Platonic forms

Platonic forms  by Marinus Jan Marijs

I think that modern physics has definitely decided in favour of Plato. In fact the smallest units of matter are not physical objects in the ordinary sense; they are forms, ideas which can be expressed unambiguously only in mathematical language.

― Werner Heisenberg

I believe that the findings of quantum physics increasingly support Plato [who taught that there is a more perfect, non-material realm of existence]. There is evidence that suggests the existence of a non-material, non-physical universe that has a reality even though it might not as yet be clearly perceptible to our senses and scientific instrumentation. When we consider out-of-body experiences, shamanic journeys and lucid dream states, though they cannot be replicated in the true scientific sense, they also point to the existence of non-material dimensions of reality.

― Professor Fred Alan Wolf

Plato’s theory of forms deals as it seems for a great part with the same issues as Sheldrake’s morphogenetic fields. But Plato’s Forms are eternal and unchanging, and Sheldrake’s morphogenetic fields are evolving, changing.

This article consists of a General introduction, a list of Items / Questions, a summary and an epilogue.

From Wikipedia:

Theory of Forms

Plato’s theory of Forms or theory of Ideas (Plato uses many different words for what is traditionally called form in English translations and idea in German and Latin translations (Cicero). These include idéa, morphē, eîdos, and parádeigma, but also génos, phýsis, and ousía. He also uses expressions such as to x auto, “the x itself” or kath’ auto “in itself”. See Christian Schäfer: Idee/Form/Gestalt/Wesen, in Platon-Lexikon, Darmstadt 2007, p. 157.) asserts that non-material abstract (but substantial) forms (or ideas), and not the material world of change known to us through sensation, possess the highest and most fundamental kind of reality. (Forms (usually given a capital F) were properties or essences of things, treated as non-material abstract, but substantial, entities. They were eternal, changeless, supremely real, and independent of ordinary objects that had their being and properties by ‘participating’ in them.

Plato’s theory of forms (or ideas) when used in this sense, the word form or idea is often capitalized. (Chapter 28: Form” of The Great Ideas: A Synopticon of Great Books of the Western World (Vol. II). Encyclopaedia Britannica (1952), p. 526–542. This source states that Form or Idea get capitalized according to this convention when they refer “to that which is separate from the characteristics of material things and from the ideas in our mind.”)

Plato speaks of these entities only through the characters (primarily Socrates) of his dialogues who sometimes suggest that these Forms are the only true objects of study that can provide us with genuine knowledge; thus even apart from the very controversial status of the theory, Plato’s own views are much in doubt. Plato spoke of Forms in formulating a possible solution to the problem of universals.To readers who approach Plato in English, the relationship between forms and sensible particulars, called in translation “participation,” seems purposely mysterious. Moreover, the claim that the sensible realm is not fully real, and that it contrasts in this respect with the “pure being” of the forms, is perplexing. A satisfactory interpretation of the theory must rely on both historical knowledge and philosophical imagination.

Linguistic and philosophical background

The terms that Plato uses to refer to forms, idea and eidos, ultimately derive from the verb eidô, “to look.” Thus, an idea or eidos would be the look a thing presents, as when one speaks of a vase as having a lovely form. (Because the mentalistic connotation of idea in English is misleading—the Parmenides shows that forms cannot be ideas in a mind—this translation has fallen from favour.) Both terms can also be used in a more general sense to refer to any feature that two or more things have in common or to a kind of thing based on that feature. The English word form is similar. The sentence “The pottery comes in two forms” can be glossed as meaning either that the pottery is made in two shapes or that there are two kinds of pottery. When Plato wants to contrast genus with species, he tends to use the terms genos and eidos, translated as “genus” and “species,” respectively. Although it is appropriate in the context to translate these as “genus” and “species,” respectively, it is important not to lose sight of the continuity provided by the word eidos: even in these passages Plato is referring to the same kind of entities as always, the forms.

Within the Academy, however, relations seem to have remained cordial. Aristotle always acknowledged a great debt to Plato; he took a large part of his philosophical agenda from Plato, and his teaching is more often a modification than a repudiation of Plato’s doctrines. Already, however, Aristotle was beginning to distance himself from Plato’s theory of Forms, or Ideas (eidos; see form). (The word Form, when used to refer to Forms as Plato conceived them, is often capitalized in the scholarly literature; when used to refer to forms as Aristotle conceived them, it is conventionally lowercased.) Plato had held that, in addition to particular things, there exists a suprasensible realm of Forms, which are immutable and everlasting. This realm, he maintained, makes particular things intelligible by accounting for their common natures: a thing is a horse, for example, by virtue of the fact that it shares in, or imitates, the Form of “Horse.” In a lost work, On Ideas, Aristotle maintains that the arguments of Plato’s central dialogues establish only that there are, in addition to particulars, certain common objects of the sciences. In his surviving works as well, Aristotle often takes issue with the theory of Forms, sometimes politely and sometimes contemptuously. In his Metaphysics he argues that the theory fails to solve the problems it was meant to address. It does not confer intelligibility on particulars, because immutable and everlasting Forms cannot explain how particulars come into existence and undergo change. All the theory does, according to Aristotle, is introduce new entities equal in number to the entities to be explained—as if one could solve a problem by doubling it.

Although Aristotle’s system makes room for forms, they differ significantly from Forms as Plato conceived them. For Aristotle, the form of a particular thing is not separate (chorista) from the thing itself—any form is the form of some thing. In Aristotle’s physics, form is always paired with matter, and the paradigm examples of forms are those of material substances.

Forms

But what were the forms? In Plato’s dialogues as well as in general speech there is a form for every object or quality in reality: forms of dogs, human beings, mountains, colors, courage, love, and goodness. 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. The problem of universals – how can one thing in general be many things in particular – was solved by presuming that Form was a distinct singular thing but caused plural representations of itself in particular objects. (For example, Parmenides 129: “Nor, again, if a person were to show that all is one by partaking of one, and at the same time many by partaking of many, would that be very astonishing. But if he were to show me that the absolute one was many, or the absolute many one, I should be truly amazed.”)

 Matter was considered particular in itself.

These Forms are the essences of various objects: they are that without which a thing would not be the kind of thing it is. For example, there are countless tables in the world but the Form of tableness is at the core; it is the essence of all of them. Plato’s Socrates held that the world of Forms is transcendent to our own world (the world of substances) and also is the essential basis of reality. Super-ordinate to matter, Forms are the most pure of all things. Furthermore, he believed that true knowledge/intelligence is the ability to grasp the world of Forms with one’s mind^.

A Form is aspatial (transcendent to space) and atemporal (transcendent to time). Atemporal means that it does not exist within any time period, rather it provides the formal basis for time. It therefore formally grounds beginning, persisting and ending. It is neither eternal in the sense of existing forever, nor mortal, of limited duration. It exists transcendent to time altogether. (The creation of the universe is the creation of time: “For there were no days and nights and months and years … but when he (God) constructed the heaven he created them also.” – Timaeus paragraph 37. For the creation God used “the pattern of the unchangeable,” which is “that which is eternal.” – paragraph 29. Therefore “eternal” – to aïdion, “the everlasting” – as applied to Form means atemporal.)

Forms are aspatial in that they have no spatial dimensions, and thus no orientation in space, nor do they even (like the point) have a location.They are non-physical, but they are not in the mind. Forms are extra-mental (i.e. real in the strictest sense of the word). A Form is an objective “blueprint” of perfection^.  (Timaeus 28: “The work of the creator, whenever he looks to the unchangeable and fashions the form and nature of his work after an unchangeable pattern, must necessarily be made fair and perfect ….”)

The Forms are perfect themselves because they are unchanging. For example, say we have a triangle drawn on a blackboard. A triangle is a polygon with 3 sides. The triangle as it is on the blackboard is far from perfect. However, it is only the intelligibility of the Form “triangle” that allows us to know the drawing on the chalkboard is a triangle, and the Form “triangle” is perfect and unchanging. It is exactly the same whenever anyone chooses to consider it; however, the time is that of the observer and not of the triangle.

Terminology

The English word “form” may be used to translate two distinct concepts that concerned Plato—the outward “form” or appearance of something, and “Form” in a new, technical nature, that never

…assumes a form like that of any of the things which enter into her; … But the forms which enter into and go out of her are the likenesses of real existences modelled after their patterns in a wonderful and inexplicable manner….

The objects that are seen, according to Plato, are not real, but literally mimic the real Forms. In the allegory of the cave expressed in Republic, the things that are ordinarily perceived in the world are characterized as shadows of the real things, which are not perceived directly. That which the observer understands when he views the world mimics the archetypes of the many types and properties (that is, of universals) of things observed.

Intelligible Realm and Separation of the Forms

Plato often invokes, particularly in the Phaedo, Republic and Phaedrus, poetic language to illustrate the mode in which the Forms are said to exist. Near the end of the Phaedo, for example, Plato describes the world of Forms as a pristine region of the physical universe located above the surface of the Earth (Phd. 109a-111c). In the Phaedrus the Forms are in a “place beyond heaven” (huperouranios topos) (Phdr. 247c ff); and in the Republic the sensible world is contrasted with the intelligible realm (noēton topon) in the famous allegory of the cave.

It would be a mistake to take Plato’s imagery as positing the intelligible world as a literal physical space apart from this one. Plato emphasizes that the Forms are not beings that extend in space (or time), but subsist apart from any physical space whatsoever. That is, they are abstract objects. Thus we read in the Symposium of the Form of Beauty: “It is not anywhere in another thing, as in an animal, or in earth, or in heaven, or in anything else, but itself by itself with itself,” (211b). And in the Timaeus Plato writes: “Since these things are so, we must agree that that which keeps its own form unchangingly, which has not been brought into being and is not destroyed, which neither receives into itself anything else from anywhere else, nor itself enters into anything anywhere, is one thing,”

Ideal state

Socrates postulated a world of ideal Forms, which he admitted were impossible to know. Nevertheless he formulated a very specific description of that world, which did not match his metaphysical principles. Corresponding to the world of Forms is our world, that of the mimes, a corruption of the real one. This world was created by the Good according to the patterns of the Forms. Man’s proper service to the Good is cooperation in the implementation of the ideal in the world of shadows; that is, in miming the Good.

To this end Plato wrote Republic detailing the proper imitation of the Good, despite his admission that Justice, Beauty, Courage, Temperance, etc., cannot be known. Apparently they can be known to some degree through the copies with great difficulty and to varying degrees by persons of varying ability.The republic is a greater imitation of Justice^.

Our aim in founding the state was not the disproportional happiness of any one class, but the greatest happiness of the whole; we thought that in a state ordered with a view to the good of the whole we should be most likely to find justice.

Evidence of Forms

Plato’s main evidence for the existence of Forms is intuitive only. Socrates later answer would be that men already know the Forms because they were in the world of Forms before birth. The mimes only recall these Forms to memory.(Wikipedia)

Characteristics of Forms

The Phaedo contains an extended description of the characteristics and functions of the forms:

• Unchangeable (78c10-d9)
• Eternal (79d2)
• Intelligible, not perceptible (79a1-5)
• Divine (80a3, b1)
• Incorporeal (passim)
• Causes of being (“The one over the many”) (100c)
• Are unqualifiedly what their instances are only with qualification (75b)

Other dialogues fill out the picture: Non-temporal (Tim. 37e-38a); non-spatial (Phaedr. 247c); they do not become, they simply are (Tim. 27d3-28a3). Phaedo 80b provides a good summary, listing all the attributes of Forms that souls also have: “Divine, deathless, intelligible, uniform, indissoluble, always the same as itself.” Forms are sometimes called “Ideas” – Plato’s words are eidos and idea, and the latter suggests the English “idea.” But this gives the wrong idea. For Plato’s Forms are not mental entities, nor even mind-dependent. They are independently existing entities whose existence and nature are graspable only by the mind, even though they do not depend on being so grasped in order to exist. (Theory of Forms  2006  S. Marc Cohen).

Plato’s theory of forms can be compared with Jung’s theory of archetypes and Rupert Sheldrake’s theory of morphogenetic fields. Plato’s forms are transcendental, eternal, unchangeable, universal, divine. Jung’s archetypes are psychological, developmental, subconscious, connected with instinctive reactions, Jung assumed archetypal forms were (mostly) transmitted through physical inheritance. Rupert Sheldrake’s morphogenetic fields are immanent, evolutionary and could be called panpsychism
(Rupert Sheldrake told me in a personal conversation that he was more a Berkeleyan than a Platonist).
However Rupert Sheldrake’s evolutionary theory of morphic resonance can be placed perfectly within a platonic worldview as describing the connection between Plato’s intermediate realm and the physical world.

While the western scientific worldview is mostly seen as monistic materialism, however the majority of mathematicians and a great number of theoretical physicists is Platonist, which concerns a dualistic worldview, be it not necessary substance dualism.

Prof. Paul C. W. Davies in: – “Where do the laws of physics come from?”
“ I think most theoretical physicists who work on fundamental problems…. regard themselves as Platonists, even if they don’t  explicitly say so”

And “We have a platonic world of mathematical objects and relationships ….
the laws are not in space and time, they transcend space and time and that’s really important, if we come to talk about Quantum cosmology, because it wouldn’t make sense if you didn’t adopt that platonic view”.
https://www.youtube.com/watch?v=pj7POKgkJTs 
10.44 – 10.57 and 11.38 – 12.05 h

Kurt Gödel who is generally seen as the greatest logician who ever lived, described mathematical insight as extrasensory perception of a platonic realm    

In the Octagon the platonic realm is in the non-local resonance corner.
Substance dualism /pluralism is in the non-physical worlds corner.

Properties of the Platonic Forms

The Platonic forms are:

1. Transcendent – the forms are not located in space and time. For example, there is no particular place or time at which redness exists.
2. Pure – the forms only exemplify one property. Material objects are impure; they combine a number of properties such as blackness, circularity, and hardness into one object. A form, such as circularity, only exemplifies one property.
3. Archetypes – The forms are archetypes; that is, they are perfect examples of the property that they exemplify. The forms are the perfect models upon which all material objects are based. The form of redness, for example, is red, and all red objects are simply imperfect, impure copies of this perfect form of redness.
4. Ultimately Real – The forms are the ultimately real entities, not material objects. All material objects are copies or images of some collection of forms; their reality comes only from the forms.
5. Causes – The forms are the causes of all things. (1) They provide the explanation of why any thing is the way it is, and (2) they are the source or origin of the being of all things.
6. Systematically Interconnected – The forms comprise a system leading down from the form of the Good moving from more general to more particular, from more objective to more subjective. This systematic structure is reflected in the structure of the dialectic process by which we come to knowledge of the forms.

