(2) We are obliged, therefore, at the start, both to establish the existence of this other Kind and to examine its nature and the mode of its Being.

Now if Matter must characteristically be undetermined, void of shape, while in that sphere of the Highest there can be nothing that lacks determination, nothing shapeless, there can be no Matter there. Further, if all that order is simplex, there can be no need of Matter, whose function is to join with some other element to form a compound: it will be found of necessity in things of derived existence and shifting nature- the signs which lead us to the notion of Matter- but it is unnecessary to the primal.

And again, where could it have come from? whence did it take its being? If it is derived, it has a source: if it is eternal, then the Primal-Principles are more numerous than we thought, the Firsts are a meeting-ground. Lastly, if that Matter has been entered by Idea, the union constitutes a body; and, so, there is Body in the Supreme.

(7) Now bodies matter [-made] are in diversity. Some are of earth, of water some, some are of air, and some of fire. But they are all composed; some are more [composite], and some are simpler. The heavier ones are more [composed], the lighter less so. It is the speed of Cosmos' Course that works the manifoldness of the kinds of births. For being a most swift Breath, it doth bestow their qualities on bodies together with the One Pleroma - that of Life.

(106) Just as was the first mass, out of which Adam became a living man, so also in like manner is every mass or seed of the Ternary or Trinity in every man. Observe:

(1) [Asclepius] And does the Cosmos have a species, O Thrice-greatest one?

[Trismegistus] Dost not thou see, Asclepius, that all has been explained to thee as though to one asleep? For what is Cosmos, or of what doth it consist, if not of all things born? This, then, you may assert of heaven, and earth, and elements. For though the other things possess more frequent change of species, [still even] heaven, [by its] becoming moist, or dry, or cold, or hot, or clear, or dull, [all] in one kind of heaven,—these [too] are frequent changes into species.

(1) [Trismegistus] ’Tis in this way, Asclepius;—by mixing it, by means of subtle expositions, with divers sciences not easy to be grasped,—such as arithmetic, and music, and geometry. But Pure Philosophy, which doth depend on godly piety alone, should only so far occupy itself with other arts, that it may [know how to] appreciate the working out in numbers of the fore-appointed stations of the stars when they return, and of the course of their procession. Let her, moreover, know how to appreciate the Earth’s dimensions, its qualities and quantities, the Water’s depths, the strength of Fire, and the effects and nature of all these. [And so] let her give worship and give praise unto the Art and Mind of God.

(46) And the third Forming was together, in the same Twinkling of an Eye, with the other Formings also at once (out of the [pure] Element) produced, just as if an earthly Seed was sown, out of which a whole Child springs forth, and took its Beginning naturally; and the new Creature (in Perfection of the Element) was the masculine Seed of the earthly Man, which the earthly Matrix of the Virgin conceived in the Bosom of the Virgin Mary; yet the Earthliness defiled not the Limbus of the new Creature in the holy Element, for the- Word of the Deity (which was the Mark of the Limit of Separation) hindered that.

(122) One quality has always generated the others alike, and none of them have vanished or gone out of sight, just as it is in the whole God; and then the whole body, as it is also in the Ternary, generated itself just as the Deity generateth itself, without or distinct from the body in the Ternary.

(9) This diagrammatic sector represents the major gradations of energy and substance between elemental earth and absolute unconditioned force. Beginning with the superior, the fifteen graduated spheres descend in the following order: Limitless and Eternal Life; the superior, the middle, and the inferior Empyrean; the seven planets; and the four elements. Energy is symbolized by Fludd as a pyramid with its base upon the concave surface of the superior Empyrean, and substance as another Pyramid with its base upon the convex surface of the sphere (not planet) of earth. These pyramids demonstrate the relative proportions of energy and substance entering into the composition of the fifteen planes of being. It will be noted that the ascending pyramid of substance touches but does not pierce the fifteenth sphere--that of Limitless and Eternal Life. Likewise, the descending pyramid of energy touches but does not pierce the first sphere--the grossest condition of substance. The plane of the sun is denominated the sphere of equality, for here neither energy nor substance predominate. The mundane monochord consists of a hypothetical string stretched from the base of the pyramid of energy to the base of the pyramid of substance.

(12) It is the corporeal, then, that demands magnitude: the Ideal-Forms of body are Ideas installed in Mass.

