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By: Jay Dyer

Immanuel Kant wrote at the close of his Critique of Pure Reason as follows:

In respect of the origin of the modes of ‘knowledge through pure reason’, the question is as to whether they are derived from experience, or whether in independence of ex-experience they have their origin in reason. Aristotle may be regarded as the chief of the empiricists, and Plato as the chief of the noologists. Locke, who in modern times followed Aristotle, and Leibniz, who followed Plato (although in con-considerable disagreement with his mystical system), have not been able to bring this conflict to any definitive conclusion. However we may regard Epicurus, he was at least much more consistent in this sensual system than Aristotle and Locke, inasmuch as he never sought to pass by inference beyond the limits of experience.1

In that paragraph Kant summed up the history of the division of philosophy into two camps with rival focii: the empirical tradition, descending loosely from Aristotle, emphasizing the immediate present, and the Platonic “noology,” stressing the permanence and eternality of the transcendent beyond, mirrored in the mind itself, which reflects the world’s own inherent, ideal structure.

However, which of these two thinkers, if either, is more correct? Is it possible to posit an external, essential structure to the world that supersedes the immediate, empirical experience?  How would such a realm be demonstrated?  The nature of these questions certainly extends beyond the scope of this paper, yet what I will claim is that Plato was more correct that Aristotle.  In fact, though Aristotle’s pioneering work in ethics, logic, politics and aesthetics cannot be overlooked, some of Aristotle’s own insights actually work to make the case for the claims of Plato, as I will argue.  This becomes particularly apparent when one considers the question of the infinity of God and numbers, which Plato and the Pythagoreans appear to have inherited from Egyptian Memphite and Hermetic traditions.  Interestingly, modern mathematical theorists and quantum physicists are coming to the very same conclusions the ancient Egyptians posited: that reality is, at base, much more than is visibly present, including higher and lower dimensions, as well as possibly a base, inherent mathematical essentialism behind the world we experience.  In effect, this means Aristotle’s empirical left turn from the Platonic Academy was in error.

Aristotle’s empiricism becomes most problematic when dealing with mathematical entities.  Aristotle argues against mathematical objects having a separate existence as Plato claimed, as follows:

That it is impossible for mathematical objects to exist in sensible things, and at the same time that the doctrine in question is an artificial one, has been said already in our discussion of difficulties we have pointed out that it is impossible for two solids to be in the same place, and also that according to the same argument the other powers and characteristics also should exist in sensible things and none of them separately. This we have said already. But, further, it is obvious that on this theory it is impossible for any body whatever to be divided; for it would have to be divided at a plane, and the plane at a line, and the line at a point, so that if the point cannot be divided, neither can the line, and if the line cannot, neither can the plane nor the solid. What difference, then, does it make whether sensible things are such indivisible entities, or, without being so themselves, have indivisible entities in them? The result will be the same; if the sensible entities are divided the others will be divided too, or else not even the sensible entities can be divided.2

And,

For if besides the sensible solids there are to be other solids which are separate from them and prior to the sensible solids, it is plain that besides the planes also there must be other and separate planes and points and lines; for consistency requires this. But if these exist, again besides the planes and lines and points of the mathematical solid there must be others which are separate. (For incomposites are prior to compounds; and if there are, prior to the sensible bodies, bodies which are not sensible, by the same argument the planes which exist by themselves must be prior to those which are in the motionless solids. Therefore these will be planes and lines other than those that exist along with the mathematical solids to which these thinkers assign separate existence; for the latter exist along with the mathematical solids, while the others are prior to the mathematical solids.) Again, therefore, there will be, belonging to these planes, lines, and prior to them there will have to be, by the same argument, other lines and points; and prior to these points in the prior lines there will have to be other points, though there will be no others prior to these. Now (1) the accumulation becomes absurd; for we find ourselves with one set of solids apart from the sensible solids; three sets of planes apart from the sensible planes-those which exist apart from the sensible planes, and those in the mathematical solids, and those which exist apart from those in the mathematical solids; four sets of lines, and five sets of points. With which of these, then, will the mathematical sciences deal? Certainly not with the planes and lines and points in the motionless solid; for science always deals with what is prior. And (the same account will apply also to numbers; for there will be a different set of units apart from each set of points, and also apart from each set of realities, from the objects of sense and again from those of thought; so that there will be various classes of mathematical numbers….It has, then, been sufficiently pointed out that the objects of mathematics are not substances in a higher degree than bodies are, and that they are not prior to sensibles in being, but only in definition, and that they cannot exist somewhere apart. But since it was not possible for them to exist in sensibles either, it is plain that they either do not exist at all or exist in a special sense and therefore do not ‘exist’ without qualification. For ‘exist’ has many senses.3

For Aristotle, Plato’s Academy’s arguments using mathematics as primary principles and forms does not constitute a strong point in their position, but rather, a weakness. In fact, Aristotle turns this around to what he sees as a central argument against the Platonic ideal forms, arguing that one will be led to various unnecessary absurdities upon adopting the notion that numerical entities, or the properties of geometry such lines, points, etc., possess a separate existence, the most famous of which was that an infinite result of forms and intermediaries would occur.

Since “existence” has different senses, or levels for Aristotle, one can speak of numbers having a kind of existence, but not any kind of substantial, ontological existence beyond that of a logical, or mental existence.  Just as “male” and “female” do not, for Aristotle, have any existence beyond any actual instantiated human beings, so likewise mathematical entities and geometrical descriptors do not have a separate existence beyond the actual objects under consideration by the mathematician or geometer.  The objects do really have the properties predicated of them, but they are predicates of the object qua-mathematics, or qua-geometry.  That is, they are under consideration as mathematically or geometrically described, not as essentially described.  Thus mathematical entities exist materially, and not actually. They are accidental to the objects under consideration, yet Aristotle does admit they have some existence relative to the object, and in some sense in the object, as he seems to say later, since he admits that the mind does “abstract from spatial magnitude.”

Has Aristotle really solved the dilemma by introducing his fundamental idea of a kind of mental, abstracted, accidental “existence” of such ideal entities?  It does not seem that he has.  In fact, Aristotle’s psychology of abstracting the universal from the phantasm produced by empirical phenomena really only moves the problem back a step.  This is because for Aristotle, a substance can only be one in an object, and all knowing is to know the universal, which is abstracted from the phantasm in the individual psyche.  If the knowing of anything is to know the universal, then the experience we have of objects must be one in which we know the essence of the things, or the substance, and can thus mentally separate the accidental qualities.   In fact, knowing essences and first principles or causes, according to Aristotle is precisely what metaphysics is, and is Wisdom itself, the highest of sciences.

Again, if the substance of a thing is only one in a thing, then numerical predicates of an object cannot be essential, for that would mean other substances entering into composition with something that is, at base, essentially one thing.  Substance is also peculiar to an individual thing, not a universal. The line, number, extension, and any conceivable attribute would thus also constitute a separate substantial existence, Aristotle argues against Plato, confusing the whole scientific process, making abstraction impossible.  In short, Aristotle’s basic metaphysical presuppositions preclude him from adopting such a stance.  It must, for his system, be the case that mathematical predicates are accidental and substance is one in individual things.  The law of identity cannot be violated: “If x is identical with y, then if x is F, y is F.”:

But if the principles are universal, either the substances composed of them are also universal, or non-substance will be prior to substance; for the universal is not a substance, but the element or principle is universal, and the element or principle is prior to the things of which it is the principle or element. All these difficulties follow naturally, when they make the Ideas out of elements and at the same time claim that apart from the substances which have the same form there are Ideas, a single separate entity.

But this is precisely where Aristotle runs into problems.  How does one exactly determine what attributes of a thing are essential?   How does the individual psyche know, given the empiricist presuppositions at work here, while going through the abstraction process, that is has properly delineated the truly universal from the truly particular?  How is it certain, empirically speaking, that the substantial element has been properly divided from the accidental predicates?  Empirical data alone will only move the question back another step, and that is all that Aristotle’s scheme can offer, more empirical data.  Certainly Aristotle thinks there are universals and essential substances that have an ontological existence, but the problem arises in his collapsed metaphysical landscape.  Because objects can only have a one-dimensional, here and now existence, Aristotle has shut out the transcendent in the process of needing it to be.

It will not do to simply say that the ontological existence of ideal entities is purely mental and accidental.  Furthermore, what is the nature of the phantasms that I abstract in my psyche?  Do they also only have an accidental existence in my mind?  In other words, what would be the ontological status of the conceptually-abstracted universals in my mind? Since they are not substantial to me, they must be accidental.  This being the case, when do I ever come into contact with something truly universal?  The individual psyche cannot, since the status of what is abstracted cannot be a substance.  This means that the individual psyche delineating what it believes to be accidental and substantial or universal or particular, is really only making arbitrary distinctions between things that are at base, one thing, with the appearance of accidental attributes and qualities.  This is brings home Kant’s quote at the beginning: The inheritor of this tradition is the nominalism of the late scholastic period and thenaïve empiricism of the Enlightenment.  In short, Aristotle’s presuppositions collapse into a reductionist metaphysical plane of either materialism or some kind of Berkeley empirical idealism.

Since the numbers have no essential existence, the same will follow for words and human speech: they do not have any necessary connection to the forms or essences of things. They are merely nominal,  social symbolical constructs.  They have only a token existence, as well as meaning itself. Meaning is not grounded in the transcendent, but in the here and now, and is ultimately of anthropological origin.  The history of the empirical tradition’s trajectory backs all this up, as well, sliding into the skepticism of the British Empiricists at the time of the Enlightenment.

What is evident, then, is that Aristotle himself took a departure from the tradition that had come to him from Egypt, through Plato and the Pythagoreans.  This Egyptian tradition claim in Plato is often scoffed at in modernity, yet Aristotle himself claims this in the Metaphysics: “Hence when all such inventions were already established, the sciences which do not aim at giving pleasure or at the necessities of life were discovered, and first in the places where men first began to have leisure. This is why the mathematical arts were founded in Egypt; for there the priestly caste was allowed to be at leisure.”

Plato famously claimed in the Timaeus and Critias to have received the tradition of the elaborate cosmology based on numerology from Egypt through from Solon as follows:

Soc.

Very good. And what is this ancient famous action of the Athenians, which Critias declared, on the authority of Solon, to be not a mere legend, but an actual fact?

Crit. I will tell an old-world story which I heard from an aged man; for Critias, at the time of telling it, was as he said, nearly ninety years of age, and I was about ten. Now the day was that day of the Apaturia which is called the Registration of Youth, at which, according to custom, our parents gave prizes for recitations, and the poems of several poets were recited by us boys, and many of us sang the poems of Solon, which at that time had not gone out of fashion. One of our tribe, either because he thought so or to please Critias, said that in his judgment Solon was not only the wisest of men, but also the noblest of poets. The old man, as I very well remember, brightened up at hearing this and said, smiling: Yes, Amynander, if Solon had only, like other poets, made poetry the business of his life, and had completed the tale which he brought with him from Egypt, and had not been compelled, by reason of the factions and troubles which he found stirring in his own country when he came home, to attend to other matters, in my opinion he would have been as famous as Homer or Hesiod, or any poet.

And,

I will tell you the reason of this: Solon, who was intending to use the tale for his poem, inquired into the meaning of the names, and found that the early Egyptians in writing them down had translated them into their own language, and he recovered the meaning of the several names and when copying them out again translated them into our language….I have before remarked in speaking of the allotments of the gods, that they distributed the whole earth into portions differing in extent, and made for themselves temples and instituted sacrifices.

The Timaeus continues its tale with an extended cosmology based on the earthly events mirroring the heavenly realm of the gods, with a special primacy given to numerology, and the descriptions of the Monad giving birth to the dyad, and the subsequent triad, an early trinity.  This sequence then includes a description of the elements and the basic shapes that make them up, as well as the planets, and the microprosopus and macroprosopus.  Number is something this realm participates in that mirrors the heavenly realm. Number is fundamental to all things in this world, from man, to the planets, to the revolution of the cycles of all things.  This is curiously absent in Aristotle, who does retain the idea of a distant god, identified as thought thinking itself, who rotates the celestial spheres through the Zodiac, however what is crucial is that the deity’s thought is irrelevant and unconnected to this immediate world, other than as a first cause.

What, then, are the central factors from Egyptian theology that are retained in Plato and relate to the Aristotelian turn?  That reality is, at base, a verbal/thought creation that relates to some mathematical structure. Egyptologist Stefan Wimmer comments:  “The Egyptians called their writing medu-netjer, “the god’s words,” while we give it a semantically very similar name, the Greek-influenced “hieroglyphics,” “holy signs.”  Anyone who has ever admired the enigmatic combinations of plants and body parts, geometric figures and birds, which are often lovingly rendered in great detail, will be able to understand the idea of visual poetry and appreciate the Egyptians’ certainty of divine inspiration behind behind their hieroglyphs.”17  In the Timaeus, it’s important to note that Plato identifies Athena, patron of Athens, with Neith, the Egyptian goddess of wisdom.

For the Egyptian theological mind, there is no distinction between the word, its meaning or essence, and the thing it represents.  All are necessarily inter-related, and as well as being connected to the vocalized form of the word.    Language, of course, can be represented mathematically, and the Egyptians pioneered the mathematics that would be used, for example, in modern computers and in A.I. Technology: both of which rely on binary structures.  One of the sources for this idea is the Memphite creation theology of the Shabaka stone.

Historian James Pritchard comments on the Memphite creation account:

When the first dynasty established its capital at Memphis, it was necessary to justify the sudden emergence of this town to central importance.  The Memphite god Ptah was therefore claimed to be the first principle, taking precedence over other recognized creator-gods….The extracts presented here are particularly interesting, because creation is treated in an intellectual sense, whereas other creation stories are given in purely physical terms.   Here the god Ptah conceives the elements of the universe with his mind (“heart”) and brings them into being by his commanding speech (“tongue”).  Thus, at the beginning of Egyptian history, there was an approach to the Logos doctrine. This extant document dates from 700 B.C.E.19

Thus from the beginning of the Egypt’s rise to dominance, there is a doctrine of the fundamental nature of reality consisting of an emanation or energeia from a “mental speech act.”  The divine thought-word gives rise to reality, emanating from the divine mind, through the Ennead.  Again, the similarities with Plato’s demiurge and the macroprosopus, as well as a remote similarity to Aristotle’s first cause deity of pure thought are evident.  The text reads:

There came into being as the heart and there came into being as the tongue (something) in the form of Atum.  The mighty Great One is Ptah, who transmitted [life to all gods], as well as (to) their ka’s, through this heart, by which Horus became Ptah, and through this tongue, by which Thoth became Ptah.

Thus it happened that the heart and the tongue gained control over every other member of the body, by teaching that he is in every body and in every mouth of all gods, all men, [all] cattle, all creeping things, and everything that lives, by thinking and commanding everything he wishes.20

Thoth is here the deity of divine speech, the lord of word magic and divine scripture.  For the Egyptians, all script is divine script, because all script reflects the principle of Thoth, representing knowledge and intellect.21  Note as well the similarity of the Memphite creation account with the biblical account of God creating the world through a divine speech-act in Genesis 1.  As mentioned, the universe takes on the qualities of Atum/Ptah here, because the universe is his body, and all bodies are his body.  The microprosopus/macroprosopus thus comes to the fore as it does in Plato.  This doctrine, however, is not present in Aristotle, nor is there an idea of the deity that is the first cause creating through some divine speech act.  The preparatory stages for the Aristotelian tradition’s acceptance of nominalism are thus seen early on. Also absent in Aristotle’s argumentation is the notion of a mathematics at the base of reality, particularly the monad, the dyad, the triad and the Ennead.  Aristotle does include the idea of the 10 categories, which are relevant to Plato, the Pythagoreans and Egypt, but in Aristotle they are divested on any mystical, essential correlation to the world due to what was shown above, given Aristotle’s metaphysical presuppositions.

Egyptologist Wim van den Dungen comments on these associations:

While there is a connection to Aristotle, it has become dim by the time it reaches fruition in his Metaphysics.  The divine Nous or mind is a first cause in Aristotle, and not an immediate emanating mathematical reality (note also the similarity with the Timaeus) using the Corpus Hermeticum:

The triad is also central as a fundamental stating point, as it was in Plato:

Thus the continuity with Plato and the discontinuity with Aristotle are apparent.  It is this key point, too, in which Aristotle has erred. Modern mathematicians and quantum physicists have given ample proof for what Aristotle denied: that there are higher dimensions in which normal physics do not operate like we appear to see them operate in our dimension.  The mathematics, in fact, confirms the existence of these higher dimensions, despite their empirical relaity.  In fact, the mathematical and geometric structure of the next dimension exhibits patterns very similar to the kinds of geometrical shapes Plato claimed the universe was made up of (Platonic solids).25  For example, the mathematical structure of a five-dimensional object is that of penrose tiling and quasi-crystals.  The breakdown of the Aristotelian world model through Newtonian physics itself eventually gave way to quantum mechanics, wherein Newtonian phyiscs does not work on the subatomic or higher-dimensional levels.26

Along with the highly structured, linguistic code-like nature of DNA, one should consider the theories in quantum physics where reality itself begins to look like it is, at base, linguistic or mathematical.  Theoretical physicist Brian Greene writes:

A datum that can answer a single yes-no question is called a bit—a familiar computer-age term that is short for binary digit, meaning a 0 or a 1, which you can think of as a numerical representation of yes or no….Notice that the value of the entropy and the amount of hidden information are equal.  That’s no accident.  The number of possible heads-tail arrangements is is the number of possible answers to the 1,000 questions – (yes, yes, no, no, yes,…) or (yes, no, yes, yes, no,…)…With entroy defined as the logarithm of the number of such arrangements—1,000 in this case—entropy is the number of yes-no questions any one such sequence answers….a system’s entropy is the number of yes-no questions that its microscopic details have the capacity to answer, and so the entropy is a measure of the system’s hidden information component….[in note] Stephen Hawking showed mathematically that the entropy of a black hole equals the number of Planck-sized cells that it takes to cover its event horizon.  It’s as if each cell covers one bit, one basic unit of information.27

In other words, when entropy is considered, one comes back to the traditional Greek and Egyptian dialectic of being and non-being, I and O.  And reality itself, when considered at the level of energy itself displays this same binary structure.

In fact, these ideas have led renowned MIT physicist Max Tegmark to come the conclusion that reality itself is a mathematical structure.  Rather than separating the two into separate worlds of a mental construct, and what isn’t out there, Tegmark claims they are one and the same, referring to his position as “Platonic,” and that the math, mind and matter can all be isomorphically collapsed:

The view that the physical world is intrinsically mathematical has scored many successes of exactly this type, which in my opinion increaseits credibility. The idea that the universe is in some sense mathematical goes back to the Pythagoreans, and appears again in Galileo’s statement that the Universe is a grand book written in the language of mathematics, and in Wigner’s discussion of the unreasonable  effectiveness of mathematics in the natural sciences. After Galileo promulgated the idea, additional mathematical regularities beyond his wildest dreams were uncovered, ranging from the motions of planets to the properties of atoms. After Wigner had writtenhis famous essay, the standard model of particle physics revealed new unreasonable mathematical order in themicrocosm of elementary particles, and my guess is that history will repeat itself again and again. I know of no other compelling explanation for this trend than that the physical world really is completely mathematical, isomorphic to some mathematical structure.

Let me briefly elaborate on what I mean by this hypothesis that mathematical and physical existence are equivalent. It can be viewed as a form of radical Platonism, asserting that the mathematical structures in Plato’s realm of ideas or Rucker’s “mindscape” exist in a physical sense. It is akin to what John Barrow refers to as “in the sky”, what Robert Nozick called the principle of fecundity and what David Lewis called modal realism.28

In other words, here are top physicists coming to verified mathematical and philosophical conclusions in quantum mechanics that serve as the basis for crucial things like transistors, nuclear power, lasers, microchips and television, admitting what the Egyptian view of the world, and Plato following the Egyptian tradition posited: that reality is, at based, connected with the possibility of other, deeper realms and dimensions, as well as that reality has a linguistic and/or mathematical structure at base.  Granted, Aristotle cannot be blamed for thinking outside the classical Pythagorean box he saw as constricting, and certainly this is not to say that Platonic idealism is necessarily correct in all it posits, but rather that time appears to be coming around to vindicating Plato and Egypt on these essential ideas, over against the empiricist tradition.  Certainly the latest discoveries are leaning in the direction of the Academy and its “Atlantean” heritage from Egypt.

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1Kant, Imannuel. Critique of Pure Reason (Buffalo, New York: Prometheus Books, 1990), 478-9.