                                                    The platonic realm

That Platonic forms are eternal, seems to be in contrast with modern thinking, which is evolutionary. Not only biological processes depend on time, but also the development of chemical elements (in nucleosynthesis), morphogenesis and a great number of other developments are in time. So it seems that Platonic forms, which are seen as static, are now replaced with a dynamic worldview.
However there are two different interpretations of the term eternal:
Eternal can mean infinite temporal duration but also timelessness.
Plato’s eternal realm should not be seen as existing in an infinite temporal duration; but, the platonic realm transcends space and time.

This can be compared with the theory that space-time is a ‘block universe’ where the past, present and future all exist together:

“Einstein once described his friend Michele Besso as “the best sounding board in Europe” for scientific ideas. They attended university together in Zurich; later they were colleagues at the patent office in Bern. When Besso died in the spring of 1955, Einstein — knowing that his own time was also running out — wrote a now-famous letter to Besso’s family. “Now he has departed this strange world a little ahead of me,” Einstein wrote of his friend’s passing. “That signifies nothing. For us believing physicists, the distinction between past, present and future is only a stubbornly persistent illusion.”

Einstein’s statement was not merely an attempt at consolation. Many physicists argue that Einstein’s position is implied by the two pillars of modern physics: Einstein’s masterpiece, the general theory of relativity, and the Standard Model of particle physics. The laws that underlie these theories are time-symmetric — that is, the physics they describe is the same, regardless of whether the variable called “time” increases or decreases. Moreover, they say nothing at all about the point we call “now” — a special moment (or so it appears) for us, but seemingly undefined when we talk about the universe at large. The resulting timeless cosmos is sometimes called a “block universe” — a static block of space-time in which any flow of time, or passage through it, must presumably be a mental construct or other illusion.”  Dan Falk

Here the picture emerges that a great part of reality consist of processes in space and time, but at a deeper, more fundamental level, space and time does not exist, or can be transcended.  

Some Christian theologians have made objections to the platonic forms being eternal, because only God is eternal. Or similar the idea within Neo-Platonism and within the Vedanta that the Absolute is one without a second.
Others say that platonic forms are thoughts in the mind of God.

Then there is the question that if platonic forms exist, how, by being outside space and time they could causally influence events within space and time.

From a theological point of view to say that platonic forms, who are outside space and time and transcendent, cannot be the cause of (physical) things, creates a fundamental theological problem: the Absolute / God being outside space and time and transcendent is seen to as the cause of all things.

There is however the difference that the Absolute is not an assemblage of parts, the Absolute is one, and there are many different Platonic forms.

Platonic forms that are non-physical, influence the physical world by non-local resonance, be it directly or indirectly.
Indirectly by influencing ontologically higher subtle matter, which can be ideoplastic formed / shaped, which in turn influences physical matter.

Roger Penrose about this matter…

ROBERT KUHN: Roger, if I ask the question What things really exist? to most scientists, they would say, The physical world. That is it. Why did you ask me such a silly question?

1. PENROSE: I think often people take the view that there is another kind of reality which is the mental reality. Certainly philosophers might have that view. Some might even regard the mental world as being in some sense primary and the physical world is somehow to be thought of as a construct from mentality. I don’t particularly like that view. In my view you have to think of a third one. I am sometimes accused of being not just a dualist but actually a trialist, which is even worse.
2. PENROSE: I think it is just a useful way of talking about things, in particular mathematics seems to have its own kind of existence. It is very important in understanding the physical world that our way of describing the physical world, certainly at its most precise, has to do with mathematics. There is no getting away from it[2]
3. PENROSE: . . . mathematics seems to have its own kind of existence. It is very important in understanding the physical world that our way of describing the physical world, certainly at its most precise, has to do with mathematics. There is no getting away from it. That mathematics has to have been there since the beginning of time. It has eternal existence. Timelessness really. It doesn’t have any location in space. It doesn’t have any location in time. Some people would take it not having a location with not having any existence at all. But it is hard to talk about science really without giving mathematics some kind of reality because that is how you describe your theories in terms of mathematical structures.
4. PENROSE: It also has this relationship to mentality because we certainly have access to mathematical truths. I think it is useful to think of the world as not being a creation of our minds because if we do then how could it have been there before we were around? If the world is obeying mathematical laws with extraordinary precision since the beginning of time, well, there were no human beings and no conscious beings of any kind around then. So how can mathematics have been the creation of minds and still been there controlling the universe?
5. PENROSE: I think it is very valuable to think of this Platonic mathematical world as having its own existence. So let’s allow that and say that there are three different kinds of existence. There may be others, but three kinds of existence: the normal, physical existence; the mental existence (which seems to have, in some sense, an even greater reality – it is what we are directly aware of or directly perceive); and the mathematical world which seems to be out there in some sense conjuring itself into existence – it has to be there in some sense.[3]
6. PENROSE: Then there is the relationship between these three worlds which I regard, all three of them, as somewhat mysterious or very mysterious. I sometimes refer to this as “three worlds and three mysteries.” Mystery number one is how is it that the physical world does in fact accord with mathematics, and not just any mathematics but very sophisticated, subtle mathematics to such a fantastic degree of precision.

See https://www.youtube.com/watch?v=H9Q6SWcTA9w (accessed May 7, 2016).

“To me the world of perfect forms is primary (as was Plato’s own belief)-its existence being almost a logical necessity-and both the other two worlds are its shadows.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

“If, as I believe, the Godel argument is consequently forcing us into an acceptance of some form of viewpoint C, the we shall also have to come to terms with some of its other implications. We shall find ourselves driven towards a Platonic viewpoint of things. According to Plato, mathematical concepts and mathematical truths inhabit an actual world of their own that is timeless and without physical location. Plato’s world is an ideal world of perfect forms, distinct from the physical world, but in terms of which the physical world must be understood. It also lies beyond our imperfect mental constructions; yet, our minds do have some direct access to this Platonic realm through an ‘awareness’ of mathematical forms, and our ability to reason about them. We shall find that whilst our Platonic perceptions can be aided on occasion by computation, they are not limited by computation. It is this potential for the ‘awareness’ of mathematical concepts involved in this Platonic access that gives the mind a power beyond what can ever be achieved by a device dependent solely upon computation for its action.”
― Roger Penrose, Shadows of the Mind: A Search for the Missing Science of Consciousness

Max Planck:

“As a man who has devoted his whole life to the most clear-headed science, to the study of matter, I can tell you as the result of my research about the atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particles of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter”.

A list of Items / Questions:  

1   What are platonic forms?
an invisible reality (it is perceived by an intuition of the mind);
immaterial and eternal;
prototypes of the reality.
within spatiotemporal non-separability

Plato believed there to be a sharp distinction between the world of perceivable objects and the world of universals or forms: one can only have mere opinions about the former, but one can have knowledge about the latter. For Plato it was not possible to have knowledge of anything that could change or was particular, since knowledge had to be forever unfailing and general. For that reason, the world of the forms is the real world, like sunlight, while the sensible world is only imperfectly or partially real, like shadows. This Platonic realism, however, in denying that the eternal Forms are mental artifacts, differs sharply with modern forms of idealism. (Wikipedia)

2   What falls within the category of platonic forms?
Forms can be thought of as abstract entities or qualities that are the essence of sensible things.
Mind-independent abstract mathematical objects or truths.” These mathematical objects include “geometric objects, natural numbers, real numbers, complex or imaginary numbers, functions, groups, sets, or categories, and truths about these objects.
Including organizing principles of the universe.
Forms expressed the ideal characteristics (shape, extension, number, set-of-all-sets, etc.)
It may also include “intentional objects” such as “meaning, propositions, concepts, or essences.”

3   How many philosophers are Platonists?

David Bourget and David Chalmers conducted an exercise in the sociology of philosophy, the largest survey of philosophers ever (3000+ respondents): the PhilPapers Surveys. Now that new results have been released, let’s look back at the findings.

First, it’s worth noting, as the editors do, that (1) the survey focuses mostly on Anglophone analytic philosophers, and (2) answer choices were often too brief for respondents to know how to answer, and that (3) though the response rate of 47% was pretty good, there is inevitably some selection bias, probably toward younger analytic philosophers.

The results for the questions of how many of the philosophers are Platonist:
Platonism 39.3%; nominalism 37.7%; other 23.0%

Modern Platonism has been endorsed by numerous philosophers, mainly in relation to the foundations of logic and mathematics.

4   How many mathematicians are Platonists?

Platonism is the view that there exist such things as abstract objects — where an abstract object is an object that does not exist in space or time and which is therefore entirely non-physical and non-mental. Platonism in this sense is a contemporary view. It is obviously related to the views of Plato in important ways, The most important figure in the development of modern platonism is Gottlob Frege (1884, 1892, 1893–1903, 1919). The view has also been endorsed by many others, including Kurt Gödel (1964), Bertrand Russell (1912), and W.V.O. Quine (1948, 1951).           
Stanford Encyclopedia of Philosophy

A majority of contemporary mathematicians (a typical, though disputed, estimate is about two-thirds) is Platonist.

5   How many physicists are Platonists?
In the early part of the 20th century almost all the famous physicists of the era—Albert Einstein, Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Wolfgang Pauli, Max Born, among others—considered the philosophical ramifications of their revolutionary discoveries in relativity and quantum mechanics, and the conclusion was that they became Platonists.

Alan Sandage (astronomer): “Physicists, by and large, are Platonists who seek reality in the archetypes behind the scenes. Non-scientists, by and large, are Kierkegaardians for whom the subjectivity of life and thought is more real than scientific models.”
Alan Sandage, “Science and religion — separate closets in the same house,” Science and the Spiritual Quest, New Essays by Leading Scientists, edited by W. Mark Richardson, Robert John Russell, Philip Clayton and Kirk Wegter-McNelly, Routledge, 2002, p.61

6   Non-interaction parallelism?
From Encyclopædia Britannica:   
Psychophysical parallelism, in the philosophy of mind, a theory that excludes all causal interaction between mind and body inasmuch as it seems inconceivable that two substances as radically different in nature could influence one another in any way. Mental and physical phenomena are seen as two series of perfectly correlated events; the usual analogy is that of two synchronized clocks that keep perfect time. Thus, for parallelism, the mental event of a man’s wishing to raise his arm is followed immediately by the physical event of his arm being raised, yet there is no need to postulate any direct causal connection.

Parallelism has been criticized on the grounds that a refusal to postulate causal connections in the face of constant correlation conflicts with the empirical procedures recognized in modern science, which call for the supposition of a cause wherever the coefficient of correlation between two sets of phenomena approaches 1. The case for parallelism, however, has been said to depend more on the validity of the arguments discrediting the possibility of interaction between mind and body than upon statistical theory.

This however leaves the main question unanswered.
The same problem arises if one postulates that platonic entities have no causal power, but according to Plato:
The Phaedo contains an extended description of the characteristics and functions of the forms: Causes of being (“The one over the many”) (100c)

Causes – The forms are the causes of all things. (1) They provide the explanation of why any thing is the way it is, and (2) they are the source or origin of the being of all things.  

7   Platonic realm and Quantum mechanics.
Heisenberg claimed, above all, that a) Plato’s philosophy had a positive impact on the development of the occidental science and b) Plato’s comments regarding the structure of the composition of matter (reversely) have empirically be enconfirmed by modern physics.

Plato’s philosophy did influence the formulation of Matrix Mechanics (1925) and the Uncertainty Relation (1927)

Heisenberg’s Platonism mostly takes the form of an ontological realism: Accordingly we can only have knowledge of certain structures regarding the world that exists independently from understanding.
“Große Zusammenhänge [sind] in der Natur von Anfang anvorhanden und nicht etwa von Menschen gemacht. “.
[Large coherences have existed in nature from the beginning and are not, for instance, human-made]

The “hidden variables” or “guiding equation” explanation for the measurement of quantum nonlocality (entanglement) effects can be interpreted as instantiation of Platonic information. Because these Bohm-deBroglie principles are already external to the material objects that they theoretically affect, interpreting them as Platonic is feasible.
This suggests that a Platonic connection to the physical world exists as quantum-level information  James C. Emerson

8   Nonlocality
Nonlocality necessitates timelessness. “Experiments with moving beam-splitters demonstrate that there is no real time ordering behind the nonlocal correlations. In Bell’s world there is no ‘before’ or ‘after.'”
In the Road to Reality, Roger Penrose (Mathematical Institute, Oxford University) contends that contemporary physics postulates that timeless, limitless, active-everywhere  conditions (including nonlocal) and substances (wave functions, entangled systems, Higgs field, mbranes, etc.) underlie existence 106
Interpreting quantum nonlocality as platonic information   James C. Emerson

9   The one and the many  (space)
Forms are not themselves ultimate onto-logical principles, both owing to their plurality and internal complexity. LP Gerson  “What is Platonism.”
This in contrast with the One, The Absolute which is one without a second

10   The one and the many  (time)
Events can be metaphysical entities and as such platonic forms and like non-localised platonic forms can instantiate  localised structures timeless platonic forms can instantiate processes in time. 

11   The block universe
There are similarities between the platonic world and the block universe where the past, present, and future all exist simultaneously 
About the block universe see: https://marinusjanmarijs.nl/theodicy/the-absolute/

12   Objective morality
Moral: can there be moral knowledge? Are there objective moral truths? Is morality founded in nature or convention?
For Plato, goodness and being are intimately connected. Plato’s universe is value-ridden at its very foundations: value is there from the start, not imposed upon an antiseptic, value-neutral reality by the likes of us – external imposers of value on what in itself has no intrinsic value.   S. Marc Cohen

Objective morality  By Marinus Jan Marijs
If stages of moral sensitivity developed over time, how can there be objective morality?
Moral values seem to be different at diverse times, places and circumstances in all cultures.
But one has to take into consideration that  within humans, developmental stages do occur.