But these Ideas enter, not into Magnitude itself but into some subject that has been brought to Magnitude. For to suppose them entering into Magnitude and not into Matter- is to represent them as being either without Magnitude and without Real-Existence or not Ideal-Forms but Reason-Principles whose sphere could only be Soul; at this, there would be no such thing as body

The multiplicity here must be based upon some unity which, since it has been brought to Magnitude, must be, itself, distinct from Magnitude. Matter is the base of Identity to all that is composite: once each of the constituents comes bringing its own Matter with it, there is no need of any other base. No doubt there must be a container, as it were a place, to receive what is to enter, but Matter and even body precede place and space; the primal necessity, in order to the existence of body, is Matter.

There is no force in the suggestion that, since production and act are immaterial, corporeal entities also must be immaterial.

Bodies are compound, actions not. Further, Matter does in some sense underlie action; it supplies the substratum to the doer: it is permanently within him though it does not enter as a constituent into the act where, indeed, it would be a hindrance. Doubtless, one act does not change into another- as would be the case if there were a specific Matter of actions- but the doer directs himself from one act to another so that he is the Matter, himself, to his varying actions.

Matter, in sum, is necessary to quality and to quantity, and, therefore, to body.

It is, thus, no name void of content; we know there is such a base, invisible and without bulk though it be.

If we reject it, we must by the same reasoning reject qualities and mass: for quality, or mass, or any such entity, taken by itself apart, might be said not to exist. But these do exist, though in an obscure existence: there is much less ground for rejecting Matter, however it lurk, discerned by none of the senses.

It eludes the eye, for it is utterly outside of colour: it is not heard, for it is no sound: it is no flavour or savour for nostrils or palate: can it, perhaps, be known to touch? No: for neither is it corporeal; and touch deals with body, which is known by being solid, fragile, soft, hard, moist, dry- all properties utterly lacking in Matter.

It is grasped only by a mental process, though that not an act of the intellective mind but a reasoning that finds no subject; and so it stands revealed as the spurious thing it has been called. No bodiliness belongs to it; bodiliness is itself a phase of Reason-Principle and so is something different from Matter, as Matter, therefore, from it: bodiliness already operative and so to speak made concrete would be body manifest and not Matter unelaborated.

(71) Magnitude is divided into two parts--magnitude which is stationary and magnitude which is movable, the stationary pare having priority. Multitude is also divided into two parts, for it is related both to itself and to other things, the first relationship having priority. Pythagoras assigned the science of arithmetic to multitude related to itself, and the art of music to multitude related to other things. Geometry likewise was assigned to stationary magnitude, and spherics (used partly in the sense of astronomy) to movable magnitude. Both multitude and magnitude were circumscribed by the circumference of mind. The atomic theory has proved size to be the result of number, for a mass is made up of minute units though mistaken by the uninformed for a single simple substance.

(33) The Turbæ Philosophorum is one of the earliest known documents on alchemy in the Latin tongue. Its exact origin is unknown. It is sometimes referred to as The Third Pythagorical Synod. As its name implies, it is an assembly of the sages and sets forth the alchemical viewpoints of many of the early Greek philosophers. The symbol reproduced above is from a rare edition of the Turbæ Philosophorum published in Germany in 1750, and represents by a hermaphroditic figure the accomplishment of the magnum opus. The active and passive principles of Nature were often depicted by male and female figures, and when these two principle, were harmoniously conjoined in any one nature or body it was customary to symbolize this state of perfect equilibrium by the composite figure above shown.

(528) solids in revolution, instead of taking solids in themselves; whereas after the second dimension the third, which is concerned with cubes and dimensions of depth, ought to have followed. That is true, Socrates; but so little seems to be known as yet about these subjects. Why, yes, I said, and for two reasons:—in the first place, no government patronises them; this leads to a want of energy in the pursuit of them, and they are difficult; in the second place, students cannot learn them unless they have a director. But then a director can hardly be found, and even if he could, as matters now stand, the students, who are very conceited, would not attend to him. That, however, would be otherwise if the whole State became the director of these studies and gave honour to them; then disciples would want to come, and there would be continuous and earnest search, and discoveries would be made; since even now, disregarded as they are by the world, and maimed of their fair proportions, and although none of their votaries can tell the use of them, still these studies force their way by their natural charm, and very likely, if they had the help of the State, they would some day emerge into light. Yes, he said, there is a remarkable charm in them. But I do not clearly understand the change in the order. First you began with a geometry of plane surfaces? Yes, I said. And you placed astronomy next, and then you made a step backward? Yes, and I have delayed you by my hurry; the ludicrous state of solid geometry, which, in natural order, should have followed, made me pass over this branch and go on to

(28) To the five symmetrical solids of the ancients is added the sphere (1), the most perfect of all created forms. The five Pythagorean solids are: the tetrahedron (2) with four equilateral triangles as faces; the cube (3) with six squares as faces; the octahedron (4) with eight equilateral triangles as faces; the icosahedron (5) with twenty equilateral triangles as faces; and the dodecahedron (6) with twelve regular pentagons as faces.

