My main concern still remains not to present all the details of a theory of the Form, while not even Plato bothered to do so (or perhaps his texts have not survived). Although we are all part of the Form, the notion of this entity, as well as the entity of the Form itself, is difficult to perceive. This is similar to saying that although we use our thoughts to understand the world, we seldom
realize what the content of our own thought is. Another way to put this is to say that although light makes everything visible, light itself is not visible. If our thought or light is an object, and what we think or see is another object, these two objects cannot be found in the same place at the same time. An equivalent expression is that,
- The world and what we think or perceive about the word are two different things.
While Plato seemed to have regressed into an infinite number of Forms, we may have solved this problem by supposing the existence of archetypes. While the number of archetypes may be infinite, the Form is One- a collection of those archetypes. When archetypes recombine, the Form transforms itself. Thus it may become another Form but still there will be One Form. Furthermore the number of archetypes needs not be infinite. We may recognize some fundamental archetypes, a definite number of basic ‘colored shapes’ corresponding to those archetypes, and an infinite number of combinations of those shapes. (In fact the word ‘archetype’ means fundamental shape or structure). But the difference between archetypes and atoms, as has already been noted, is that archetypes (the ‘colored shapes’) express both geometry (the shape) and the psyche (the color, or emotion, or corresponding psychological aspect). The exact
correspondence which could be described between geometry and the human character is not yet known. But this is what we should be looking for.
The notion of the Form is analogous to that of the Universe, or God. While the universe in physics is treated as a mechanical entity (making thus intelligent life a logical paradox), god in religion is treated as a supreme entity separated from the human being (depriving thus humans of the prospect of divinization). But the Form is both mechanical (physical) and instinctual
(psychic). Furthermore the Form is not separated from us but we exist within the Form. Thus the aspect of Oneness also becomes an aspect of Wholeness.
If we identify the property of the One with the number 1, and the property of Wholeness with the number 0, then we can imagine a symbol Φ to represent the union of 1 and 0. What could be the mathematical value of such a symbol I don’t know, but the point is that according to such a definition the formula 1 + 0 = 1 is meaningless, since it treats 0 as ‘nothing’ while it is at least
something if not everything. This is an example of how inappropriate our mathematics may be in order to describe the difference between unity and uniqueness, and the corresponding analogies. We may also call the previous process by which the number 1 merges with the number 0
‘attachment.’ This would be the attachment of consciousness to the object. In other words it is the process by which the uniqueness of the mind realizes the completeness of its own thought. This is very different from, in fact opposite to, the common function of attachment. Most people become attached to the object by forgetting their own consciousness which realized the object in the first place. But by forgetting the symmetry of the problem one becomes as unconscious as the object one begins to adore. This is a common misinterpretation of the meaning of religion for those who treat God (or the Form) as an object of their own interests.
Another problem related to that between oneness, or uniqueness, and wholeness, or completeness, is that between infinity and indefiniteness. Commonly the problem can be
illustrated with the use of a circle. We may say that the circle is infinite but bounded. It is infinite because if one travels along the circumference one will pass from the same point again and again without reaching any end. It is also bounded because we may define the circumference as the limit between an ‘interior’ and an ‘exterior’ region. In fact the circle is defined by that limit. But if we stretch the circumference of a circle to form a straight line then the length of such a line will be equal to the diameter of another circle π times bigger than the previous circle. Thus we may define a process to cover all successive ‘exteriors’ indefinitely. But in such a case, although the number π is infinite, infinity can be well described. Thus the diameter Δ of the circle becomes the aspect of Uniqueness, or Oneness, while the circumference Π expresses the aspect of
Wholeness, or Completeness. But if again we identify uniqueness with the number Δ=1 and wholeness with the number Π=0, then we may also define a mathematical operation such that 0/1= Π/Δ = π. Although the syllogism is just indicative, it makes more sense than the common assumption that 0/1 = 0, or the reciprocal 1/0 = ∞.
The latter symbol is that of infinity. But according to the previous example infinity could be no more than the perimeter of the defining circle, thus no more than π times the diameter. Thus no matter how ‘far away’ infinity may be located, it has to be bounded by our own approach. In
such a sense infinity always lies within the limits of the symbol which is used to express the meaning of the notion. For example since the number π is infinite then we may assume that infinity has not to do with the difficulty in reaching the limit but with the indefiniteness of the process. Thus the difficulty in solving a problem in general may not have to do with the exhaustion of our mental powers when we are close to the solution but with the difficulty in finding a method to make the problem unfold. Such a method is related to the uniqueness of the problem, which is also a process of thought, while the solution to the problem is related to the understanding of the conditions under which the problem was created, thus also to the properties of the mind which tries to solve the problem. In such a sense we may say that it may take an infinite number of steps to solve the problem even if the problem is well- defined and
understood. However the infinity of all possible steps has not to do with how ‘big’ the problem is but with the uniqueness of its properties. Thus we may say that the problem of infinity lies in uniqueness.
Concerning Plato’s theory of Forms, according to Wikipedia, the pre-Socratic philosophers, starting with Thales, noted that appearances change quite a bit and began to ask what the thing changing ‘really’ is. The answer was substance, which stands under the changes and is the actually existing thing being seen. Form answers the question, “What is that?” Plato was going a step further and asking what Form itself is. He supposed that the object was essentially or ‘really’ the Form and that the phenomena were mere shadows mimicking the Form; that is, momentary portrayals of the Form under different circumstances.
[https://en.wikipedia.org/wiki/Theory_of_Forms]
The problem of the Form as put forward by Plato is further explored in his dialogue
‘Parmenides.’ This dialogue approaches the problem in relation to the notions of wholeness and oneness, infinity and finiteness, knowledgeability and existence. The dialogue unfolds between Socrates and Parmenides. Here I will mention a couple of abstracts. The full dialogue can be found in Perseus Digital Library.
[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0174%3Atext %3DParm.]
Parmenides argues that,
- If the Form exists on its own then it cannot be perceived by us. Therefore the Form must be relativistic:
““(Parmenides) Well then,” “if the one exists, the one cannot be many, can it?” “(Socrates) No, of course not.” “Then there can be no parts of it, nor can it be a whole.” “How is that?” “The part surely is part of a whole.” “Yes.” “And what is the whole? Is not a whole that of which no part is wanting?” “Certainly.” “Then in both cases the one would consist of parts, being a whole and having parts.” “Inevitably.” “Then in both cases the one would be many, not one.” “True.” “Yet it must be not many, but one.” “Yes.” “Then the one, if it is to be one, will not be a whole and will not have parts.” “No.” “And if it has no parts, it can have no beginning, or middle, or end, for those would be parts of it?” “Quite right.” “Beginning and end are, however, the limits of
everything.” “Of course.” “Then the one, if it has neither beginning nor end, is unlimited.” “Yes, it is unlimited.” “And it is without form, for it partakes neither of the round nor of the straight.” “How so?” “The round, of course, is that of which the extremes are everywhere equally distant from the center.” “Yes.” “And the straight, again, is that of which the middle is in the nearest line between the two extremes.” “It is.” “Then the one would have parts and would be many, whether it partook of straight or of round form.” “Certainly.” “Then it is neither straight nor round, since it has no parts.” “Moreover, being of such a nature, it cannot be anywhere, for it could not be either in anything else or in itself.” “How is that?” “If it were in something else, it would be encircled by that in which it would be and would be touched in many places by many parts of it; but that which is one and without parts and does not partake of the circular nature cannot be touched by a circle in many places.” “No, it cannot.” “But, furthermore, being in itself it would also be surrounding with itself naught other than itself, if it were in itself; for nothing can be in anything which does not surround it.” “No, it cannot.” “Then that which surrounds would be other than that which is surrounded; for a whole cannot be both active and passive in the same action; and thus one would be no longer one, but two.” “True.” “Then the one is not anywhere, neither in itself nor in something else.” “No, it is not.””
The point Parmenides makes is that if the Form (the ‘One’) is absolute then there will be nothing to be compared with. It cannot be the Whole because the Whole has parts. But if the Form has no
parts (at least a part to be compared with) it cannot have shape (because there will be nothing else so that the Form be contained in). Thus the Form may not have even its own Self. Therefore the absolute Form may not exist, either within its Self or within the Whole. Parmenides further argues that the absolute Form is also unknowledgeable since there will be nothing else to know about. Thus Parmenides concludes that the Form must be relative (it must partake of essence as he says), so that it has contents, while at the same time it is the whole and includes the part. Parmenides also mentions the aspect that the Form is born and destroyed ‘at the instant.’ He defines the notion as a state between ‘motion’ and ‘stillness,’ between ‘existence’ and ‘non- existence.’ The fact that Parmenides ignored at his time the notion of instantaneous velocity and the meaning of infinitesimals, as put forward by Newton and Leibnitz, does not play down his argument. Still, in our times, nobody understands how quantum entanglement works (how action may be transported instantaneously), or even how attention may produce the quantum Zeno effect (attention delaying the time of events it focuses on). Perhaps there is some connection between these mysteries and what Parmenides calls ‘the sudden,’ or ‘the instant’ at which systems change state,
““Does this strange thing, then, exist, in which it would be at the moment when it changes?” “What sort of thing is that?” “The instant. For the instant seems to indicate a something from which there is a change in one direction or the other. For it does not change from rest while it is still at rest, nor from motion while it is still moving; but there is this strange instantaneous nature, something interposed between motion and rest, not existing in any time, and into this and out from this that which is in motion changes into rest and that which is at rest changes into motion.” “Yes, that must be so.” “Then the one, if it is at rest and in motion, must change in each direction; for that is the only way in which it can do both. But in changing, it changes
instantaneously, and when it changes it can be in no time, and at that instant it will be neither in motion nor at rest.” “No.” “And will the case not be the same in relation to other changes?” “When it changes from being to destruction or from not being to becoming, does it not pass into an intermediate stage between certain forms of motion and rest, so that it neither is nor is not, neither comes into being nor is destroyed?” “Yes, so it appears.” “And on the same principle, when it passes from one to many or from many to one, it is neither one nor many, is neither in a
process of separation nor in one of combination. And in passing from like to unlike or from unlike to like, it is neither like nor unlike, neither in a process of assimilation nor in one of dissimilation; and in passing from small to great and to equal and vice versa, it is neither small nor great nor equal, neither in a process of increase, nor of diminution, nor of equality.”
“Apparently not.” “All this, then, would happen to the one, if the one exists.” “Yes, certainly.”” Parmenides defines the ‘instant’ as an intermediate or indeterminate state in which the Form or any system is found when it passes from stillness to motion (or vice versa), from existence to non- existence. This reminds me of the notion of superposition in quantum mechanics- that the system is found in an eternally indeterminate state before it is measured and thus transformed. The notion of the instant is also related to the meaning of simultaneity. What is simultaneous is also instantaneous. But even if the instant (the thing that is instantaneous) is found beyond space and time, it is something which must be found somewhere, thus it is expressed with dimensions in space and time- even if space and time had not yet existed at the moment the instant appeared. Thus it is something like a pre-condition of space and time. This is similar to the notion of Projection we have put forward. Two ‘things’ are simultaneously projected out of nowhere (out of the eternal Nothingness). One thing is the ‘real’ Form while the other thing is the ‘image’ of the Form. As soon as the Form ‘looks’ at its own image, its real part also materializes. While we don’t perceive an object, the object may or may not exist. But as soon as we acquire knowledge of the object then we can be certain that the object is there. However at the same time we can also be sure that our mind is there. Therefore the object can be our own thought which realizes its own existence. Such a syllogism or process, although self- referential, is as much fundamental as it can be. Thus, to come back to Parmenides’ instant, this is the condition which pre-determines all possible actions which will take place later on.
Picture: The evolution of the Form from a ‘Singularity’ at the center towards the limits at the ‘Horizon.’
In such a sense we may conceive the Form as an eternal condition which is manifested at the moment it transforms. This is an instant or snapshot at a certain point in space and time of all possible configurations of the Form. However the snapshot or image which we take depicts the whole Form, not just a part of it. We may say that at the instant all possible motions in a
landscape freeze for a while before things begin to move again. This is similar to the notion of the ‘collapse’ of the wave-function in quantum mechanics. But the wave-function may depict the whole universe. In such a case the ‘instant’ becomes a snapshot of the whole universe in a certain configuration. Such a snapshot could have been taken at the moment when the universe was born. But, as we may now imagine, at that instant the whole universe was born.
Where does space-time as well motion fit into this picture? The theory of the Big Bang in cosmology expresses a similar notion. The universe is thought to have been created from a singularity, and then it began to expand together with space-time. But we can also imagine a halo of ‘dark matter’ surrounding the singularity since the beginning. In such a sense the singularity is expanding outwards in order to cover all the area occupied by the dark matter. This kind of process is depicted in the previous image. But instead of the universe the picture depicts the evolution of the Form. The expansion of the singularity is at the same time the expansion of consciousness into the unconscious. While we may find some equivalence between the
we treat the universe just like a hot balloon which is expanding and cooling down, we will never understand how we are able to conceive such a notion (if consciousness did not simultaneously arise within such a ‘hot balloon’). Thus we will have to find a model to describe the evolution of the universe not just from a ‘Big Bang’ towards a ‘Big Freeze,’ but also from unconsciousness to awareness, even if oblivion will be the final stage. Thus we may say that,
- The Form evolves.
Three key aspects of the Form can be summarized as follows:
- Structure: This is Parmenides’ ‘partaking of substance.’ This substance is the psychic content of the Form (the archetypes).
- Cause: This is Parmenides’ ‘knowledgeability.’ If we are able to understand then there must be some ‘property of understanding’ in the universe.
- Meaning: This is Parmenides’ ‘existentiality.’ While personality is located at a very certain point is space and time, existence is found in all places and at all times.
Aspects of archetypes
1. The surface of consciousness. 2. The sphere of internal ‘order.’
3. The routes through which contents are submerged into the unconscious.