Relating to Space perception / structuration:
A house,
street,
city,
region,
country,
continent,
planet,
solar system,
galaxy and
the Universe.

And:

Relating to Time perception / structuration:
Personal time,
cultural time,
archaeological time,
paleo logical time,
geological time and
 cosmological time

Further:

The discovery of universal mathematical truths are realised in advancing developmental phases.
Nevertheless they are universal and not subjective points of view, which can be interpreted arbitrary.

 Morality, like Space perception / structuration, Time perception / structuration and the discoveries of universal mathematical truths, progresses through stages toward universal, objective principles.
While the frame ofreference changes, there may be a current state of development, however, moral laws are objective, invariant and are built into the structure of reality.
 
If morality is seen as subjective, it can be neglected or corrupted easily. 
This can be seen in historical developments of many cultures especially within wars where ethical principles are totally absent.
For example in the second world war Stalin and Hitler completely threw aside what few morals and restrictions they had, utterly disregarding any costs in life, both military and civilian.

13   Gödel and (mathematical) intuition
Kurt Gödel who is generally seen as the greatest logician who ever lived, described mathematical insight as extrasensory perception of the platonic realm   

“I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato’s world of mathematical concepts… When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through the process of ‘seeing’. ”     Roger Penrose

14   Platonic realm and Causality
Platonic realism (also called “extreme realism“) is the view that universals or forms in this sense, are the causal explanation behind the notion of what things exactly are; (the view that universals are real entities existing independent of particulars). (Wikipedia).

Roger Penrose argues that contemporary physics assumes that timeless, limitless, active-everywhere conditions and substances (wave functions, entangled systems, Higgs field, mbranes, etc.) underlie existence. He finds “causality violations in which closed timeline curves can occur, and it becomes possible for a signal to be sent from some event into the past of that same event.”
Roger Penrose: “The Road to Reality: A Complete Guide to the Laws of the Universe.”

15  A-causal relation
A Form is aspatial (transcendent to space) and atemporal (transcendent to time). Atemporal means that it does not exist within any time period, rather it provides the formal basis for time. It therefore formally grounds beginning, persisting and ending. It is neither eternal in the sense of existing forever, nor mortal, of limited duration. It exists transcendent to time altogether.^[13] Forms are aspatial in that they have no spatial dimensions, and thus no orientation in space, nor do they even (like the point) have a location.^[14] They are non-physical, but they are not in the mind. Forms are extra-mental (i.e. real in the strictest sense of the word). (Wikipedia)

In a situation of entanglement there is no causal link; the two particles are synchronised.

16   Active information
Relevant to the way platonic forms influence temporarily structures:

Active Information, Meaning and Form  F. David Peat

Information

The breakthrough in giving information a more “physical” role comes with Bohm’s proposal that information plays an active role in quantum systems. Bohm’s 1952 Hidden Variable papers proposed an alternative approach to quantum theory in which the electron is a real particle guided by a new kind of force, the quantum potential. While at first sight Bohm’s theory appears somewhat “classical” – electrons have real paths – the quantum potential is entirely novel. Unlike all other potentials in physics its effects do not depend upon the strength or “size” of the potential but only on its form. It is for this reason that distant objects can exert a strong influence on the motion of an electron.

In the double slit experiment, a paradigm-shifting experiment of quantum theory, the effects of the slits are be experienced by electrons located many centimeters away. This is very difficult to explain in conventional terms but follows quite naturally once a quantum potential has been introduced. Indeed, it is this quantum potential that is responsible for all the novel effects exhibited by quantum theory. The form of the quantum potential is extremely complex and reflects the entire physical set-up of a quantum measurement. The complexity of its form is also what gives rise to the apparently random processes of the quantum world, such as the disintegration of a radio-active nucleus, or the dual wave-particle nature of the electron.

Bohm’s approach to his own theory became more subtle over the years and he soon began to speak of not only of the form of the quantum potential and also of the “information” it contains. The action of the quantum potential is not to push or pull the electron along its path. Rather, Bohm likened it to a radar signal that guides a ship approaching a harbor. The information within the radar signal acts, via a computer or automated steering device, to change the direction of the ship. Information itself does not push the ship, rather it “in-forms” the gross energy of the engines.

Information therefore allows a distinction to be made between what could be called raw or “un-formed” energy an a more subtle energy, an activity that can be identified with information. This information acts on raw energy to give it form.

Later versions of Bohm’s theory pictured the electron not so much as a real physical particle but as a process, a wave continually collapsing inward to a localized region and then expanding outward. This process is guided by a super-quantum potential. An activity of information is responsible for the existence quantum particles and quantum events.

In discussing the quantum measurement problem Bohm, and his coworkers, further developed the notion of “Active Information”. Take the double slit experiment, as an example. In Bohm’s theory an electron has the potentiality to take a multiplicity of paths that pass through either one of the two slits. In actuality, an electron takes only a single path. Bohm suggested that the quantum potential contains information about the experimental set-up. This information is potentially active, but once the electron has “chosen”, and begun to move along a particular path the information about alternative paths becomes inactive.

For reasons of space this is an oversimplification of Bohm’s approach, but the essential idea should be clear. Information, in this case about the context of an experimental set-up, is carried, in some sort of active form, at the quantum level. This information acts directly on matter, (eg via the form it imposes on the “unformed”). Information is being used in an objective way. It is not something that depends on the point of view of a human observer.

The actual nature of the information and the way it is carried is not yet entirely clear. Is it really correct, for example, to speak of a “field” of information, since information does not fall off with distance, neither is it associated with energy in the usual sense. Possibly the notion of field should be widened or, at the quantum level. we should be talking about pre-space structures, or about algebraic relationships that precede the structure of space and time.”

17   Collapse of the wave function
While: “After more than seven decades, no one understands how or even whether the collapse of a probability wave really happens.”
Greene, Brian, The Fabric of the Cosmos. New York: Vintage Books, 2005..

……this thesis defines hidden variables/guiding equation as information. This approach enables us to bridge the divide between the abstract Platonic realm and the physical world. The unobservable quantum wavefunction collapse is interpreted as Platonic instantiation. At each interaction, the wave function for a quantum system collapses. Instantly, Platonic information is instantiated in the system.
“Interpreting quantum nonlocality as platonic information” James C. Emerson

About the wavefunction: 
https://www.informationphilosopher.com/introduction/physics/interpretation/ 

About the collaps of the wavefunction: 
https://www.informationphilosopher.com/solutions/experiments/wave-function_collapse/

18   Attractors
Attractors can be seen as platonic forms which exist, but are not yet instantiated. 
About the attractors:
https://marinusjanmarijs.nl/evidence-based-approach/14-research-areas/cosmological-planning/attractors/

19   Teleology
Teleology, (from Greek telos, “end,” and logos, “reason”), explanation by reference to some purpose, end, goal, or function. Traditionally, it was also described as final causality, in contrast with explanation solely in terms of efficient causes (the origin of a change or a state of rest in something). Human conduct, insofar as it is rational, is generally explained with reference to ends or goals pursued or alleged to be pursued, and humans have often understood the behaviour of other things in nature on the basis of that analogy, either as of themselves pursuing ends or goals or as designed to fulfill a purpose devised by a mind that transcends nature. The most-celebrated account of teleology was that given by Aristotle when he declared that a full explanation of anything must consider its final cause as well as its efficient, material, and formal causes (the latter two being the stuff out of which a thing is made and the form or pattern of a thing, respectively). (Encyclopædia Britannica)

An example of the reintroduction of teleology into modern language is the notion of an attractor.

Julian Bigelow, Arturo Rosenblueth, and Norbert Wiener have conceived of feedback mechanisms as lending a teleology to machinery. Wiener, a mathematician, coined the term ‘cybernetics’ to denote the study of “teleological mechanisms.” Cybernetics is the study of the communication and control of regulatory feedback both in living beings and machines, and in combinations of the two. In the cybernetic classification presented in “Behavior, Purpose and Teleology”, teleology is feedback controlled purpose. (Wikipedia)

If platonic entities can instantiate processes in the physical world, than this could also be an explanation for teleological processes.
As the platonic world is timeless, and all platonic forms are there a-temporal, like in Einstein’s block-universe,  then what would be future situations for the physical world, would be there as platonic forms.
They could function as attractors, and by this create a teleology.    

About teleology: click here: https://marinusjanmarijs.nl/evidence-based-approach/14-research-areas/cosmological-planning/teleological-principles/

20   Non-local resonance
The active aspect of the platonic forms.
An example of local resonance is the following:
Imagine a harp and one pulls one string, let’s say the sixth string from the left.
This vibrating string creates a specific sound. One records this specific sound on a recording device. After this one places several identical harps in the same room.
In the same room the recorded sound is played amplified back through a sound system.
This will have the result that on all the harps which are placed in the same room, the sixth string from the left shall resonate with the recorded sound.
Non-local resonance between a platonic form with a physical form would work in a similar way, by correspondence, be it non-local.

21   Similarity
Non-local resonance works by analogy, resemblance, being identical.

22   Form creating structures
Instantiation from the platonic world, which is not located in space and time, generates patterns in the ideoplastic world which at their turn guide the shaping of  physical structures.
This ideoplastic world is the intermediate realm of Plato. Between the platonic realm and the physical world.

23   Scale invariant
In the abstract, mathematical realm the infinitely large and infinitely small readily co-exist.
In the abstract platonic realm, where there is no physical distance, infinity takes no room; there is no physical difference between infinitely large and infinitely small abstract entities or qualities.

24   Fractal structures
A fractal is a never-ending pattern. Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos. Geometrically, they exist in between our familiar dimensions. Fractal patterns are extremely familiar, since nature is full of fractals. For instance: trees, rivers, coastlines, mountains, clouds, seashells, hurricanes, etc. Abstract fractals – such as the Mandelbrot Set – can be generated by a computer calculating a simple equation over and over.
Similarity between mathematical fractal patterns and physical structures.

25   Non locality
While this aspect was already an aspect in Plato’s philosophy, it became a part of modern physics within the twentieth century. 

26   Non sequential
Platonic forms do not interact in a normal causal way.

27   Consciousness and non-locality.
Consciousness is non-localised. 

If as many spiritual traditions claim that the Absolute is identical to consciousness, which seems to indicate that platonic forms are “closer” to the Absolute than the physical world.

28   Octagon corners
The platonic realm is situated in the non-local resonance corner of the Octagon.
It interacts with the other corners. See:  https://marinusjanmarijs.nl/octagon/

29   Ontology
Plato postulated a hierarchy of values within the platinic realm, so it is a non-local realm, which has different ontological levels.

30   Platonic hierarchy
Plato’s Form of Good
Plato believed that the Forms were interrelated, and arranged in a hierarchy. The highest Form is the Form of the Good, which is the ultimate principle.

According to Plato, reality is very much associated with objectivity. His argument from objectivity asserts that the more objective concepts are of higher reality, and that because what we perceive via our senses is usually deceitful, the objects of experience cannot be real entities. Besides, it is possible to form different subjective views of the same objects; depending on the perceptual or mental states of the observer. However, forms represent a higher objectivity, and thereby reality through a dialectic process, which is illustrated in the hierarchical system of forms and physical objects, “good” being first among others

2) The systematic unity is an explanatory hierarchy. The Platonic view of the world—the key to the system—is that the universe is to be seen in hierarchical manner. It is to be understood uncompromisingly from the top-down. The hierarchy is ordered basically according to two criteria. First, the simple precedes the complex and second, the intelligible precedes the sensible. The precedence in both cases is not temporal, but ontological and conceptual. That is, understanding the complex and the sensible depends on understanding the simple and the intelligible because the latter are explanatory of the former. The ultimate explanatory principle in the universe, therefore, must be unqualifiedly simple. For this reason, Platonism is in a sense reductivist, though not in the way that a bottom-up philosophy is. It is conceptually reductivist, not materially reductivist. The simplicity of the first principle is contrasted with the simplicity of elements out of which things are composed according to a bottom-up approach. Whether or to what extent the unqualifiedly simple can also be intelligible or in some sense transcends intelligibility is a deep question within Platonism.

(3) The divine constitutes an irreducible explanatory category. An essential part of the systematic hierarchy is a god adduced first and foremost to explain the order of the sensible world or the world of becoming. Platonism converges on the notion that the divine has complete explanatory “reach.” That is, there is nothing that it cannot explain. Thus, ontology and theology are inseparable. The Platonic notion of divinity includes an irremovable personal element, though this is frequently highly attenuated. This attenuation in part follows along the diverse efforts to employ both the intelligible and the simple, as well as the divine, to explain everything else. The residual personhood of the divine agent of transient order is retained in part owing to the fundamental Platonic exhortation to person to “become like god” (see (5)below). Additionally, benevolence and providence are viewed as essential features of the divine, equally in an attenuated sense corresponding to the “depersonalization” of the divine.
WHAT IS PLATONISM? Journal of the History of Philosophy, vol. 43, no. 3 (2005) 253–276[253]*
Lloyd P. Gerson is Professor of Philosophy at the University of Toronto.
What is Platonism? LLOYD P. GERSON

31   Unchangeable forms
Platonic forms are transcendent to our material world in that they exist
beyond space and time, where as material objects occupy a specific
place at a specific time. Atemporal and aspatial features of platonic forms
have very important implications. First, this explains why the form of platonic forms does not change, and remains stable beyond a Spatio-temporal world while particulars are subject to continuous change. Second, since platonic forms does not exist in space, it can be instantiated in many particulars at once or need not even be instantiated to exist.
Sinem Hümeydan   Why did Plato believe in Forms?

There is, indeed, continuous change in the sensible world, but there is also some stability, and there are patterns and regularities in the change.

32   Form of the good.
“This reality, then, that gives their truth of the objects of knowledge and the power of knowing to the knower, you must say is the idea of the good, and you must conceive it as being the cause of knowledge and of truth in so far as known.
Plato, Republic, 508e, Republic II, translated by Paul Shorey, Loeb Classical Library, Harvard University Press, 1930, 1969, pp.102-105,

From Encyclopædia Britannica:   
One further feature of the theory of Forms must be mentioned here: the view that there is a supremely important Form, the Form of goodness, or of the Good, which somehow determines the contents of the world of Forms and brings order into it. In a celebrated but brief and tantalizing passage in Politeia, the Form of the Good is spoken of as being to the intelligible realm what the sun is to the visible realm; just as the sun makes living things grow and renders them visible, so the Good is responsible for the existence and intelligibility of Forms, though it is itself “on the other side of Being.” This passage had a tremendous historical influence on the Neoplatonists, who saw it as anticipating the ultimate ineffable reality—the One, from which everything describable was in some way an emanation—in which they came to believe.

33   Static, evolutionary or trans temporal?
How does one explain growth or evolution in terms of unchangeable platonic entities? While there are infinitely many counting numbers, 1, 2, 3, 4, ….. they together form a single mathematical structure that mathematicians call integers.

The question is how everything seems both to be changing and permanent at the same time. We know that the physical world we perceive through our senses is exposed to continuous change by “becoming” and “ceasing to be”. Nonetheless, there is also permanence beyond what seems to be changing and that can only be grasped by reasoning.
 
David Hilbert (a German mathematician and one of the most influential and universal mathematicians of the 19th and early 20th centuries) about this question:
“the totality of the numbers 1, 2, 3, 4, itself as a completed unity…This kind of infinity is designated as the actual infinite” (David Hilbert 1925:167)
Hilbert, D. 1925. Über das Unendliche. In Mathematische Annalen, 1925(95):161-190.

Indestructibility versus transformability ……..Stegmüller proceeds by referring to another problem: i. The apparent indestructibility of matter; and ii. The apparent or real limitless transformability of matter (Stegmüller 1987:91).This second problem-complex concerns the relation between constancy(indestructibility) and change (transformability) which makes an appeal to the kinematic and physical aspects of reality. That the meaning of constancy is presupposed in change was seen by Plato, for in order to secure the possibility of knowledge he postulated the constancy of the essential (ontic) being of things (their static eidos). These transcendent ontic forms were supposed to lack change (Cratylus, 439 c – 440 a). Without an awareness of endurance (persistence), the very notion of change becomes problematic, for the difficult question is then: ‘what’ changes? For example, only when we are referring to the same person is it meaningful to state that such a person is ageing. That one can detect changes only on the basis of constancy is the lasting insight of Plato’s theory of ideas. While we may distance ourselves from the speculative (metaphysical) construction of transcendent ideal forms (static essences), we still have to account for the brilliant insight that change presupposes constancy. The legacy of Plato in this regard is threefold: iii. Plato’s insight that change presupposes constancy forms the basis of Galileo’s law of inertia. This law states that a body in motion will continue its movement endlessly unless something impinges upon it, such as friction or gravity

1. This insight constitutes the core of Einstein’s special theory of relativity, for according to this, all movement is relative to the vacuum velocity of light.16Strictly speaking, this theory is therefore first of all one of constancy. v. The first main law of thermodynamics, namely the law of the so-called conservation of energy, could be formulated in a more precise way (on the basis of Plato’s insight), simply by designating it as the law of energy constancy. The notion of conserving suggests an (unintended) energy-input – a misunderstanding not supported by the phrase “energy constancy”. In his work on the harmony of the universe, Kepler accepts elements of the traditional realistic metaphysics, in particular the presence of creational ideas in God’s mind (where these ideas are understood as Plato’s eidē). Von Weizsäcker explains that since physics has to think the divine thoughts of God, it is the true religion (Gottesdienst) (Von Weizsäcker 2002:54)
   
   Source: Plato’s heritage to Western philosophy, European intellectual tradition and some special sciences Danie Strauss

School of Philosophy, North-West University, Potchefstroom Campus

34   Platonic forms: thoughts in the mind of God
Augustine of Hippo also believed in the existence of a realm of immutable forms. He thought that such forms are needed to maintain the uninterrupted and reliable essence of things. He also believed that these forms don’t exist somewhere on this globe or in the visible universe, but in the mind of God.
https://www.iep.utm.edu/pla-thei/

While platonic forms do not just exist in the mental realm (as mental concepts), they are sometimes described as thoughts in a universal mind.

Ramanujan:
“An equation for me has no meaning unless it represents a thought of God”
“The Man Who Knew Infinity”, (1991), Kanigel, Robert, page 7 of Prologue.

(Ramanujan  was one of India’s greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series).
His work is used within black hole physics, the theory of Mach theta functions, the pursuit of Quantum gravity theory and string theory.

Henri Poincare:

“It is through science that we prove, but through intuition that we discover.”

Nikola Tesla:

“My brain is only a receiver. In the universe there is a core from which we obtain knowledge, strength and inspiration.”

Sir James Jeans (11 September 1877 – 16 September 1946) was a British physicist, astronomer and mathematician:

“Today there is a wide measure of agreement, which on the physical side of science approaches almost to unanimity, that the stream of knowledge is heading towards a non-mechanical reality; the universe begins to look more like a great thought than like a great machine. Mind no longer appears as an accidental intruder into the realm of matter; we are beginning to suspect that we ought rather to hail it as a creator and governor of the realm of matter… 
In: The Mysterious Universe a book by the British astrophysicist Sir James Jeans first published in 1930 by the Cambridge University Press. p. 137, 1937 ed.”

35  The Absolute                                                                 
Both the Absolute and the platonic forms are non-local, but the Absolute is one without a second and the platonic forms are multiple.
The Absolute has no properties, the platonic forms have properties.

36   Non-material realm of existence
A Form is aspatial (transcendent to space) and atemporal (transcendent to time). Atemporal means that it does not exist within any time period, rather it provides the formal basis for time. It therefore formally grounds beginning, persisting and ending. It is neither eternal in the sense of existing forever, nor mortal, of limited duration. It exists transcendent to time altogether. Forms are aspatial in that they have no spatial dimensions, and thus no orientation in space, nor do they even (like the point) have a location. They are non-physical, but they are not in the mind. Forms are extra-mental (i.e. real in the strictest sense of the word).  (Wikipedia)

37   Platonic forms, physical laws and mathematical truths 
The modus operandi of physics relies on the epistemological assumption that physical laws, perhaps not “eternal”, are reasonably timeless since a moment belonging to the immediate neighborhood of the Big Bang. A physical law outdated following a new paradigm still remains as a special case of a broader law. In contrast, the idea of physical laws changing anytime would not be operating in physics. Far from being a metaphysical belief, the epistemological presupposition of reasonable timelessness of physical laws is. until further notice empirically confirmed. Since astrophysical observation goes back in time, intrinsic variations in physical laws would be empirically detected.
“A Defense of Scientific Platonism without Metaphysical Presuppositions.”
Peter Punin

Roger Penrose contends that the foundations of mathematics can’t be understood absent the Platonic view that “mathematical truth is absolute, external and eternal, and not based on man-made criteria … mathematical objects have a timeless existence of their own…”
Penrose, Roger (1989). The Emperor’s New Mind: Concerning Computers, Minds, and the Laws of Physics. Oxford: Oxford University Press. p. 151. ISBN 9780198519737.

38   Mathematics and the Platonic realm
Mathematics expresses some kind of fundamental external reality which is independent of the physical world, a separate reality.
The Platonic realm underlies the physical world, generates it. As shown in the finetuning.

39   Interaction between platonic forms and the physical world
Mathematical structures that are discovered everywhere lend weight to the idea that there is an underlying order underpinning the physical world.  

40   Different forms of instantiation
(Definition: Instantiation is the action of causing an event or situation to happen by making a set of actions or a formal process begin)

Instantiation comes into being when ideoplastic structures intermediate between the platonic entities and do structure  the physical world. These structures are (other than the platonic realm) within space and time, developmental and are changing in time.
This describes how non-spatial platonic forms can instantiate spatial structures (By non-local resonance). The energy that is necessary to shape the ideoplastic world is extremely small, or zero.

The intermediate realm has two fundamental structures, the ideoplastic and the subtle energetic.

While platonic instigation on quantum level can explain the micro structure of the physical world or even on a macro level, it cannot explain non-geometrical  platonic forms such as beauty, truth, justice.

The spatial subtle energy fields on the other hand are activated by intentional platonic entities, by non-geometrical platonic entities such as beauty, truth, justice and so on.

Plato claims that, next to sensible entities and Forms, there are the mathematical entities, an intermediate stage between the two other realms

It is Plato’s claim that numbers are intermediate between Forms and sensible objects

The intermediates link fully separate intelligible entities with those in the realm of what is coming-to-be

From these questions also arises, as mentioned, the insistence on the possibility of intermediates being the essential intermediary in order to know sensible nature and to achieve a contact between higher and lower entities.

41   Non-geometrical platonic entities such as courage, love, and goodness
Platonic forms are not only geometrical shapes but among others also abstract entities that are related to the qualia.
This means that their instantiation must be fundamentally different.
The geometrical platonic forms interact via ideoplastic higher ontological  structures, the non- geometrical platonic forms interact via subtle energies on higher ontological levels. Both the ideoplastic structures and the subtle energies are situated in the Non-physical worlds of the Octagon who are spatial and in time.

42   Form as a distinct singular thing but causing plural representations of itself in particular objects
According to Plato, “partaking” in any form is what makes things share similar attributes. All material objects owe their existence to these forms; whereas each form exists by itself, independently of the object that exemplifies the particular form.

43   Physical and mental substances
While the platonic realm has no substance, no spatiality,
The physical and mental worlds have substances, are both spatial, and in time..

44   The laws of nature
Kant asks himself how the physical laws obtained empirically can take an mathematical form, knowing that mathematics is not based on experience.

James Robert Brown (Philosophy Department, University of Toronto) affirms the existence of Platonic entities, including organizing principles of the universe. He finds that “laws of nature are relations among universals … among abstract entities which exist independently of physical objects, independently of us and outside of space and time. Laws on the Platonic view are not parasitic on existing objects and events. They have life… of their own.”

James C. Emerson: “Widely accepted laws of physics are frequently symbolically represented in Platonic-like symmetries. Physical observations have verified many of these regularities.”
Interpreting quantum nonlocality as platonic information.
James C. Emerson

The laws of nature may be descriptions of abstract relationships but they are not just descriptions, they refer to fundamental structures. They are not just  artificial constructs, but universal truths.

“The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”

Eugene Wigner (1902-1995), 1960

45   Causes of being
While many modern thinkers claim that platonic forms have no causal power, Plato himself claimed they were the causes of being.

While platonic forms are abstract, they are not just descriptive (that would imply without causal power), but they are prescriptive, they undoubtedly have causal power in the real world.  

46   Ideoplasticity
The platonic forms can interact with the physical world via the ideoplasticity or the subtle energies on higher ontological levels.
About ideoplasticity see:
https://marinusjanmarijs.nl/life-after-death/characteristics/ideoplasticity/

47   The correspondence between mathematics and the physical world
Peter Punin : “Scientific Platonism says that directly mathematizable physical phenomena – the research field of physics – are governed by entities belonging to this immaterial, immutable, eternal, and objectively existing mathematical world.”

This indicate that the platonic world is a fundamental part of reality.

48   The matrix of all matter
Max Planck: “As a man who has devoted his whole life to the most clear-headed science, to the study of matter, I can tell you as the result of my research about the atoms this much: There is no matter as such. All matter originates and exists only by virtue of a force which brings the particles of an atom to vibration and holds this most minute solar system of the atom together. We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter”. Max Planck, The New Science

Our world is modelled after the patterns of the Forms.

49   Nonlocality and locality (influence)
It is possible for non-spatio-temporal objects to stand in some spatio-temporal relation to the physical world.

50   Microscopic to macroscopic events
While platonic forms are scale invariant, their instigation could be on a microscopic level, which could be multiplied to a macroscopic level, like atomic lattices.

51   Guiding principles (Archetype and crystal structures)
From Wikipedia:
Lattices …..Jung was fond of comparing the form of the archetype to the axial system of a crystal, which preforms the crystalline structure of the mother liquid, although it has no material existence of its own. This first appears according to the specific way in which the ions and molecules aggregate. The archetype in itself is empty and purely formal: a possibility of representation which is given a priori. The representations themselves are not inherited, only the forms, and in that respect they correspond to the instincts. The existence of the instincts can no more be proved than the existence of the archetypes, so long as they do not manifest themselves concretely.

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of the constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.
The smallest group of particles in the material that constitutes this repeating pattern is the unit cell of the structure. The unit cell completely reflects the symmetry and structure of the entire crystal, which is built up by repetitive translation of the unit cell along its principal axes.

Lattice systems are a grouping of crystal structures according to the axial system used to describe their lattice. Each lattice system consists of a set of three axes in a particular geometric arrangement.

52   John Stuart Bell in 1964 on Bell’s Theorem
The work of John Stuart Bell in 1964 on Bell’s Theorem and the experiments of Alain Aspect in 1982 demonstrated that quantum physics requires a notion of reality substantially different from that of classical physics.
It is especially the concept of non-locality that is relevant to Plato’s philosophy of platonic forms which are non-local.

53   Universal vs. Particular
Universals are not just mental descriptions of particulars, but non-localised trans temporal structures.

54   How could abstract objects cause anything to happen or influence the material world?
The central problem of platonic instigation.
This would work primarily through imposing patterns on otherwise indeterminate or probabilistic processes.
A field imposing a formal pattern on them, restricting the probabilistic processes, a pattern can be imposed.

55   Abstract objects and the brain
If the objects of mathematics exist apart from us, living in a Platonic heaven that transcends the physical world of space and time, then how does the human mind comes in contact with them and learn about their properties and relations?
Plato claimed that this could only be by the ability to grasp the world of Forms with one’s mind.
This means by intuition, by non-sensory perception.

56   Gödel the incompleteness theorems
“The existence of abstract objects” is supported by the consensus of many scientists. The Incompleteness Theorems of Gödel may demonstrate the existence of abstract mathematical objects. Items that he would include as Platonic, are “geometric objects, natural numbers, real numbers, complex or imaginary numbers, functions, groups, sets, or categories, and truths about these objects.”

Both Kurt Gödel and Roger Penrose insist upon the necessary existence of abstract objects, Gödel asserted that the incompleteness theorems demonstrate the likely existence of abstract mathematical objects.

57   Mind-independent abstract mathematical objects or truths.
Plato – New World Encyclopedia:
Plato recognized that everything in the material world is constantly changing. And yet, if we can acquire knowledge (and Plato thought we could), something must be stable or permanent such that when we know “it” we know the truth. For this reason Plato held that our “Ideas” were these stable and permanent entities that did not change. To know or “see” these Ideas is to know the truth, the unchangeable. Today, these ideas are often called “universals.”

The true or essential nature of all things. And that these truths are eternal. 

58   Intentional objects
“Intentional objects” include entities such as “meaning, propositions,  concepts, or essences,” are included in the possible realm of the mathematically real.

59   Are mathematical objects mind-dependent?
Richard Tieszen:
“The mind-independent abstract (or ideal) mathematical objects that are thought to exist by mathematical realists are usually taken to have the following properties: As the formulation obviously indicates, they are mind-independent. This means several things. First they are not themselves mental entities. They are not the subjective ideas, thoughts or images of human beings. They are not immanent to human consciousness but they are supposed to transcend human consciousness. They are not internal to human consciousness but are in some sense external to it. They are supposed to exist whether there are minds in the universe or not. They would exist even if there were no minds, or had never been any minds.
The properties of “being expressed” or “being thought of” are not essential to mathematical objects. Mathematical objects are external to human consciousness but not in the sense of sensory, physical or material objects. This is what it means to say they are abstract.”
Richard Tieszen in: “Phenomenology and Mathematics.”

60   Platonism at the Planck level
Roger Penrose (Mathematical Institute, Oxford University) endorses a Platonism of interdependent mentality, Planck level physicality, and mathematical truth. He presents his view in The Emperor’s New Mind (1989),  Shadows of the Mind (1994), and the Road to Reality (2004). Speculating about neurophysics as well as theoretical physics, Penrose finds quantum entanglement in many places and Platonism at the Planck level.

61   Is mathematics invented  or discovered ?
From Wikipedia, the free encyclopedia:
“Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. In this point of view, there is really one sort of mathematics that can be discovered; triangles, for example, are real entities, not the creations of the human mind.

Many working mathematicians have been mathematical realists; they see themselves as discoverers of naturally occurring objects. Examples include Paul Erdős and Kurt Gödel. Gödel believed in an objective mathematical reality that could be perceived in a manner analogous to sense perception. Certain principles (e.g., for any two objects, there is a collection of objects consisting of precisely those two objects) could be directly seen to be true, but the continuum hypothesis conjecture might prove undecidable just on the basis of such principles. Gödel suggested that quasi-empirical methodology could be used to provide sufficient evidence to be able to reasonably assume such a conjecture.

Within realism, there are distinctions depending on what sort of existence one takes mathematical entities to have, and how we know about them. Major forms of mathematical realism include Platonism.”

There is an inherent mathematical nature within reality.

The language of mathematic is invented, but the structures of mathematic are discovered. The concepts are invented, but the relationships are discovered.

If mathematics was invented, then it wouldn’t be so all-encompassing.

The external physical reality corresponds with the things that are discovered in mathematical structures.

Alain Connes holder of the Chair of Analysis and Geometry at the College de France: “The Platonist attitude consists in saying that there exists a mathematical reality that precedes the elaboration of concepts”
It means that the entities that mathematicians study are no mere artifacts of the human mind: these entities are discovered, not invented…

G. H. Hardy an English mathematician, who after seeing Ramanujan’s theorems on continued fractions on the last page of the manuscripts, said the theorems “defeated me completely; I had never seen anything in the least like them before”, and that they “must be true, because, if they were not true, no one would have the imagination to invent them“.

See: Roger Penrose – Is Mathematics Invented or Discovered?
https://www.youtube.com/watch?v=ujvS2K06dg4

62   Redness isn’t a property of the physical world (Qualia)
While a certain frequency in the electromagnetic spectrum may give the appearance of red, the colour red itself isn’t physical, but a secondary quality which is mental in origin.
About secondary qualities see:
https://marinusjanmarijs.nl/evidence-based-approach/14-research-areas/non-physical-matter-subtle-energies/primary-and-secondary-qualities/

63   Metaphysical Realism
The school of realism makes the claim that universals are real and that they exist distinctly from the particulars that instantiate them. Two major forms metaphysical realism are Platonic realism (universalia ante res), meaning “‘universal before things'” and Aristotelian realism (universalia in rebus), meaning “‘universals in things'”. Platonic realism is the view that universals are real entities existing independent of particulars. Aristotelian realism, on the other hand, is the view that universals are real entities, but their existence is dependent on the particulars that exemplify them.

Realists tend to argue that universals must be posited as distinct entities in order to account for various phenomena. A common realist argument said to be found in Plato’s writings, is that universals are required for certain general words to have meaning and for the sentences in which they occur to be true or false. (Wikipedia)

64   Beauty
Beauty is a property that exists in an ideal form independently of any mind or description.
Many forms of beauty deal with symmetries….

65   The perception of platonic forms
Plato’s main evidence for the existence of Forms is intuitive only

Plato believed that long before our bodies ever existed, our souls existed and inhabited heaven, where they became directly acquainted with the forms themselves. Real knowledge, to him, was knowledge of the forms. But knowledge of the forms cannot be gained through sensory experience because the forms are not in the physical world. Therefore, our real knowledge of the forms must be the memory of our initial acquaintance with the forms in heaven.
Kurt Gödel’s Platonism postulates a special kind of mathematical intuition that lets us perceive mathematical objects directly. (This view bears resemblances to many things Husserl said about mathematics, and supports Kant‘s idea that mathematics is synthetic a priori.)  (Wikipedia)

Gödel, K., (1951) “Some Basic Theorems on the Foundations of Mathematics and Their Implications,” in Gödel’s Collected Works, Volume III, S. Peterman, J.W. Dawson, Jr., W. Goldfarb, C. Parsons, and R.N. Solovay (eds.), Oxford University Press, Oxford, 304–23.

66   Are numbers active agents in nature?
While numbers are abstract entities, they also have all kinds of intricate relationships, mathematical rules and patterns infiltrate everything in nature.
Nor randomness, coincidence  or non-interactive parallelism does explain this.

The platonic theory of mathematics asserts that numerical systems underline the very structure of reality.

67   Wigner
The Unreasonable Effectiveness of Mathematics in the Natural Sciences    by Eugene Wigner:
“The first point is that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it. Second, it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories. In order to establish the first point, that mathematics plays an unreasonably important role in physics, it will be useful to say a few words on the question, “What is mathematics?”, then, “What is physics?”, then, how mathematics enters physical theories, and last, why the success of mathematics in its role in physics appears so baffling. Much less will be said on the second point: the uniqueness of the theories of physics. A proper answer to this question would require elaborate experimental and theoretical work which has not been undertaken to date.” (February 1960) https://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Furthermore mathematics is extremely effective through science technology and engineering in transforming human society.
Mathematics is the underlying language in which the universe is written and in which it is understood.

Mathematics is all-encompassing

The laws of physics and the universe follow mathematical models.
Mathematics has an amazing predictive power and makes it possible to make extremely accurate calculations.

Mathematics made it possible to predict the existence of subatomic particles.

Mathematics reveals the secrets of the universe.

With the use of mathematics it was possible to create the scientific and industrial revolutions.

68   The Fibonacci sequence
The Fibonacci sequence appears quite frequently in nature
Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the Fibonacci Quarterly. Applications of Fibonacci numbers include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems.

They also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone’s bracts.
(Wikipedia)

There are mysterious connections between the physical world and mathematics.

69   What are abstract objects?
Abstract objects are nonlocal resonances which do not interact by proximity but nonlocal by similarity, resemblance, by analogy.

70   The fine-tuning
The different kinds of fine-tuning could be initiated from the platonic realm.
About fine-tuning see:
https://marinusjanmarijs.nl/evidence-based-approach/14-research-areas/cosmological-planning/cosmological-constants-and-fine-tuning/

71   Arguments in support for the existence of Platonic forms
If mathematics is only a human construct, it is difficult to see why the universe at the big bang definitely had a mathematical structure that did not depend on rational observers born more than 13 billion years later. Viewed in this light, the full version of mathematical Platonism becomes a logical necessity and an essential prerequisite for our very existence. Mathematical Platonism is any metaphysical account of mathematics that implies mathematical entities exist, that they are abstract, and that they are independent of all our rational activities. For example, a Platonist might assert that the number pi exists outside of space and time and has the characteristics it does regardless of any mental or physical activities of human beings. (IEP)

72   Newton’s theory has an accuracy of 1 to 10⁷  
Quantum mechanics has an accuracy of 1 to 10¹⁰  
Einstein’s relativity theory has an accuracy of 1 to 10¹⁴ 
It is difficult to see that this exceptional accuracy could be explained by  subjective human mental constructions and coincidences, as mere modes of thought, as merely artificial combinations made for convenience.
It indicates that mathematics is something that is in the structure of reality.

“The mathematical world possesses an objectivity that transcends mere opinion. Platonic existence refers to the existence of an objective external standard that is not dependent upon our individual opinions nor upon our particular culture. Platonic existence is simply a matter of objectivity”
Two examples of the relation between the contemporary science and Plato  Elio Antonello  Mathematic is something that isn’t a human construct, it’s a human discovery.
There is something about the physical world that is deeply structured in its mathematical essence. Mathematics is fundamental to the workings of the universe.

73   Objects of knowledge
Because platonic forms are the only objects of knowledge, individuals should endeavour to reach the intelligible realm and endow themselves with the knowledge of forms in order to achieve a happy and fulfilling life.
Sinem Hümeydan  Why did Plato believe in Forms?

“The basic Platonist assumptions have been characterized as two claims: (I) the world is only intelligible through the structure and order imposed on it by ontologically prior immaterial principles; and (II) knowledge accordingly presupposes (non-empirical) cognitive access to these immaterial principles.”

74   Understanding
Lloyd P. Gerson   in  Aristotle and Other Platonists :
“1) The universe has a systematic unity. The practice of systematizing Platonism may be compared with the formulation of a theology based upon Scriptures as well as other canonical evidentiary sources. The hypothesis that a true systematic philosophy is possible at all rests upon an assumption of cosmic unity. This is Platonism’s most profound legacy from the Pre-Socratics philosophers. These philosophers held that the world is a unity in the sense that its constituents and the laws according to which it operates are really and intelligibly interrelated. Because the world is a unity, a systematic understanding of it is possible. Thus, particular doctrines in metaphysics, epistemology, ethics, and so on are ultimately relatable within the system.”

For Plato, in the act of understanding, the mind grasps the Idea through a kind of immediate intuition, a flash of illuminating recognition where we “see the truth.”

Understanding implies consciousness.

75   Instantiation
The dialogues of Plato does present a very real difficulty with the Theory of Forms. One difficulty lies in the conceptualization of the “participation” of an object in a form.

Instantiation is the creation of a real instance or particular realization of an abstraction or template, such as a class of objects or a process.

Roger Penrose claims that the physical realm emerges from the Platonic mathematical realm (Source: CERN Open Data Portal)

76   Morality
In the Republic, Plato poses questions about moral concepts in an effort to demonstrate that the life committed to knowledge and virtue will result in happiness and self-fulfilment. To achieve happiness, one should render himself immune to changes in the material world and strive to gain the knowledge of the eternal, immutable forms that reside in the intelligible realm.

77   Five main groups
While the platonic realm is a transcendent realm, which is on a higher ontological level transcendent to space and time, there is also another  realm, that is also on a higher ontological level but isn’t  transcendent to space and time.
This is a realm where subtle energies and form-structures are situated who are both spatial and spatial located, they occupy a specific place at a specific time (which are perceived during an Out of the Body Experience).
These lie at the interface between the abstract and concrete aspects of reality.
The form-structures on a higher ontological level are ideoplastic and create an interface between the abstract and the physical extensional shapes.
The subtle energies on a higher ontological level create an interface between the abstract and intentional objects such as beauty, truth, sincerity , justice and meaning.
There are five main groups:
aesthetic / beautiful,
cognitive / logical,
social / inclusiveness,
moral / justness,
meaningfulness
Each with their own subtle energy group. See:
https://marinusjanmarijs.nl/methods-of-transformation/the-five-major-domains-of-reality/

78   Justice
Plato in the “Republic” about Justice:
^“Our aim in founding the state was not the disproportional happiness of any one class, but the greatest happiness of the whole; we thought that in a state ordered with a view to the good of the whole we should be most likely to find justice.”

79   Flux
Plato: But if the very nature of knowledge changes, at the time when the change occurs there will be no knowledge, and, according to this view, there will be no one to know and nothing to be known: but if that which knows and that which is known exist ever, and the beautiful and the good and every other thing also exist, then I do not think that they can resemble a process of flux, as we were just now supposing.”

80   Jungian archetypes
From Wikipedia, the free encyclopedia:
Jung suggested that not only do the archetypal structures govern the behavior of all living organisms, but that they were contiguous with structures controlling the behavior of inorganic matter as well.

The archetype was not merely a psychic entity, but more fundamentally, a bridge to matter in general. Jung used the term unus mundus to describe the unitary reality which he believed underlay all manifest phenomena. He conceived archetypes to be the mediators of the unus mundus, organizing not only ideas in the psyche, but also the fundamental principles of matter and energy in the physical world.

Jung was fond of comparing the form of the archetype to the axial system of a crystal, which preforms the crystalline structure of the mother liquid, although it has no material existence of its own. This first appears according to the specific way in which the ions and molecules aggregate. The archetype in itself is empty and purely formal: a possibility of representation which is given a priori.

A contemporary definition is given by O’Brien (2017) as follows: “Archetypes are universal organizing themes or patterns that appear regardless of space, time, or person. Appearing in all existential realms and at all levels of systematic recursion, they are organized as themes in the unus mundus, which Jung (1970 Vol. 14. Mysterium coniunctionis. (1970), p. 505) described as “the potential world outside of time,” and are detectable through synchronicities”.

https://en.wikipedia.org/wiki/Jungian_archetypes

81   Property dualism v.s. substance dualism.
The relationship between the physical world and platonic forms is property dualism.
The relationship between the physical world and the mental is substance dualism.

Property dualism describes a category of positions in the philosophy of mind which hold that, although the world is composed of just one kind of substance—the physical kind—there exist two distinct kinds of properties: physical properties and non-physical properties.

Substance dualism, on the other hand, is the view that there exist in the universe two fundamentally different kinds of substance: physical (matter) and non-physical (mind)

82   Shift from one platonic form to another
A tree, a wooden table, and a wooden disk, they each represent a different platonic form. This means that if one makes a  wooden table from a tree and after that a wooden disk from the table, the platonic forms do not change but the physical objects shift from one platonic form to another.
This could explain why growth and change can take place, while platonic forms do not change.

83   The platonic and the mental
A quotation from Roger Penrose (an English mathematical physicist, mathematician and philosopher of science. He is Emeritus Rouse Ball Professor of Mathematics):

“Platonic-mathematical, physical, and mental – has its own kind of reality, and where each is (deeply and mysteriously) founded in the one that preceeds it (the worlds being taken cyclicly). I like to think that , in a sense, the Platonic world may be the most primitive of the three, since mathematics is a kind of necessity, virtually conjuring its very self into existence.” 
Roger Penrose, “The Road to Reality: A Complete Guide to the Laws of the Universe”, Knopf (2005), p:1029

84   The mind
If we accept the existence of the mathematical realm and assume that it is more fundamental than the physical realm then we have to accept that mind has “mathematical” components as well as “physical” components. Therefore, this seems to suggest that mind is not a “physical object”

85   The aim of Platonism
The philosophy of Plato and his Neoplatonic successors such as Plotinus and Proclus described a way of life and a means of realizing higher states of human consciousness. Their objective was to establish a physical and psychological practice which could enable the practitioner to achieve harmony with the cosmos, attain enlightenment of individual consciousness, and arrive at a communion with the higher orders or levels of reality (the three Hypostases) that transcend the physical and/or phenomenal world. The Platonists and Neoplatonists of Classical Antiquity aimed at the transmission of essential and unchangeable knowledge of methods to achieve higher levels of human consciousness.

The aim of philosophical activity, according to the Neoplatonists, was not so much the mental comprehension of the metaphysical structure of the universe as the mystical union of the individual soul with the intelligible divinities and, if possible, with the One beyond Being, i.e, the soul’s redemption. For the Neoplatonists no less than Socrates and Plato, philosophy was a way of life. However, Neoplatonism came to stress the mystical element that was latent in Plato’s dialogues and to bridge the apparent divide between philosophy and religion.   Phil Norfleet

86   Structures
It has become popular to maintain that the items that are fundamental to mathematical ontology are structures rather than objects. Stewart Shapiro [1997, pp. 73-4], a prominent defender of this thesis, offers the following definition of a structure:

I define a system to be a collection of objects with certain relations. … A structure is the abstract form of a system, highlighting the interrelationships among the objects, and ignoring any features of them that do not affect how they relate to other objects in the system.

According to structuralists, mathematics’ subject matter is mathematical structures. Individual mathematical entities (for example, the complex number 1 + 2i) are positions or places in such structures. (IEP)

87   Eternal
 Eternality: where this could be interpreted as either
a. omnitemporality: the item exists at all times, or
b. atemporality: the item exists outside of the network of temporal relations
Philosophers of mathematics invariably mean to convey that mathematical entities have feature a or b, when they claim that mathematical objects or structures are abstract.

88   Applicability
Mathematical objects or structures are indispensable to our best scientific theories.
The physical world happens to operate according to certain mathematical principles, in an extraordinary precise way.
This seems to indicate some organising principle.

89   String theory
The philosophical mode of thought that string theorists operate in is Platonism.
It isn’t an empirical approach.

90   Spheres
J. Mittelstrass, in  “World Pictures: The World of the History and Philosophy of Science”:
With Plato’s world, i.e. with Plato’s cosmological concept, the idea of a philosophical as well as a scientific cosmology is born. Here, in Plato’s dialogue Timaios, a powerful craftsman creates the world according to a perfect model, namely the ‘cosmos’ of the Platonic ideas. Like a perfect living being, the cosmos turns out to be an animated rational being, as a visible god in the form of a perfect sphere. Its soul, the ‘world soul’, has an astronomical nature: it is formed by the mathematical order of the trajectories of the planets. At the same time the planets function as ‘tools of time’; time (καιρός), arising with the heavens, is an image of eternity (αἰών). The planets are visible and created gods, the earth the ‘most venerable goddess in the heavens’. Man in the cosmos, which consists of purely godlike entities and is itself a living god, is compared with a plant, which roots ‘not in the earth but in the heavens’; he connects the earth with the heavens related to him. Later on, in Christian thought, i.e. in Christian Platonism, the world of Platonic ideas to which the craftsman refers as a perfect model, becomes the realm of thoughts of God creating the world.

Unlike a Plato world, which, apart from the mythical language in which it is presented, is governed by mathematical (geometrical) and astronomical laws, Aristotle’s world is a world of natural things that consist of matter and form and have within themselves a source of motion. Motions caused by such a ‘natural’ source are ‘teleological’ motions, i.e. they make a thing into what, according to its own nature, it really is, or they lead it, in the form of a ‘natural’ local motion, to its ‘natural’ place. A theory of natural positions, incorporated in a theory of elements, corresponds in this sense to a theory of simple (natural) bodies (bodies that have a source of motion in themselves) and simple motion (the motion of simple bodies). In the cosmological dimension, an Aristotle world consists of eleven spheres grouped around the central body, earth. Each such sphere is constituted by two concentric spherical surfaces: the three inner spheres housing the elements and the eight outer spheres housing the then known planets and the system of fixed stars (with a daily rotation about the axis of the heavens). The geocentrism of the Aristotle world is a result of the Aristotelian theory of elements or the theory of natural positions. That a heavy body falls to the earth is a result of the centre of the cosmos’ being the natural position for this body, i.e. the motion of heavy bodies is not toward the earth (this is only per accidens), but toward the centre of the cosmos (per essentiam)

The geocentrism of the Aristotle world, with next to the physical world the eleven spheres, could be seen as a metaphor for twelve ontological levels which are not situated concentric but are dimensional stratified.  

91   Timelessness
It is characteristic of the special as well as the general theory of relativity that the essential geometric quantity is a four-dimensional metric interval. This can be divided into a spatial and a temporal component, and yet this division is dependent on the system of coordinates used. Einstein draws the conclusion from this situation that the ‘transient now’ (the idea of a shifting present) possesses no objective meaning. He draws the same conclusion from the symmetry of equations in mechanics and quantum mechanics against time reversal. In all elementary processes there is no difference between past and future. Such a difference is a mere illusion. In reality there is no development, no actual change. All that is real is a static, four-dimension- al state of being. In this sense the Einstein world is neither Aristotelian nor hermetic nor Newtonian, but Parmenidean.   J. Mittelstrass

“Objective mathematical notions must be thought of as timeless entities and are not to be regarded as being conjured into existence at the moment that they are first humanly perceived.”
― Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe.

92   Quantum theory and causality
In the world of quantum mechanics, a Planck or Heisenberg world, in which particles no longer move on trajectories like in classical physics and the law of causality no longer holds.
J. Mittelstrass

93   Aesthetically “beautiful” art, paintings, statues
The platonic entities that are within the aesthetic group, interact / instantiate from the non-spatiotemporal platonic realm into the spatiotemporal non-physical realm (see the Octagon)
This is the red subtle energy group.

Timespan of activation: directly

94   Aesthetically “beautiful” mathematics, logic, science and technology
The platonic entities that are within the cognitive group, interact / instantiate from the non-spatiotemporal platonic realm into the spatiotemporal non-physical realm (see the Octagon)
This is the yellow subtle energy group.

Timespan of activation: Short

Mathematics, rightly viewed, possesses not only truth, but supreme beauty a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. –BERTRAND RUSSELL, Study of Mathematics

95   Aesthetically “beautiful” language, communication, music, social structures
The platonic entities that are within the social / communicative group, interact / instantiate from the non-spatiotemporal platonic realm into the spatiotemporal non-physical realm (see the Octagon)
This is the green subtle energy group.
Timespan of activation:  Sequential

96   Aesthetically “beautiful” justice, morality, fairness
The platonic entities that are within the moral group, interact / instantiate from the non-spatiotemporal platonic realm into the spatiotemporal non-physical realm (see the Octagon)
This is the blue subtle energy group.
Timespan of activation: middle

“But I think it is a serious issue to wonder about the other platonic absolutes of say beauty and morality.”           Roger Penrose

97   Aesthetically “beautiful” meaning, teleology, ultimate significance
The platonic entities that are within the meaning / significance group, interact / instantiate from the non-spatiotemporal platonic realm into the spatiotemporal non-physical realm (see the Octagon)
As synchronicities are meningfull coincidences they belong, interact with this energygroup.
This is the violet subtle energy group.
Timespan of activation: long

98   Potentiality waves
If everything that is empirical is an actualization of potentiality waves, then this principle must also apply to the appearance of consciousness in this world and to its contents. Thus, we can think that the cosmic potentiality is the source not only of the material things in this world but also of the principles of our mind. This is the basis of our ability to understand the external world.
(Lothar Schäfer  Is quantum physics a sort of idealism?)

99   Implicate orders
Within theoretical physics one finds a description of the different levels of existence written by theoretical physicist David Bohm, who developed an ontological interpretation of quantum mechanics.
Bohm put forward a theory of an explicate order (the physical matter) and a series of implicate orders (each consisting of a different subtle non-physical matter).
In Bohm’s ontological interpretation of quantum theory we find a series of implicated orders: “Little reflection shows that the whole idea of implicate order could be extended in a natural way. For if there are two levels of implicate order, why should there not be more? Thus if we regard the super-implicate order as the second level, then we might consider a third level which was related to the second as the second is to the first. That is to say, the third implicate order would organize the second which would thereby become non-linear. (The Undivided Universe, David Bohm and Basil Hiley 1993).
David Bohm’s implicate orders have a great resemblance to Plato’s hierarchical
platonic realms.

If everything that is empirical is an actualization of potentiality waves, then this principle must also apply to the appearance of consciousness in this world and to its contents. Thus, we can think that the cosmic potentiality is the source not only of the material things in this world but also of the principles of our mind. This is the basis of our ability to understand the external world.

In the eighteenth century the idealist philosopher Georg Wilhelm Friedrich Hegel developed the theory that the “Absolute” or “the self-motivated Spirit” is the basis of reality and everything that exists is an actualization of spirit. Hegel’s philosophy is called absolute idealism. It got its name because spirit is the source of everything and creates everything; thinking and being, subject and object, the real and the ideal, the human and the divine—all are One.
(Lothar Schäfer  Is quantum physics a sort of idealism?)

Platonism is firmly committed to the existence of an intelligible, that is, immaterial or incorporeal realm, that is ontologically prior to the sensible realm.

“incorporeal” what is not composed of physical stuff, and is indivisible, dimensionless, not spatially located, and existing without a body.

100   Platonism and evolution

The static world of ontic forms and the dynamic world of becoming Plato’s theory of ideas crucially depends on these developments within early Greek philosophy. It first of all responds to the lasting problem of constancy and change, for if everything changes no knowledge would be possible. According to Plato, knowledge presupposes enduring ontic forms, each with its own essence (auto to eidos). This entails another lasting problem, namely how to relate diversity to a unity (the problem of the one and the many). Add to this that the motivating basic motive of matter and form directed Plato’s thought towards an attempt to bridge the gulf between the intelligible realm of eternal ontic forms and the phenomenal world of becoming which is subject to the matter principle (see Politeia 509 d – 511 e). The dialogue Phaedo distinguishes between what is invisible and constant and that which is visible and changeable (thought and the senses).6The static unity of the eidē had to provide a foundation for the (composite) world of becoming by allowing the phenomena to partake or share in the eidē (methexis, parousia, koinonia) (Phaedo 100 D). Implicit in this issue is the problem of the one and the many. How can what is simple and one cause the many? Surely, if Plato continues the initial Eleatic understanding of the eidos as something simple and indivisible, this problem cannot be solved. The authentic Platonic theory of ideas probably ensued from what Parmenides and the Pythagoreans thought, combined with the conceptual method of Socrates (regarding the dynamic tendency in the thought of Socrates see Plato Euthyphro 5 D).In the dialogue Cratylus it is argued that if something is caught up in continuous change, then knowledge of it would be impossible, for the moment it is approached in knowledge, it has become something different already (Cratylus 439 e – 440 a). This coheres directly with the problem of change that will exclude knowledge: if the auto to eidos of knowing changed into another eidos, no knowledge (to subject and object) will be possible (Cratylus 440 a-b). Apparently Aristotle has this in mind when he points out that Plato was acquainted with the doctrines of Heraclitus according to which “all sensible things are ever in a state of flux and there is no knowledge about them” (Metaph. 987 a 30; Aristotle 2001:700). This highlights a basic problem that still needs to be addressed by any critical theory of science in service both of philosophy and the special sciences.
From: Plato’s heritage to Western philosophy, European intellectual tradition and some special sciences      Danie Strauss

Is evolution a problem for Platonists? Can there be a form for organisms that changes by their nature, while platonic forms do not?

Evolution (biological or otherwise), can be placed within a platonic framework.    Growth (from small to big) is not a problem because platonic forms are scale invariant. But then there is the question how can a platonic form which is unchangeable, can instantiate an evolutionary process which changes in time.
This is possible when the developmental structure which changes in function, or fundamental nature, shifts to another platonic form, or sequentially shifts through different platonic forms.
For example: One can make a wooden table from a tree, and a can make a circle shaped object from that table, which are represented by three totally different platonic forms, who each are unchangeable themselves.

101   How many different Platonic forms are there?
There must be an enormous amount of different platonic forms, but they are all one of a kind (and nonlocalised and trans-temporal)

102   Where are Platonic forms located?
They have no spatial dimensions, and no orientation in space, nor do they even (like the point) have a location. But they can be described as non local resonance which is everywhere. But they can influence spatiotemporal structures by  non-local resonance which operates everywhere.

103   Platonism: a top down approach
What is Platonism?      LLOYD P. GERSON:
“The feature common to virtually all varieties of Platonism is a commitment to what I would characterize as a top-down metaphysical approach to the entire budget of philosophical problems extant in any particular period.27 What is most distinctive about Platonism is that it is resolutely and irreducibly top-down rather than bottom-up. A top-down approach to philosophical problems rejects and a bottom-up approach accepts the claim that the most important and puzzling phenomena we encounter in this world can be explained by seeking the simplest elements out of which these are composed. The top-down approach appeals to irreducible, intelligible principles to account for these phenomena. Among these are human personhood, and the personal attribute of freedom, cognition, the presence of evil, and the very existence of a universe. The top-down approach holds that answers to questions about these phenomena are never going to be satisfactorily given in terms of, say, elementary physical particles from which things “evolve” or upon which the phenomena “supervene.” According to this position, “Platonism” is ur “top-downism” and its authentic opposite is ur “bottom-upism.” Varieties of “bottom-upism” are practically coextensive with varieties of materialism.28 By materialism I mean, basically, the position that holds that the only things that exist in the world are bodies and their attributes, however the latter be construed. All materialists, that is, all anti-Platonists, share the view that, even if attributes are taken to be immaterial in the anodyne sense that they are real and that they are not themselves bodies, they are dependent upon bodies for their existence and explicable entirely in materialistic terms. Thus, for the materialist there are no immaterial or incorporeal entities. Hence, the explanation or account of problematic features of life are obviously not going to be top-down. The explanations must begin and end ultimately with bodies or their parts and the scientific laws governing these. Here, then, is a brief and very schematic compendium of the features of the “top-downism” that is Platonism.”

104   Why is the universe is intelligible?
The influence of the Timaeus on later scientific and theological thought is hard to overstate. Prior to the systematic re-introduction of Greek philosophical works to the Latin West in the twelfth and thirteenth centuries, Calcidius’ Latin translation and commentary on the Timaeus (ca. A.D. 360) was the only Platonic work widely known in the West. It is important to remember that Plato’s ventures into science all serve a philosophical-ethical end. The universe is a kosmos, an organized and rationally accessible whole. It can be understood only because it is the product of intelligence, and intelligence always orders things for the best. This teleological emphasis is clear in very early dialogues (e.g. Gorgias), in those of Plato’s middle period (e.g. Phaedo, Republic), and in those of his later years (e.g. Timaeus, Philebus, Laws). The presence in late dialogues of a divine craftsman or Demiurge may or may not have been intended literally (this too was a matter hotly debated in the Academy); but the central point, that the universe is intelligible because and to the degree that it is the product of intelligence, is undeniably Platonic.
Peter Losin   Plato and Platonism  The History of Science and Religion in the Western Tradition: An Encyclopedia. New York: Garland Publishing, Inc., 2000. pp. 109-14.)

105   Emanations
“Plotinus, drawing on Platonic images and metaphors, posited an ineffable One as the basic constituent of the universe. From this One there arise, by a series of emanations, the Intellect, then the Soul, then Nature, and finally Matter. Corresponding to these emanations is a diminution in reality: Matter, which is inert unless acted on by mind, is hardly real at all. Adequate explanations even of material phenomena, then, must exhibit the workings of the non-material world of mind.”
Peter Losin   Plato and Platonism  The History of Science and Religion in the Western Tradition: An Encyclopedia. New York: Garland Publishing, Inc., 2000. pp. 109-14.)

106   Vertical and lateral connections
There is a difference between vertical / ontological and lateral / complexity development.

107   Emergent laws
In science one encounters emergent laws. However, this isn’t necessarily in conflict with a platonic worldview, because the instantiation is trans temporal.

108   Are the Laws of Nature unchangeable?
Were the Laws of Nature at the big bang different ?
Do the light measurements of star systems that emitted the light that we see now 12 billion years ago indicate that?
Was E = mc²  always true?
Was pi = 3,14….. different in the past?
Were there more or less than 5 platonic solids in the past?
However the question itself is highly relevant.

109   Are there feedback loops between future states and the past?
Retro causal phenomena are suggested within quantum theory.

110   Synchronicity
Synchronicity is a particular kind of |platonic instigation.

111   Platonism within biology

Stephen Jay Gould, an American paleontologist, evolutionary biologist, and historian of science, also one of the most influential and widely read authors of  science of his generation:
“I worked piecemeal, producing a set of accreting revisionary items along of each of the branches of the Darwinian central logic, until I realised that a “Platonic” something “Up there” in ideological space could coordinate all these critiques and fascinations into a revised general theory, with a retained Darwinian base.”
Stephen Jay Gould, “The structure of evolutionary theory.” Page 41.

112  The Logos

The logos is really like the platonic realm of forms or ideas:

Written By:  The Editors of Encyclopaedia Britannica:
Logos, (Greek: “word,” “reason,” or “plan”)plural logoi, in Greek philosophy and theology, the divine reason implicit in the cosmos, ordering it and giving it form and meaning. Though the concept defined by the term logos is found in Greek, Indian, Egyptian, and Persian philosophical and theological systems, it became particularly significant in Christian writings and doctrines to describe or define the principle of God active in the creation and the continuous structuring of the cosmos.

The idea of the logos in Greek thought harks back at least to the 6th-century-bc philosopher Heracleitus, who discerned in the cosmic process a logos analogous to the reasoning power in man. Later, the Stoics, philosophers who followed the teachings of the thinker Zeno of Citium (4th–3rd century bc), defined the logos as an active rational and spiritual principle that permeated all reality. They called the logos providence, nature, god, and the soul of the universe, which is composed of many seminal logoi that are contained in the universal logos. Philo of Alexandria, a 1st-century-ad Jewish philosopher, taught that the logos was the intermediary between God and the cosmos, being both the agent of creation and the agent through which the human mind can apprehend and comprehend God. According to Philo and the Middle Platonists, philosophers who interpreted in religious terms the teachings of the 4th-century-bc Greek master philosopher Plato, the logos was both immanent in the world and at the same time the transcendent divine mind.  

Summary: 

The existence of platonic forms as objective entities has been accepted by the majority of mathematicians and theoretical physicists, including almost all the famous physicists —Albert Einstein, Niels Bohr, Erwin Schrödinger, Werner Heisenberg, Wolfgang Pauli, Max Born, among others—
They  accept that adequate explanations of physically verified phenomena frequently rely upon mathematical objects.
Heisenberg remarked: “The particles of modern physics are representations of symmetry groups and to that extent they resemble the symmetrical bodies of Plato’s philosophy.”

Platonic forms and mathematical structures are not merely subjective conceptions but objective realities.

Forms are transcendent to our material world in that they exist beyond space and time, whereas material objects occupy a specific place at a specific time

As Plato indicated, a mental recognition of Beauty or a mathematical object occurs in time. Platonic objects remain unchanging and non-spatiotemporal, but they are experienced in spacetime.

Plato’s forms are transcendental, eternal, unchangeable, universal, divine

Platonic information content is instantiated in both mental activities and mind-independent physical events.

Many theorists have questioned Platonism because of the connectivity problem. How can an external Platonic form (often referred to as a “universal”) be connected to or associated with a material object (also known as “physical particular”), or how can it cause or be involved in an instantiation in the physical world, the spatio-temporal realm?

Platonic information content is instantiated in both mental activities and mind-independent physical events.

Many theorists have questioned Platonism because of the connectivity problem. How can an external Platonic form (often referred to as a “universal”) be connected to or associated with a material object (also known as “physical particular”), or how can it cause or be involved in an instantiation in the physical world, the spatio-temporal realm?

One could argue that a Platonic form’s intrinsic property (e.g., circle shape) is extrinsically expressed in a spacetime instantiation.

Some type of causal interaction between platonic entities and human brains is clearly present in mathematical intuition.

Quantum phenomena, wave function collapse or reduction, is a physical event that correlates to Platonic instantiation.

Platonic information content is instantiated in both mental activities and mind-independent physical events. For example, regular geometric structures emerge as crystals “grow.” Minds observe crystals, possibly recognizing their Platonic shapes.

113  Heisenberg on Platonism
the debate between Plato and Democritus by Werner Heisenberg.

It was here in this part of the world, on the coast of the Aegean Sea, that the philosophers Leucippus and Democritus pondered about the structure of matter, and down there in the marketplace, where twilight is now falling, that Socrates disputed about the basic difficulties in our modes of expression and Plato taught that the Idea, the form, was the truly fundamental pattern behind the phenomena. The problems first formulated in this country two and a half thousand years ago have occupied the human mind almost unceasingly ever since and have been discussed again and again in the course of history whenever new developments have altered the light in which the old lines of thought appeared.

If I endeavor today to take up some of the old problems concerning the structure of matter and the concept of natural law, it is because the development of atomic physics in out own day has radically altered our whole outlook on nature and the structure of matter. It is perhaps not an improper exaggeration to maintain that some of the old problems have quite recently found a clear and final solution. So it is permissible today to speak about this new and perhaps conclusive answer to questions that were formulated here thousands of years ago.

There is, however, yet another reason for renewing consideration of these problems. The philosophy of materialism, developed in antiquity by Leucippus and Democritus, has been the subject of many discussions since the rise of modern science in the seventeenth century and, in the form of dialectical materialism, has been one of the moving forces in the political changes of the nineteenth and twentieth centuries. If philosophical ideas about the structure of matter have been able to play such a role in human life, if in European society they have operated almost like an explosive and may yet perhaps do so in other parts of the world, it is even more important to know what our present scientific knowledge has to say about this philosophy. To put it in rather general and precise terms, we may hope that a philosophical analysis of recent scientific developments will contribute to a replacement of conflicting dogmatic opinions about the basic problems we have broached, by a sober readjustment to a new situation, which, in itself, can even now be regarded as a revolution in human life on this earth. But even aside from this influence of science upon our time, it may be of interest to compare the philosophical discussions in ancient Greece with the findings of experimental science and modern atomic physics. If I may already anticipate at this point the outcome of such a comparison; it seems that, in spite of the tremendous success that the concept of the atom has achieved in modern science, Plato was very much nearer to the truth about the structure of matter than Leucippus or Democritus. But it will doubtless be necessary to begin by repeating some of the most important arguments adduced in the ancient discussions about matter and life, being and becoming, before we can enter into the findings of modern science.

The Concept of Matter in Ancient Philosophy

At the beginning of Greek philosophy there stood the dilemma of the “one” and the “many.” We know that there is an ever-changing variety of phenomena appearing to our senses. Yet we believe that ultimately it should be possible to trace them back somehow to some one principle.

The founders of atomism, Leucippus and Democritus, tried to avoid the difficulty by assuming the atom to be eternal and indestructible, the only thing really existing. All other things exist only because they are composed of atoms. The antithesis of “being” and “non being” in the philosophy of Parmenides is here coarsened into that between the “full” and the “void.” Being is not only one; it can be repeated infinitely many times. Being is indestructible, and therefore the atom, too, is indestructible. The void, the empty space between the atoms, allows for position and motion, and thus for properties of the atom, whereas by definition, as it were, pure being can have no other property than that of existence. This latter part of the doctrine of Leucippus and Democritus is at once its strength and its weakness. On the one hand, it provides an immediate explanation of the different aggregate states of matter, such as ice, water, and steam, since the atoms may lie densely packed and in order beside each other, or be caught in disorder and irregular motion, or finally be separated at fairly large relative intervals in space. This part of the atomic hypothesis was therefore to prove exceedingly fruitful at a later stage. One the other hand, the atom becomes in this fashion a mere building block of matter; its properties, position, and motion in space turn it into something quite different from what was meant by the original concept of “being.” The atoms can even have a finite extension, and here we have finally lost the only convincing argument for their indivisibility. If the atom has spacial properties, why should it not be divided? At least its indivisibility then becomes a physical, not a fundamental property. We can now again ask questions about the structure of the atom, and we run the risk of losing all the simplicity we had hoped to find among the smallest parts of matter. We get the impression, therefore, that in its original form the atomic hypothesis was not sufficiently subtle to explain what the philosophers really wished to understand: the simple element in the phenomena and in the structure of matter.

Still, the atomic hypothesis does go a large part of the way in the right direction. The whole multiplicity of diverse phenomena, the man observed properties of matter, can be reduced to the position and motion of the atoms. Properties such as smell or color or taste are not present in atoms. But their position and motion can evoke these properties indirectly. Position and motion seem to be much simpler concepts than the empirical qualities of taste, smell, or color. But then it naturally remains to ask what determines the position and motion of the atoms. The Greek philosophers did not attempt at this point to formulate a law of nature; the modern concept of natural law did not fit into their way of thought. Yet they seem to have thought of some kind of causal description or determinism, since they spoke of necessity, of cause and effect.

The intention of the atomic hypothesis had been to point the way from the “many” to the “one,” to formulate the underlying principle, the material cause, by virtue of which all phenomena can be understood. The atoms could be regarded as the material cause, but only a general law determining their positions and velocities could actually play the part of the fundamental principle. However, when the Greek philosophers discussed the laws of nature, their thoughts were directed to static forms, geometrical symmetries, rather than to processes of space and time. The circular orbits of the planets, the regular geometrical solids, appeared to be the permanent structures of the world. The modern idea, that the position and velocity of the atom at a given time could be uniquely connected by a mathematical law with its position and velocity at a later time, did not fit into the pattern of thought of that era since it employs the concept of time in a manner that arose only out the the thinking of a much later epoch.![][1]

When Plato himself took up the problems raised by Leucippus and Democritus, he adopted the idea of smallest units of matter, but he took the strongest exception to the tendency of that philosophy to suppose the atoms to be the foundation of all existence, the only truly existing material objects. Plato’s atoms were not strictly material, being thought of as geometrical forms, the regular solids of the mathematicians. These bodies, in keeping with the starting point of his idealistic philosophy, were in some sense the Ideas underlying the structure of matter and characterizing the physical behavior of the elements to which they belonged. The cube, for example, was the smallest particle of the element earth and thereby symbolized at the same time the earth’s stability. The tetrahedron, with its sharp point, represented the smallest particle of the element fire. The icosahedron, which comes closest among the regular solids to a sphere, stood for the mobility of the element water. In this way the regular solids were able to serve as symbols for certain tendencies in the physical behavior of matter.

But they were not strictly atoms, not indivisible basic units like those of the materialist philosophy. Plato regarded then as composed from the triangles forming their surfaces; therefore, by exchanging triangles, these smallest particles could be commuted into each other. Thus two atoms of air, for example, and one of fire could be compounded into an atom of water. In this was Plato was able to escape the problem of the indefinite divisibility of matter. For as two-dimensional surfaces the triangles were not bodies, not matter any longer; hance matter could not be further divided ad infinitum. At the lower end, therefore, in the realm, that is, of minimal spatial dimensions, the concept of matter is resolved into that of mathematical form. This form determines the behavior, first of the smallest parts of matter, then of matter itself. To a certain extent it replaces the natural law of later physics; for without making explicit references to the course of time, it characterizes the tendencies in the behavior of matter. One might say, perhaps, that the fundamental tendencies were represented by the geometrical shape of the smallest units, while the finer details of those tendencies found expression in the relative position and velocity of these units.

This whole description fits exactly into the central ideas of Plato’s idealist philosophy. The structure underlying the phenomena is not given by material objects like the atoms of Democritus but by the form that determines the material objects. The Ideas are more fundamental then the objects. And since the smallest parts of matter have to be the objects whereby the simplicity of the world becomes visible, whereby we approximate to the “one” and the “unity” of the world, the Ideas can be described mathematically—they are simply mathematical forms. The saying “God is a mathematician,” which in this form assuredly derives from a later period of philosophy, has its origin in this passage from the Platonic philosophy.

The importance of this step in philosophical thought can hardly be reckoned too highly. It can be seen as the decisive beginning of the mathematical science of nature, and hence be made responsible also for the later technical applications that have altered the whole picture of the world. By this step it is also first established what the term “understanding” is to mean. Among all the possible forms of understanding. Whereas all language, indeed, al art and all poetry in some way mediate understanding, it is here maintained that only the employment of a precise, logically consistent language, a language so far capable of formalization that proofs become possible, can lead to true understanding. One feels the strength of the impression made upon the Greek philosophers by the persuasive force of logical and mathematical arguments. They are obviously overwhelmed by this force. But perhaps they surrendered too early at this point.

The Answer of Modern Science to the Old Problems

If we trace the history of physics from Newton to the present day, we see that, despite the interest in details, very general laws of mature have been formulated on several occasions. The nineteenth century saw an exact working out of the statistical theory of heat. The theories of electromagnetism and special relativity have proved susceptible of combination into a very general group of natural laws containing statements not only about electrical phenomena but also about the structure of space and time. In our own century, the mathematical formulation of the quantum theory has led to an understanding of the outer shells of chemical atoms, and thus of the chemical properties of matter generally. The relations and connections between these different laws, especially between relativity and quantum theory, are not yet fully explained. But the latest developments in particle physics permit one to hope that these relations may be satisfactorily analyzed in the relatively near future. We are thus already in a position to consider what answers can be given by this whole scientific development to the questions of the old philosophers.

During the nineteenth century, the development of chemistry and the theory of heat conformed very closely tot he ideas first put forward by Leucippus and Democritus. A revival of the materialist philosophy in its modern form, that of dialectical materialism, was this a natural counterpart to the impressive advances made during this period in chemistry and physics. The concept of the atom had proved exceptionally fruitful in the explanation of chemical bonding and the physical behavior of gases. It was soon, however, that the particles called atoms by the chemist were composed of still smaller units. But these smaller units, the electrons, followed by the atomic nuclei and finally the elementary particles, protons and neutrons, also still seemed to be atoms from the standpoint of the materialist philosophy. The fact that, at least indirectly, one can actually see a single elementary particle—in a cloud chamber, say, or a bubble chamber—supports the view that the smallest units of matter are real physical objects, existing in the same sense that stones or flowers do.

But the inherent difficulties of the materialist theory of the atom, which had become apparent even in the ancient discussions about smallest particles, have also appeared very clearly in the development of physics during the present century.

This difficulty relates to the question whether the smallest units are ordinary physical objects, whether they exist in the same way as stones or flowers. Here, the development of quantum theory some forty years ago has created a complete change in the situation. The mathematically formulated laws of quantum theory show clearly that our ordinary intuitive concepts cannot be unambiguously applied to the smallest particles. All the words or concepts we use to describe ordinary physical objects, such as position, velocity, color, size, and so on, become indefinite and problematic if we try to use then of elementary particles. I cannot enter here into the details of this problem, which has been discussed so frequently in recent years. But it is important to realize that, while the behavior of the smallest particles cannot be unambiguously described in ordinary language, the language of mathematics is still adequate for a clear-cut account of what is going on.

During the coming years, the high-energy accelerators will bring to light many further interesting details about the behavior of elementary particles. But I am inclined to think that the answer just considered to the old philosophical problems will turn out to be final. If this is so, does this answer confirm the views of Democritus or Plato?

I think that on this point modern physics has definitely decided for Plato. For the smallest units of matter are, in fact, not physical objects in the ordinary sense of the word; they are forms, structures or—in Plato’s sense—Ideas, which can be unambiguously spoken of only in the language of mathematics. Democritus and Plato both had hoped that in the smallest units of matter they would be approaching the “one,” the unitary principle that governs the course of the world. Plato was convinced that this principle can be expressed and understood only in mathematical form. The central problem of theoretical physics nowadays is the mathematical formulation of the natural law underlying the behavior of elementary particles. From the experimental situation we infer that a satisfactory theory of the elementary particles must at the same time be a theory of physics in general, and hence, of everything else belonging to this physics.

In this way, a program could be carried out that in modern times was first proposed by Einstein: a unified theory of matter—and hence, simultaneously, a quantum theory of matter—could be formulated, which might serve quite generally as a foundation for physics. We do not yet know whether the mathematical forms proposed for this unifying principle are already adequate or will have to be replaced by forms more abstract still. But our present knowledge of the elementary particles is certainly enough for us to say what the main content of this law has to be. It must essentially set forth a small number of fundamental symmetry properties in nature, which have been known empirically for some years; in addition to these symmetries, it must contain the principle of causality as understood in relativity theory. The most important of the symmetries are the so-called “Lorentz group” of space and time, and the so-called “isospin group,” which has to do with the electric charge on the elementary particles. There are also other symmetries, but of these I shall say nothing here. Relativistic causality is connected with the Lorentz group but must be considered an independent principle.

This situation reminds us at once of the symmetrical bodies introduced by Plato to represent the fundamental structures of matter. Plato’s symmetries were not yet the correct ones, but he was right in believing that ultimately, at the heart of nature, among the smallest units of matter, we find mathematical symmetries. It was an unbelievable achievement of the ancient philosophers to have asked the right questions. But, lacking all knowledge of the empirical details, we could not have expected them to find answers that were correct in detail as well.

Consequences for the Evolution of Human Thought in Our Own Day

The search for the “one,” for the ultimate source of all understanding, has doubtless played a similar role in the origin of both religion and science. But the scientific method that was developed in the sixteenth and seventeenth centuries, the interest in those details which can be tested by experiment, has for a long time pointed science along a different path. It is not surprising that this attitude should have led to a conflict between science and religion, as soon as a law contradicted, in some particular and perhaps very important detail, the general picture, the mode and manner, in which the facts had been spoken of in religion. This conflict, which began in modern times with the celebrated trial of Galileo, has been discussed often enough, and I need not repeat this discussion here. One may recall that, even in ancient Greece, Socrates was condemned to death because his teachings seemed to contradict the traditional religion. In the nineteenth century, this conflict reached its peak in the attempt of some philosophers to replace traditional Christianity by a scientific philosophy, based upon a materialist version of the Hegelian dialectic. It might be said that, in directing their gaze upon a materialistic interpretation of the “one,” the scientists were attempting to find their way back again to this “one” from the multitude of details.

If modern science has something to contribute to this problem, it is not by deciding for or against one of these doctrines; for example, as was possibly believed in the nineteenth century, by coming down in favor of materialism and against the Christian philosophy, or, as I now believe, in favor of Plato’s idealism and against the materialism of Democritus. On the contrary, the chief profit we can derive in these problems from the progress of modern science is to learn how cautious we have to be with language and with the meaning of words. I would therefore like to devote the last part of my address to a few remarks about the problem of language in modern science and ancient philosophy.

If we may take our cue at this point from Plato’s dialogues, the unavoidable limitations of our means of expression were already a central theme in the philosophy of Socrates; one might even say that his whole life was a constant battle with these limitations. Socrates never wearied of explaining to his countrymen, here on the streets of Athens. That they did not know exactly what they meant by the words they were employing. The story goes that one of Socrates’ opponents, a sophist who was annoyed at Socrates’ constant reference to this insufficiency of language, criticized him and said: “But Socrates, this is a bore; you are always saying the same about the same.” Socrates replied: “But you sophists, who are so clever, perhaps never say the same about the same.”

The reason for laying such stress on this problem of language was doubtless that Socrates was aware, on the one hand, of how many misunderstandings can be engendered by a careless use of language, how important it is to use precise terms and to elucidate concepts before employing them. One the other hand, he probably also realized that this may ultimately be an insoluble task. The situation confronting us in our attempt to “understand” may drive us to conclude that our existing means of expression do not allow for a clear and unambiguous description of the facts.

The tension between the demand for complete clarity and the inevitable inadequacy of existing concepts has been especially marked in modern science. In atomic physics we make use of a highly developed mathematical language that satisfies all the requirements in regard to clarity and precision. At the same time, we recognize that we cannot describe atomic phenomena without ambiguity in any ordinary language; we cannot, for example, speak unambiguously about the behavior of an electron in the interior of an atom. It would premature, however, to insist that we should avoid the difficulty by confining ourselves to the use of mathematical language. This is no genuine way out, since we do not know how far the mathematical language can be applied to phenomena. In the last resort, even science must rely upon ordinary language, since it is the only language in which we can be sure of really grasping the phenomena.

This situation throws some light on the tension between the scientific method, on the one hand, and the relation of society to the “one,” the fundamental principle behind phenomena, on the other. It seems obvious that this latter relation cannot and should not be expressed in a precise and highly sophisticated language whose applicability to the real world may be very restricted. The only thing that will do for this purpose is the natural language everyone can understand. Reliable results in science, however, can be secured only by unambiguous statement; here we cannot do without the precision and clarity of an abstract mathematical language.

The necessity of constantly shuttling between the two languages is, unfortunately, a chronic source of misunderstandings, since in many cases the same words are employed in both. The difficulty is unavoidable. But it may yet be of some help always to bear in mind that modern science is obliged to make use of both languages, that the same word may have very different meanings in each of them, that different criteria of truth apply, and that one should not, therefore, talk too hastily of contradictions.

If we wish to approach the “one” in the terms of a precise scientific language, we must turn our attention to that center of science described by Plato, in which the fundamental mathematical symmetries are to be found. In the concepts of this language we must be content with the statement that “God is a mathematician”; for we have freely chosen to confine our vision to that realm of being which can be understood in the mathematical sense of the word “understanding,” which can be described in rational terms.

Plato himself was not content with this restriction. Having pointed out with the utmost clarity the possibilities and limitations of precise language, he switched to the language of poetry, which evokes in the hearer images conveying understanding of an altogether different kind. I shall not seek to discuss here what this kind of understanding can really mean. These images are probably connected with the unconscious mental patterns the psychologists speak of as archetypes, forms of strongly emotional character that, in some way, reflect the internal structures of the world. But whatever the explanation for these other forms of understanding, the language of images and likenesses is probably the only way of approaching the “one” from more general domains. If the harmony in a society rests on a common interpretation of the “one,” the unitary principle behind the phenomena, then the language of poetry may be more important here than the language of science.
Werner Heisenberg.

 

 

Platonic forms  and the Octagon corners

                             

   Platonic realm              Intermediate realm               Physical realm
       Non-local                              Localised                            Material

Platonic instigation:

Platonic realm            Intermediate realm              Physical realm

Non-local                       Localised                                  Material

Information                    Localisation                              Structuralisation

“Ideal” forms                  Instigation                                Physical objects

Universals                     Intermediate                             Individual

Principles                      Mental                                       Physical

Static                             Dynamic                                   Evolutionary

Simultaneous                Parallel                                     Sequential

Being                             Localising                                 Becoming

Intuition (insight)           Calculating                               Acting

Spirit                              Soul (psyche)                          Body

Platonic forms               Mathematical entities               Sensible entities

Ideal numbers (not        Arithmetical numbers               Physical objects 
   liable to calculus)            (countable)

Noesis = immediate      Dianioa = mind, discursive       Reflex, instincts
      apprehension                thinking

Oneness                       One among many,                    One as a property of                         
                                             multiplicity                                 bodies

Eidetic number              Mathematical number              Physical number

Spirit                              Rational                                   Appetite

One of a kind                 Similar                                     Diversification

Monad                           Multiplicity                                Composite

Indivisible                      Divisible                                   Sequential

Potentially                     Instigation                                 Actuality

Transcendent                Immanent                                 Structure

Resonance                    Synchronicity                           Seriality

Formless form               Shape                                       Substance

Unrepeatable                 Repeatable                              Converted  

Unreproducible              Reproducible                           Multiplied

Platonic forms                Geometrical figures                 Sensible things

Scale-invariant               Dimensional                             Magnitude

Immaterial                      Subtle matter                           Physical matter

Non-local                       Local but non-physical             Local, Physical     

Truth                              Knowledge                              Structure    

Trans-temporal              Temporal                                 Evolutionary

Platonic idea                  Concept                                  Object

Order                             Negentropy                             Entropy

Octagon corner:            Octagon corner:                      Octagon corner:  

 

 

 

Non-geometrical Platonic forms:

Beauty                     Truth              Social                       Justice             Meaning  

Red                          Yellow            Green                      Blue                 Violet

Aesthetic                  Logic              Communicative       Moral               Spiritual

 

12                            Oneness                                                                 Deification

11  Kosmic              Union                Unitary                                            Unification
      harmonious

10  Epiphanic          Revelation      Transformative                                 Synergism

9  Autonomic          Inspiration       Wholeness              Pacifism            Transendentism

8  Sublime                 Intuition         Interactive              Animal               Immanentism
                                                                                          Rights

7  Organic              Integration       Flexible                  Livelihood           Universalism 
                                                                                          Rights

6  Harmonious        Pluralistic        Contextual              Universal           Ecumenism
         Balance                                                                    Rights

5  Objective            Abstract          Autonomy               Free speech       Rationalism

4  Proportional        Concrete         Authority                Fairness in law    Scholastic  
                                                                                        Due process

3  Dainty                 Concept          Respect                 Habeas corpus   Ritualism

2  Pleasing             Image              Family                    Abolitionism       Shamanism                                                                           
1                             Reflex             Subconscious         Physical             Animism
                                                                                         integrity