(2) Our first observations must be directed to what passes in the Sensible realm for Substance. It is, we shall agree, only by analogy that the nature manifested in bodies is designated as Substance, and by no means because such terms as Substance or Being tally with the notion of bodies in flux; the proper term would be Becoming.

But Becoming is not a uniform nature; bodies comprise under the single head simples and composites, together with accidentals or consequents, these last themselves capable of separate classification.

Alternatively, Becoming may be divided into Matter and the Form imposed upon Matter. These may be regarded each as a separate genus, or else both may be brought under a single category and receive alike the name of Substance.

But what, we may ask, have Matter and Form in common? In what sense can Matter be conceived as a genus, and what will be its species? What is the differentia of Matter? In which genus, Matter or Form, are we to rank the composite of both? It may be this very composite which constitutes the Substance manifested in bodies, neither of the components by itself answering to the conception of Body: how, then, can we rank them in one and the same genus as the composite? How can the elements of a thing be brought within the same genus as the thing itself? Yet if we begin with bodies, our first-principles will be compounds.

Why not resort to analogy? Admitted that the classification of the Sensible cannot proceed along the identical lines marked out for the Intellectual: is there any reason why we should not for Intellectual-Being substitute Matter, and for Intellectual Motion substitute Sensible Form, which is in a sense the life and consummation of Matter? The inertia of Matter would correspond with Stability, while the Identity and Difference of the Intellectual would find their counterparts in the similarity and diversity which obtain in the Sensible realm.

But, in the first place, Matter does not possess or acquire Form as its life or its Act; Form enters it from without, and remains foreign to its nature. Secondly, Form in the Intellectual is an Act and a motion; in the Sensible Motion is different from Form and accidental to it: Form in relation to Matter approximates rather to Stability than to Motion; for by determining Matter's indetermination it confers upon it a sort of repose.

In the higher realm Identity and Difference presuppose a unity at once identical and different: a thing in the lower is different only by participation in Difference and in relation to some other thing; Identity and Difference are here predicated of the particular, which is not, as in that realm, a posterior.

As for Stability, how can it belong to Matter, which is distorted into every variety of mass, receiving its forms from without, and even with the aid of these forms incapable of offspring.

This mode of division must accordingly be abandoned.

(11) To Pythagoras music was one of the dependencies of the divine science of mathematics, and its harmonies were inflexibly controlled by mathematical proportions. The Pythagoreans averred that mathematics demonstrated the exact method by which the good established and maintained its universe. Number therefore preceded harmony, since it was the immutable law that governs all harmonic proportions. After discovering these harmonic ratios, Pythagoras gradually initiated his disciples into this, the supreme arcanum of his Mysteries. He divided the multitudinous parts of creation into a vast number of planes or spheres, to each of which he assigned a tone, a harmonic interval, a number, a name, a color, and a form. He then proceeded to prove the accuracy of his deductions by demonstrating them upon the different planes of intelligence and substance ranging from the most abstract logical premise to the most concrete geometrical solid. From the common agreement of these diversified methods of proof he established the indisputable existence of certain natural laws.

(6) We may now consider the question whether fire is the sole element existing in that celestial realm and whether there is any outgoing thence with the consequent need of renewal.

Timaeus pronounced the material frame of the All to consist primarily of earth and fire for visibility, earth for solidity- and deduced that the stars must be mainly composed of fire, but not solely since there is no doubt they are solid.

And this is probably a true account. Plato accepts it as indicated by all the appearances. And, in fact, to all our perception- as we see them and derive from them the impression of illumination- the stars appear to be mostly, if not exclusively, fire: but on reasoning into the matter we judge that since solidity cannot exist apart from earth-matter, they must contain earth as well.

