato’s idea that the forest is number, we will find Aristotle among our critics.

This problem really is one we are going to have to face up to here and now. It would be highly distasteful to try refereeing philosophers’ opinions: ‘In this instance, we agree with Plato and oppose Aristotle.’ We need either to agree with Aristotle’s criticism of Plato or to disagree with it. We are really not going to start haranguing Aristotle along the lines of progressivist scholarship: ‘He committed the error of … failed to take account of, did not understand …’ It would be just too grotesque to ‘referee’ in this manner a thinker who lived 2,300 years ago. The only respectable and elegant way out of our predicament over Aristotle’s criticism of Pythagoreanism is either to manfully jettison everything we have said about number within the forest, about the forest as number, or find precisely that same thought in Aristotle: the forest as number; the forest as the Cross, pure geometry.

Immediately, as if for our boldness, we are rewarded, although matter is one of the most difficult topics in Aristotle. The difficulties are of two kinds. Aristotle does not tie himself down: having propounded one thesis, he does not consider himself disqualified from later putting forward a different one. His truth is on the move. The second difficulty, which is a difficulty for Aristotle himself, is that primal matter must not be ‘like this here’, because then it would be possible to imagine a different kind of matter, meaning there were two or maybe more. There needs to be just one kind of primal matter, but if that is so, where does the difference between substances come from? From different structures of the primal matter? But if we are saying that there are within it proto-structures with the potential for further formation, we are back to dealing with structures, and we wanted to be dealing with pure matter. Certainly, we find different kinds of matter in Aristotle, but the difference comes about from the depth of our scrutiny of it: the immediate matter for illness, for example, is humankind, but humankind itself is eidos, and matter is placed at one remove.

One thing Aristotle is predictably definite about is his refusal to accept that matter can be located anywhere beyond the boundaries of things and separate from them. Just as there is only imaginary donkeyness separate from this particular donkey in front of us, so matter, too, will either be here in front of us or it will be a mental construct. We can understand from this why Aristotle should emphatically object, as he does at the beginning of Book 2 of On Generation and Corruption, that ‘those thinkers are in error who postulate, beside the bodies [four elements, Bibikhin] we have mentioned, a single matter – and that a corporeal and separable matter’.⁶ Aristotle’s immediate objection is that this matter would duplicate the already known elements: it would either be light like air and fire, or heavy like earth, and so on. It might perhaps be even more basic than the elements, but certainly not of a different kind from them.

Why? Was Aristotle really incapable of imagining imperceptible matter? We are only too good at that, in the case of radiation, say. Ultraviolet and infrared rays are imperceptible. Quantum leaps are imperceptible. Why is it that for Aristotle a body, and any primary matter will be a body, ‘cannot possibly exist without a “perceptible contrariety”’? (329a). Because his perception was more refined. Radiation, owing to its effects on the body, would definitely be considered perceptible: the boundary of perception extended to include that. The same would be true of ultraviolet light: that ‘different’ light, or ‘different’, ‘higher’, ethereal fire was perceived, so to speak, as a change of mood before it was noticed that it caused a suntan. We are mistaken also in thinking that quantum mechanics as an intellectual (which is not the same as a mathematical) system was not elaborated by classical thinking in the topic of the automaton and spontaneity: there was an intellectual system of analogous complexity in the teaching about the soul.

When Aristotle talks of ‘perception by the senses’, he includes intuition and mood; at all events, he includes more than just direct impingement on the sensory organs. If the soul is in some way everything, then everything in a specific way will affect it. Today we have a foreboding that somewhere, in some dark, still place, someone – aliens, the government, the mafia, an international conspiracy – is up to something we cannot detect, do not know about, cannot perceive, cannot influence; or that in the bowels of substance, processes beyond our ken are brewing. Aristotle would have called that induced, superstitious. Everything affects me in one way or another; I react effectively to it in my own individual way, and can influence it just as long as I do not close my eyes or numb myself with noise.

Aristotle’s objection to Plato’s geometrical matter is precisely that such matter would be separate from what affects me personally, just as abstract values do not affect me. But we have already said that identity and unity affect all of me more than some random passing donkey. Again we are back with the problem of so-called substantial numbers. So that is the root of the difficulty! For Aristotle, numbers are apart, like geometric shapes. That is why, without explanation, he rails against Plato’s tetrahedrons again and again. It is impossible for abstract planes to be the wet-nurse (i.e. primary matter) (329a). Being is complete being, the being of things, which means that ‘things’ must be understood differently. And that is how Aristotle does understand them; they are not peeled away from eidos. And that is where we need to look for what we are surmising in Aristotle: ontological numbers, number as being? Almost certainly.

For the present, if Aristotle says something ‘exists’, he is automatically conferring fullness of being on it. He does not look for ‘existence’ among intellectual abstractions. ‘Our own doctrine is that although there is a matter of the perceptible bodies (a matter out of which the so-called “elements” come-to-be), it has no separate existence, but is always bound up with a contrariety’ (329a).

With great aplomb, taking a good swing, Aristotle approaches the topic of matter at the beginning of his Physics, and the examples he gives there for matter, or the substratum, the underlying hypokeimenon, speak volumes.⁷ The examples are of education and formation: first the becoming of a musical man from a not-musical man; and then the forming of an image, a statue from bronze. We can say, from being not-musical, the man becomes musical. Was being not-musical the substratum underlying the musical man? No, because the condition of being not-musical ceased to be, and the substratum is so called because it continues to lie beneath. On the other hand, we do not say from being a man he came to be musical. That would imply that we had in mind that a man is always unmusical. That is something we do not know. He may be as yet not-musical, but it is not necessarily the nature of man to be unmusical. Another example: we speak of ‘a statue coming to be out of bronze’. A form out of something formless? Here we need to differentiate. Just as it is not necessarily the case that before becoming musical a man was unmusical, so bronze before a sculptor gives it form is not necessarily formless. It is only carelessness that makes it seem so to us. Formlessness is no more the natural state of bronze than being a sculpture is, and in just the same way it is not necessarily formless. Formlessness is not the substratum of the statue: bronze is.

Note that a person is not entirely neutral, not wholly indifferent to becoming musical; it is not meaningless to say that people want to be, are attracted to being, musical. Matter is not chaos. It is not meaningless for a sculptor to say that the bronze wants to be a statue. Aristotle’s third example of a substratum clarifies this situation (190b). There is always something that underlies, from which that which comes to be proceeds: for instance, animals and plants from seed. In this third example, it is quite clear that the substratum has a reserve of movement in it. A person reaches out for the art of music the way a seed reaches out to develop into a living being. In order to understand how bronze reaches out to be a sculpture, we must remember that the Greeks were not at all interested in the microscopic world: for them the world they knew was their microscope and telescope. The bronze reaches out to the sculpture … we need now to return to this idea of Aristotle’s, to seek to penetrate it with the aid of the theories of modern physics about self-organization. We shall ask, however, as physicists cannot: what do we mean by ‘self-’?

I shall read out, to reprise and consolidate what has already been said, a long quotation from the Physics (190b), the point of which is that it introduces nothing new. ‘Thus, clearly, from what has been said, whatever comes to be is always complex. There is, on the one hand, (a) something which comes into existence, and again (b) something which becomes that – the latter (b) in two senses, either the subject or the opposite. By the “opposite” I mean the “unmusical”, by the “subject” “man”’ (190b, 10).⁸

To repeat: the ‘matter’ for becoming musical was, make no mistake, not the chaos of ‘unmusical’ but human; the chaos of unmusical is the contrary of musical and, paradoxically, it is lodged not in the person but in the musical: until the aim of becoming musical was formulated there was no unmusical; ‘the absence of shape or form or order are the “opposite”, and the bronze or stone or gold the subject”’ (190b, 15). We tend to think that the matter itself was chaos and that it is overcome by eidos. Not a bit of it. Before eidos, matter is not chaos. As soon as eidos comes on the scene, the absence of shape or form or order also appears.

Now, just as the seed wants to develop, does every substratum contain this movement within it? Exactly so, we read in the Physics, Book 1; and in Book 2 we find matter and movement placed side by side (200a, 31). Matter and its movements, the forest and its history. If the forest is like the seed, it, too, will have its history of development.