But what place could there be for the other elements? It is impossible to imagine water amid so vast a conflagration; and if air were present it would be continually changing into fire.

Admitting that two self-contained entities, standing as extremes to each other need for their coherence two intermediaries; we may still question whether this holds good with regard to physical bodies. Certainly water and earth can be mixed without any such intermediate. It might seem valid to object that the intermediates are already present in the earth and the water; but a possible answer would be, "Yes, but not as agents whose meeting is necessary to the coherence of those extremes."

None the less we will take it that the coherence of extremes is produced by virtue of each possessing all the intermediates. It is still not proven that fire is necessary to the visibility of earth and earth to the solidarity of fire.

On this principle, nothing possesses an essential-nature of its very own; every several thing is a blend, and its name is merely an indication of the dominant constituent.

Thus we are told that earth cannot have concrete existence without the help of some moist element- the moisture in water being the necessary adhesive- but admitting that we so find it, there is still a contradiction in pretending that any one element has a being of its own and in the same breath denying its self-coherence, making its subsistence depend upon others, and so, in reality, reducing the specific element to nothing. How can we talk of the existence of the definite Kind, earth- earth essential- if there exists no single particle of earth which actually is earth without any need of water to secure its self-cohesion? What has such an adhesive to act upon if there is absolutely no given magnitude of real earth to which it may bind particle after particle in its business of producing the continuous mass? If there is any such given magnitude, large or small, of pure earth, then earth can exist in its own nature, independently of water: if there is no such primary particle of pure earth, then there is nothing whatever for the water to bind. As for air- air unchanged, retaining its distinctive quality- how could it conduce to the subsistence of a dense material like earth?

Similarly with fire. No doubt Timaeus speaks of it as necessary not to the existence but to the visibility of earth and the other elements; and certainly light is essential to all visibility- we cannot say that we see darkness, which implies, precisely, that nothing is seen, as silence means nothing being heard.

But all this does not assure us that the earth to be visible must contain fire: light is sufficient: snow, for example, and other extremely cold substances gleam without the presence of fire- though of course it might be said that fire was once there and communicated colour before disappearing.

As to the composition of water, we must leave it an open question whether there can be such a thing as water without a certain proportion of earth.

But how can air, the yielding element, contain earth?

Fire, again: is earth perhaps necessary there since fire is by its own nature devoid of continuity and not a thing of three dimensions?

Supposing it does not possess the solidity of the three dimensions, it has that of its thrust; now, cannot this belong to it by the mere right and fact of its being one of the corporeal entities in nature? Hardness is another matter, a property confined to earth-stuff. Remember that gold- which is water- becomes dense by the accession not of earth but of denseness or consolidation: in the same way fire, with Soul present within it, may consolidate itself upon the power of the Soul; and there are living beings of fire among the Celestials.

But, in sum, do we abandon the teaching that all the elements enter into the composition of every living thing?

For this sphere, no; but to lift clay into the heavens is against nature, contrary to the laws of her ordaining: it is difficult, too, to think of that swiftest of circuits bearing along earthly bodies in its course nor could such material conduce to the splendour and white glint of the celestial fire.

(58) An interesting application of the Pythagorean doctrine of geometric solids as expounded by Plato is found in The Canon. "Nearly all the old philosophers," says its anonymous author, "devised an harmonic theory with respect to the universe, and the practice continued till the old mode of philosophizing died out. Kepler (1596), in order to demonstrate the Platonic doctrine, that the universe was formed of the five regular solids, proposed the following rule. 'The earth is a circle, the measurer of all. Round it describe a dodecahedron; the circle inclosing this will be Mars. Round Mars describe a tetrahedron; the sphere inclosing this will be Jupiter. Describe a cube round Jupiter; the sphere containing this will be Saturn. Now inscribe in the earth an icosahedron; the circle inscribed in it will be Venus. Inscribe an octahedron in Venus; the circle inscribed in it will be Mercury' (Mysterium Cosmographicum, 1596). This rule cannot be taken seriously as a real statement of the proportions of the cosmos, fox it bears no real resemblance to the ratios published by Copernicus in the beginning of the sixteenth century. Yet Kepler was very proud of his formula, and said he valued it more than the Electorate of Saxony. It was also approved by those two eminent authorities, Tycho and Galileo, who evidently understood it. Kepler himself never gives the least hint of how his precious rule is to be interpreted." Platonic astronomy was not concerned with the material constitution or arrangement of the heavenly bodies, but considered the stars and planers primarily as focal points of Divine intelligence. Physical astronomy was regarded as the science of "shadows," philosophical astronomy the science of "realities."

(9) The elements in their totality, as they stand produced, may be thought of as one spheric figure; this cannot be the piecemeal product of many makers each working from some one point on some one portion. There must be one cause; and this must operate as an entire, not by part executing part; otherwise we are brought back to a plurality of makers. The making must be referred to a partless unity, or, more precisely, the making principle must be a partless unity not permeating the sphere but holding it as one dependent thing. In this way the sphere is enveloped by one identical life in which it is inset; its entire content looks to the one life: thus all the souls are one, a one, however, which yet is infinite.

It is in this understanding that the soul has been taken to be a numerical principle, while others think of it as in its nature a self-increasing number; this latter notion is probably designed to meet the consideration that the soul at no point fails but, retaining its distinctive character, is ample for all, so much so that were the kosmos vaster yet the virtue of soul would still compass it- or rather the kosmos still be sunk in soul entire.

Of course, we must understand this adding of extension not as a literal increase but in the sense that the soul, essentially a unity, becomes adequate to omnipresence; its unity sets it outside of quantitative measurement, the characteristic of that other order which has but a counterfeit unity, an appearance by participation.

The essential unity is no aggregate to be annulled upon the loss of some one of the constituents; nor is it held within any allotted limits, for so it would be the less for a set of things, more extensive than itself, outside its scope; or it must wrench itself asunder in the effort to reach to all; besides, its presence to things would be no longer as whole to all but by part to part; in vulgar phrase, it does not know where it stands; dismembered, it no longer performs any one single function.

Now if this principle is to be a true unity- where the unity is of the essence- it must in some way be able to manifest itself as including the contrary nature, that of potential multiplicity, while by the fact that this multiplicity belongs to it not as from without but as from and by itself, it remains authentically one, possessing boundlessness and multiplicity within that unity; its nature must be such that it can appear as a whole at every point; this, as encircled by a single self-embracing Reason-Principle, which holds fast about that unity, never breaking with itself but over all the universe remaining what it must be.

The unity is in this way saved from the local division of the things in which it appears; and, of course, existing before all that is in place, it could never be founded upon anything belonging to that order of which, on the contrary, it is the foundation; yet, for all that they are based upon it, it does not cease to be wholly self-gathered; if its fixed seat were shaken, all the rest would fall with the fall of their foundation and stay; nor could it be so unintelligent as to tear itself apart by such a movement and, secure within its own being, trust itself to the insecurity of place which, precisely, looks to it for safety.

(10) Another method of division is possible: substances may be classed as hot-dry, dry-cold, cold-moist, or however we choose to make the coupling. We may then proceed to the combination and blending of these couples, either halting at that point and going no further than the compound, or else subdividing by habitation- on the earth, in the earth- or by form and by the differences exhibited by living beings, not qua living, but in their bodies viewed as instruments of life.

Differentiation by form or shape is no more out of place than a division based on qualities- heat, cold and the like. If it be objected that qualities go to make bodies what they are, then, we reply, so do blendings, colours, shapes. Since our discussion is concerned with Sensible Substance, it is not strange that it should turn upon distinctions related to sense-perception: this Substance is not Being pure and simple, but the Sensible Being which we call the Universe.

We have remarked that its apparent subsistence is in fact an assemblage of Sensibles, their existence guaranteed to us by sense-perception. But since their combination is unlimited, our division must be guided by the Form-Ideas of living beings, as for example the Form-Idea of Man implanted in Body; the particular Form acts as a qualification of Body, but there is nothing unreasonable in using qualities as a basis of division.

We may be told that we have distinguished between simple and composite bodies, even ranking them as opposites. But our distinction, we reply, was between material and organic bodies and raised no question of the composite. In fact, there exists no means of opposing the composite to the simple; it is necessary to determine the simples in the first stage of division, and then, combining them on the basis of a distinct underlying principle, to differentiate the composites in virtue of their places and shapes, distinguishing for example the heavenly from the earthly.

These observations will suffice for the Being , or rather the Becoming, which obtains in the Sensible realm.

(106) Now, as the Ternary of the Deity is one only being or substance in all parts in the whole Father, and is united together, as the members in man's body, and all places are as one place, though one place may have a different function from the others, as also the members of men have; yet it is the one body of God: