(17) Nor can we, on the other hand, think that matter is simply Absolute Magnitude.

Magnitude is not, like Matter, a receptacle; it is an Ideal-Principle: it is a thing standing apart to itself, not some definite Mass. The fact is that the self-gathered content of the Intellectual Principle or of the All-Soul, desires expansion : in its images- aspiring and moving towards it and eagerly imitating its act- is vested a similar power of reproducing their states in their own derivatives. The Magnitude latent in the expansive tendency of the Image-making phase runs forth into the Absolute Magnitude of the Universe; this in turn enlists into the process the spurious magnitude of Matter: the content of the Supreme, thus, in virtue of its own prior extension enables Matter- which never possesses a content- to exhibit the appearance of Magnitude. It must be understood that spurious Magnitude consists in the fact that a thing not possessing actual Magnitude strains towards it and has the extension of that straining. All that is Real Being gives forth a reflection of itself upon all else; every Reality, therefore, has Magnitude which by this process is communicated to the Universe.

The Magnitude inherent in each Ideal-Principle- that of a horse or of anything else- combines with Magnitude the Absolute with the result that, irradiated by that Absolute, Matter entire takes Magnitude and every particle of it becomes a mass; in this way, by virtue at once of the totality of Idea with its inherent magnitude and of each several specific Idea, all things appear under mass; Matter takes on what we conceive as extension; it is compelled to assume a relation to the All and, gathered under this Idea and under Mass, to be all things- in the degree in which the operating power can lead the really nothing to become all.

By the conditions of Manifestation, colour rises from non-colour . Quality, known by the one name with its parallel in the sphere of Primals, rises, similarly, from non-quality: in precisely the same mode, the Magnitude appearing upon Matter rises from non-Magnitude or from that Primal which is known to us by the same name; so that material things become visible through standing midway between bare underlie and Pure Idea. All is perceptible by virtue of this origin in the Intellectual Sphere but all is falsity since the base in which the manifestation takes place is a non-existent.

Particular entities thus attain their Magnitude through being drawn out by the power of the Existents which mirror themselves and make space for themselves in them. And no violence is required to draw them into all the diversity of Shapes and Kinds because the phenomenal All exists by Matter and because each several Idea, moreover, draws Matter its own way by the power stored within itself, the power it holds from the Intellectual Realm. Matter is manifested in this sphere as Mass by the fact that it mirrors the Absolute Magnitude; Magnitude here is the reflection in the mirror. The Ideas meet all of necessity in Matter : and Matter, both as one total thing and in its entire scope, must submit itself, since it is the Material of the entire Here, not of any one determined thing: what is, in its own character, no determined thing may become determined by an outside force- though, in becoming thus determined, it does not become the definite thing in question, for thus it would lose its own characteristic indetermination.

(16) An Ideal-Principle approaches and leads Matter towards some desired dimension, investing this non-existent underlie with a magnitude from itself which never becomes incorporate- for Matter, if it really incorporated magnitude, would be a mass.

Eliminate this Ideal-Form and the substratum ceases to be a thing of magnitude, or to appear so: the mass produced by the Idea was, let us suppose, a man or a horse; the horse-magnitude came upon the Matter when a horse was produced upon it; when the horse ceases to exist upon the Matter, the magnitude of the horse departs also. If we are told that the horse implies a certain determined bulk and that this bulk is a permanent thing, we answer that what is permanent in this case is not the magnitude of the horse but the magnitude of mass in general. That same Magnitude might be fire or earth; on their disappearance their particular magnitudes would disappear with them. Matter, then, can never take to itself either pattern or magnitude; if it did, it would no longer be able to turn from being fire, let us say, into being something else; it would become and be fire once for all.

In a word, though Matter is far extended- so vastly as to appear co-extensive with all this sense-known Universe- yet if the Heavens and their content came to an end, all magnitude would simultaneously pass from Matter with, beyond a doubt, all its other properties; it would be abandoned to its own Kind, retaining nothing of all that which, in its own peculiar mode, it had hitherto exhibited.

Where an entrant force can effect modification it will inevitably leave some trace upon its withdrawal; but where there can be no modification, nothing can be retained; light comes and goes, and the air is as it always was.

That a thing essentially devoid of magnitude should come to a certain size is no more astonishing than that a thing essentially devoid of heat should become warm: Matter's essential existence is quite separate from its existing in bulk, since, of course, magnitude is an immaterial principle as pattern is. Besides, if we are not to reduce Matter to nothing, it must be all things by way of participation, and Magnitude is one of those all things.

In bodies, necessarily compounds, Magnitude though not a determined Magnitude must be present as one of the constituents; it is implied in the very notion of body; but Matter- not a Body- excludes even undetermined Magnitude.

(13) We turn to ask why Quantity is not included among the primary genera, and Quality also.

Quantity is not among the primaries, because these are permanently associated with Being. Motion is bound up with Actual Being , since it is its life; with Motion, Stability too gained its foothold in Reality; with these are associated Difference and Identity, so that they also are seen in conjunction with Being. But number is a posterior. It is posterior not only with regard to these genera but also within itself; in number the posterior is divided from the prior; this is a sequence in which the posteriors are latent in the priors . Number therefore cannot be included among the primary genera; whether it constitutes a genus at all remains to be examined.

Magnitude is in a still higher degree posterior and composite, for it contains within itself number, line and surface. Now if continuous magnitude derives its quantity from number, and number is not a genus, how can magnitude hold that status? Besides, magnitudes, like numbers, admit of priority and posteriority.

If, then, Quantity be constituted by a common element in both number and magnitude, we must ascertain the nature of this common element, and consider it, once discovered, as a posterior genus, not as one of the Primaries: thus failing of primary status, it must be related, directly or indirectly, to one of the Primaries.

We may take it as clear that it is the nature of Quantity to indicate a certain quantum, and to measure the quantum of the particular; Quantity is moreover, in a sense, itself a quantum. But if the quantum is the common element in number and magnitude, either we have number as a primary with magnitude derived from it, or else number must consist of a blending of Motion and Stability, while magnitude will be a form of Motion or will originate in Motion, Motion going forth to infinity and Stability creating the unit by checking that advance.

But the problem of the origin of number and magnitude, or rather of how they subsist and are conceived, must be held over. It may, thus, be found that number is among the primary genera, while magnitude is posterior and composite; or that number belongs to the genus Stability, while magnitude must be consigned to Motion. But we propose to discuss all this at a later stage.

(14) How are we to classify the straight line? Shall we deny that it is a magnitude?

The suggestion may be made that it is a qualified magnitude. May we not, then, consider straightness as a differentia of "line"? We at any rate draw on Quality for differentiae of Substance.

The straight line is, thus, a quantity plus a differentia; but it is not on that account a composite made up of straightness and line: if it be a composite, the composite possesses a differentiae of its own.

But why is not the product of three lines included in Quantity? The answer is that a triangle consists not merely of three lines but of three lines in a particular disposition, a quadrilateral of four lines in a particular disposition: even the straight line involves disposition as well as quantity.

Holding that the straight line is not mere quantity, we should naturally proceed to assert that the line as limited is not mere quantity, but for the fact that the limit of a line is a point, which is in the same category, Quantity. Similarly, the limited surface will be a quantity, since lines, which have a far better right than itself to this category, constitute its limits. With the introduction of the limited surface- rectangle, hexagon, polygon- into the category of Quantity, this category will be brought to include every figure whatsoever.

If however by classing the triangle and the rectangle as qualia we propose to bring figures under Quality, we are not thereby precluded from assigning the same object to more categories than one: in so far as it is a magnitude- a magnitude of such and such a size- it will belong to Quantity; in so far as it presents a particular shape, to Quality.

It may be urged that the triangle is essentially a particular shape. Then what prevents our ranking the sphere also as a quality?

To proceed on these lines would lead us to the conclusion that geometry is concerned not with magnitudes but with Quality. But this conclusion is untenable; geometry is the study of magnitudes. The differences of magnitudes do not eliminate the existence of magnitudes as such, any more than the differences of substances annihilate the substances themselves.

Moreover, every surface is limited; it is impossible for any surface to be infinite in extent.

Again, when I find Quality bound up with Substance, I regard it as substantial quality: I am not less, but far more, disposed to see in figures or shapes varieties of Quantity. Besides, if we are not to regard them as varieties of magnitude, to what genus are we to assign them?

Suppose, then, that we allow differences of magnitude; we commit ourselves to a specific classification of the magnitudes so differentiated.

(13) It has been remarked that the continuous is effectually distinguished from the discrete by their possessing the one a common, the other a separate, limit.

The same principle gives rise to the numerical distinction between odd and even; and it holds good that if there are differentiae found in both contraries, they are either to be abandoned to the objects numbered, or else to be considered as differentiae of the abstract numbers, and not of the numbers manifested in the sensible objects. If the numbers are logically separable from the objects, that is no reason why we should not think of them as sharing the same differentiae.

But how are we to differentiate the continuous, comprising as it does line, surface and solid? The line may be rated as of one dimension, the surface as of two dimensions, the solid as of three, if we are only making a calculation and do not suppose that we are dividing the continuous into its species; for it is an invariable rule that numbers, thus grouped as prior and posterior, cannot be brought into a common genus; there is no common basis in first, second and third dimensions. Yet there is a sense in which they would appear to be equal- namely, as pure measures of Quantity: of higher and lower dimensions, they are not however more or less quantitative.

Numbers have similarly a common property in their being numbers all; and the truth may well be, not that One creates two, and two creates three, but that all have a common source.

Suppose, however, that they are not derived from any source whatever, but merely exist; we at any rate conceive them as being derived, and so may be assumed to regard the smaller as taking priority over the greater: yet, even so, by the mere fact of their being numbers they are reducible to a single type.

What applies to numbers is equally true of magnitudes; though here we have to distinguish between line, surface and solid- the last also referred to as "body"- in the ground that, while all are magnitudes, they differ specifically.

It remains to enquire whether these species are themselves to be divided: the line into straight, circular, spiral; the surface into rectilinear and circular figures; the solid into the various solid figures- sphere and polyhedANSWER: whether these last should be subdivided, as by the geometers, into those contained by triangular and quadrilateral planes: and whether a further division of the latter should be performed.

(4) We are told that number is Quantity in the primary sense, number together with all continuous magnitude, space and time: these are the standards to which all else that is considered as Quantity is referred, including motion which is Quantity because its time is quantitative- though perhaps, conversely, the time takes its continuity from the motion.

If it is maintained that the continuous is a Quantity by the fact of its continuity, then the discrete will not be a Quantity. If, on the contrary, the continuous possesses Quantity as an accident, what is there common to both continuous and discrete to make them quantities?

Suppose we concede that numbers are quantities: we are merely allowing them the name of quantity; the principle which gives them this name remains obscure.

On the other hand, line and surface and body are not called quantities; they are called magnitudes: they become known as quantities only when they are rated by number-two yards, three yards. Even the natural body becomes a quantity when measured, as does the space which it occupies; but this is quantity accidental, not quantity essential; what we seek to grasp is not accidental quantity but Quantity independent and essential, Quantity-Absolute. Three oxen is not a quantity; it is their number, the three, that is Quantity; for in three oxen we are dealing with two categories. So too with a line of a stated length, a surface of a given area; the area will be a quantity but not the surface, which only comes under that category when it constitutes a definite geometric figure.

Are we then to consider numbers, and numbers only, as constituting the category of Quantity? If we mean numbers in themselves, they are substances, for the very good reason that they exist independently. If we mean numbers displayed in the objects participant in number, the numbers which give the count of the objects- ten horses or ten oxen, and not ten units- then we have a paradoxical result: first, the numbers in themselves, it would appear, are substances but the numbers in objects are not; and secondly, the numbers inhere in the objects as measures , yet as standing outside the objects they have no measuring power, as do rulers and scales. If however their existence is independent, and they do not inhere in the objects, but are simply called in for the purpose of measurement, the objects will be quantities only to the extent of participating in Quantity.

So with the numbers themselves: how can they constitute the category of Quantity? They are measures; but how do measures come to be quantities or Quantity? Doubtless in that, existing as they do among the Existents and not being adapted to any of the other categories, they find their place under the influence of verbal suggestion and so are referred to the so-called category of Quantity. We see the unit mark off one measurement and then proceed to another; and number thus reveals the amount of a thing, and the mind measures by availing itself of the total figure.

It follows that in measuring it is not measuring essence; it pronounces its "one" or "two," whatever the character of the objects, even summing contraries. It does not take count of condition- hot, handsome; it simply notes how many.

Number then, whether regarded in itself or in the participant objects, belongs to the category of Quantity, but the participant objects do not. "Three yards long" does not fall under the category of Quantity, but only the three.

Why then are magnitudes classed as quantities? Not because they are so in the strict sense, but because they approximate to Quantity, and because objects in which magnitudes inhere are themselves designated as quantities. We call a thing great or small from its participation in a high number or a low. True, greatness and smallness are not claimed to be quantities, but relations: but it is by their apparent possession of quantity that they are thought of as relations. All this, however, needs more careful examination.

In sum, we hold that there is no single genus of Quantity. Only number is Quantity, the rest quantities only in a secondary degree. We have therefore not strictly one genus, but one category grouping the approximate with the primary and the secondary.

We have however to enquire in what sense the abstract numbers are substances. Can it be that they are also in a manner quantitative? Into whatever category they fall, the other numbers can have nothing in common with them but the name. 5. Speech, time, motion- in what sense are these quantities?

Let us begin with speech. It is subject to measurement, but only in so far as it is sound; it is not a quantity in its essential nature, which nature is that it be significant, as noun and verb are significant. The air is its Matter, as it is Matter to verb and noun, the components of speech.

To be more precise, we may define speech as an impact , though it is not so much the impact as the impression which the impact produces and which, as it were, imposes Form . Speech, thus, is rather an action than a quantity- an action with a significance. Though perhaps it would be truer to say that while this motion, this impact, is an action, the counter-motion is an experience ; or each may be from different points of view either an action or an experience: or we may think of speech as action upon a substrate and experience within that substrate.

If however voice is not characteristically impact, but is simply air, two categories will be involved: voice is significant, and the one category will not be sufficient to account for this significance without associating with a second.

With regard to time, if it is to be thought of as a measure, we must determine what it is that applies this measure. It must clearly be either Soul or the Present Moment. If on the contrary we take time to be something measured and regard it as being of such and such extension- a year, for example- then we may consider it as a quantity: essentially however time is of a different nature; the very fact that we can attribute this or that length to it shows us that it is not length: in other words, time is not Quantity. Quantity in the strict sense is the Quantity not inbound with things; if things became quantities by mere participation in Quantity, then Substance itself would be identical with Quantity.

Equality and inequality must be regarded as properties of Quantity-Absolute, not of the participants, or of them not essentially but only accidentally: such participants as "three yards' length," which becomes a quantity, not as belonging to a single genus of Quantity, but by being subsumed under the one head, the one category.

(17) The division, then, of a whole into the parts, is, for the most part, conceived with reference to magnitude; that into the accidents can never be entirely explicated, if, necessarily, essence is inherent in each of the existences.

(11) "But, given Magnitude and the properties we know, what else can be necessary to the existence of body?"

Some base to be the container of all the rest.

"A certain mass then; and if mass, then Magnitude? Obviously if your Base has no Magnitude it offers no footing to any entrant. And suppose it sizeless; then, what end does it serve? It never helped Idea or quality; now it ceases to account for differentiation or for magnitude, though the last, wheresoever it resides, seems to find its way into embodied entities by way of Matter."

"Or, taking a larger view, observe that actions, productive operations, periods of time, movements, none of these have any such substratum and yet are real things; in the same way the most elementary body has no need of Matter; things may be, all, what they are, each after its own kind, in their great variety, deriving the coherence of their being from the blending of the various Ideal-Forms. This Matter with its sizelessness seems, then, to be a name without a content."

Now, to begin with: extension is not an imperative condition of being a recipient; it is necessary only where it happens to be a property inherent to the recipient's peculiar mode of being. The Soul, for example, contains all things but holds them all in an unextended unity; if magnitude were one of its attributes it would contain things in extension. Matter does actually contain in spatial extension what it takes in; but this is because itself is a potential recipient of spatial extension: animals and plants, in the same way, as they increase in size, take quality in parallel development with quantity, and they lose in the one as the other lessens.

No doubt in the case of things as we know them there is a certain mass lying ready beforehand to the shaping power: but that is no reason for expecting bulk in Matter strictly so called; for in such cases Matter is not the absolute; it is that of some definite object; the Absolute Matter must take its magnitude, as every other property, from outside itself.

A thing then need not have magnitude in order to receive form: it may receive mass with everything else that comes to it at the moment of becoming what it is to be: a phantasm of mass is enough, a primary aptness for extension, a magnitude of no content- whence the identification that has been made of Matter with The Void.

But I prefer to use the word phantasm as hinting the indefiniteness into which the Soul spills itself when it seeks to communicate with Matter, finding no possibility of delimiting it, neither encompassing it nor able to penetrate to any fixed point of it, either of which achievements would be an act of delimitation.

In other words, we have something which is to be described not as small or great but as the great-and-small: for it is at once a mass and a thing without magnitude, in the sense that it is the Matter on which Mass is based and that, as it changes from great to small and small to great, it traverses magnitude. Its very undeterminateness is a mass in the same sense that of being a recipient of Magnitude- though of course only in the visible object.

In the order of things without Mass, all that is Ideal-Principle possesses delimitation, each entity for itself, so that the conception of Mass has no place in them: Matter, not delimited, having in its own nature no stability, swept into any or every form by turns, ready to go here, there and everywhere, becomes a thing of multiplicity: driven into all shapes, becoming all things, it has that much of the character of mass.

(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.

(11) Passing to Quantity and the quantum, we have to consider the view which identifies them with number and magnitude on the ground that everything quantitative is numbered among Sensible things or rated by the extension of its substrate: we are here, of course, discussing not Quantity in isolation, but that which causes a piece of wood to be three yards long and gives the five in "five horses,"

Now we have often maintained that number and magnitude are to be regarded as the only true quantities, and that Space and Time have no right to be conceived as quantitative: Time as the measure of Motion should be assigned to Relation, while Space, being that which circumscribes Body, is also a relative and falls under the same category; though continuous, it is, like Motion, not included in Quantity.

On the other hand, why do we not find in the category of Quantity "great" and "small"? It is some kind of Quantity which gives greatness to the great; greatness is not a relative, though greater and smaller are relatives, since these, like doubleness, imply an external correlative.

What is it, then, which makes a mountain small and a grain of millet large? Surely, in the first place, "small" is equivalent to "smaller." It is admitted that the term is applied only to things of the same kind, and from this admission we may infer that the mountain is "smaller" rather than "small," and that the grain of millet is not large in any absolute sense but large for a grain of millet. In other words, since the comparison is between things of the same kind, the natural predicate would be a comparative.

Again, why is not beauty classed as a relative? Beauty, unlike greatness, we regard as absolute and as a quality; "more beautiful" is the relative. Yet even the term "beautiful" may be attached to something which in a given relation may appear ugly: the beauty of man, for example, is ugliness when compared with that of the gods; "the most beautiful of monkeys," we may quote, "is ugly in comparison with any other type." Nonetheless, a thing is beautiful in itself; as related to something else it is either more or less beautiful.

Similarly, an object is great in itself, and its greatness is due, not to any external, but to its own participation in the Absolute Great.

Are we actually to eliminate the beautiful on the pretext that there is a more beautiful? No more then must we eliminate the great because of the greater: the greater can obviously have no existence whatever apart from the great, just as the more beautiful can have no existence without the beautiful.

(9) But how can we conceive a thing having existence without having magnitude?

We have only to think of things whose identity does not depend on their quantity- for certainly magnitude can be distinguished from existence as can many other forms and attributes.

In a word, every unembodied Kind must be classed as without quantity, and Matter is unembodied.

Besides quantitativeness itself does not possess quantity, which belongs only to things participating in it, a consideration which shows that Quantitativeness is an Idea-Principle. A white object becomes white by the presence of whiteness; what makes an organism white or of any other variety of colour is not itself a specific colour but, so to speak, a specific Reason-Principle: in the same way what gives an organism a certain bulk is not itself a thing of magnitude but is Magnitude itself, the abstract Absolute, or the Reason-Principle.

This Magnitude-Absolute, then, enters and beats the Matter out into Magnitude?

Not at all: the Matter was not previously shrunken small: there was no littleness or bigness: the Idea gives Magnitude exactly as it gives every quality not previously present.

(1) It is suggested that multiplicity is a falling away from The Unity, infinity being the complete departure, an innumerable multiplicity, and that this is why unlimit is an evil and we evil at the stage of multiplicity.

A thing, in fact, becomes a manifold when, unable to remain self-centred, it flows outward and by that dissipation takes extension: utterly losing unity it becomes a manifold since there is nothing to bind part to part; when, with all this outflowing, it becomes something definite, there is a magnitude.

But what is there so grievous in magnitude?

Given consciousness, there will be, since the thing must feel its exile, its sundrance from its essence. Everything seeks not the alien but itself; in that outward moving there is frustration or compulsion; a thing most exists not when it takes multiplicity or extension but when it holds to its own being, that is when its movement is inward. Desire towards extension is ignorance of the authentically great, a movement not on the appropriate path but towards the strange; to the possession of the self the way is inward.

Consider the thing that has taken extension; broken into so many independent items, it is now those several parts and not the thing it was; if that original is to persist, the members must stand collected to their total; in other words, a thing is itself not by being extended but by remaining, in its degree, a unity: through expansion and in the measure of the expansion, it is less itself; retaining unity, it retains its essential being.

Yet the universe has at once extension and beauty?

Yes; because it has not been allowed to slip away into the limitless but is held fast by unity; and it has beauty in virtue of Beauty not of Magnitude; it needed Beauty to parry that magnitude; in the degree of its extension it was void of beauty and to that degree ugly. Thus extension serves as Matter to Beauty since what calls for its ordering is a multiplicity. The greater the expansion, the greater the disorder and ugliness.

(12) It follows that we must allow contrariety to Quantity: whenever we speak of great and small, our notions acknowledge this contrariety by evolving opposite images, as also when we refer to many and few; indeed, "few" and "many" call for similar treatment to "small" and "great."

"Many," predicated of the inhabitants of a house, does duty for "more": "few" people are said to be in the theatre instead of "less."

"Many," again, necessarily involves a large numerical plurality. This plurality can scarcely be a relative; it is simply an expansion of number, its contrary being a contraction.

The same applies to the continuous , the notion of which entails prolongation to a distant point.

Quantity, then, appears whenever there is a progression from the unit or the point: if either progression comes to a rapid halt, we have respectively "few" and "small"; if it goes forward and does not quickly cease, "many" and "great."

What, we may be asked, is the limit of this progression? What, we retort, is the limit of beauty, or of heat? Whatever limit you impose, there is always a "hotter"; yet "hotter" is accounted a relative, "hot" a pure quality.

In sum, just as there is a Reason-Principle of Beauty, so there must be a Reason-Principle of greatness, participation in which makes a thing great, as the Principle of beauty makes it beautiful.

To judge from these instances, there is contrariety in Quantity. Place we may neglect as not strictly coming under the category of Quantity; if it were admitted, "above" could only be a contrary if there were something in the universe which was "below": as referring to the partial, the terms "above" and "below" are used in a purely relative sense, and must go with "right" and "left" into the category of Relation.

Syllable and discourse are only indirectly quantities or substrates of Quantity; it is voice that is quantitative: but voice is a kind of Motion; it must accordingly in any case be referred to Motion, as must activity also.

(18) The Ideal Principle possessing the Intellection of Magnitude- assuming that this Intellection is of such power as not merely to subsist within itself but to be urged outward as it were by the intensity of its life- will necessarily realize itself in a Kind not having its being in the Intellective Principle, not previously possessing the Idea of Magnitude or any trace of that Idea or any other.

What then will it produce by virtue of that power?

Not horse or cow: these are the product of other Ideas.

No: this Principle comes from the source of Magnitude and therefore Matter can have no extension, in which to harbour the Magnitude of the Principle, but can take in only its reflected appearance.

To the thing which does not enjoy Magnitude in the sense of having mass-extension in its own substance and parts, the only possibility is that it present some partial semblance of Magnitude, such as being continuous, not here and there and everywhere, that its parts be related within it and ungapped. An adequate reflection of a great mass cannot be produced in a small space- mere size prevents- but the greater, pursuing the hope of that full self-presentment, makes progress towards it and brings about a nearer approach to adequate mirroring in the parallel from which it can never withhold its radiation: thus it confers Magnitude upon that which has none and cannot even muster up the appearance of having any, and the visible resultant exhibits the Magnitude of mass.

Matter, then, wears Magnitude as a dress thrown about it by its association with that Absolute Magnitude to whose movement it must answer; but it does not, for that, change its Kind; if the Idea which has clothed it were to withdraw, it would once again be what it permanently is, what it is by its own strength, or it would have precisely the Magnitude lent to it by any other form that happens to be present in it.

The Soul- containing the Ideal Principles of Real-Beings, and itself an Ideal Principle- includes all in concentration within itself, just as the Ideal Principle of each particular entity is complete and self-contained: it, therefore, sees these principles of sensible things because they are turned, as it were, towards it and advancing to it: but it cannot harbour them in their plurality, for it cannot depart from its Kind; it sees them, therefore, stripped of Mass. Matter, on the contrary, destitute of resisting power since it has no Act of its own and is a mere shadow, can but accept all that an active power may choose to send. In what is thus sent, from the Reason-Principle in the Intellectual Realm, there is already contained a degree of the partial object that is to be formed: in the image-making impulse within the Reason-Principle there is already a step or we may put it that the downward movement from the Reason-Principle is a first form of the partial: utter absence of partition would mean no movement but repose. Matter cannot be the home of all things in concentration as the Soul is: if it were so, it would belong to the Intellective Sphere. It must be all-recipient but not in that partless mode. It is to be the Place of all things, and it must therefore extend universally, offer itself to all things, serve to all interval: thus it will be a thing unconfined to any moment but laid out in submission to all that is to be.

But would we not expect that some one particularized form should occupy Matter and so exclude such others as are not able to enter into combination?

No: for there is no first Idea except the Ideal Principle of the Universe- and, by this Idea, Matter is all things at once and of the particular thing in its parts- for the Matter of a living being is disparted according to the specific parts of the organism: if there were no such partition nothing would exist but the Reason-Principle.

(1) Seen from a distance, objects appear reduced and close together, however far apart they be: within easy range, their sizes and the distances that separate them are observed correctly.

Distant objects show in this reduction because they must be drawn together for vision and the light must be concentrated to suit the size of the pupil; besides, as we are placed farther and farther away from the material mass under observation, it is more and more the bare form that reaches us, stripped, so to speak, of magnitude as of all other quality.

Or it may be that we appreciate the magnitude of an object by observing the salience and recession of its several parts, so that to perceive its true size we must have it close at hand.

Or again, it may be that magnitude is known incidentally from the observation of colour. With an object at hand we know how much space is covered by the colour; at a distance, only that something is coloured, for the parts, quantitatively distinct among themselves, do not give us the precise knowledge of that quantity, the colours themselves reaching us only in a blurred impression.

What wonder, then, if size be like sound- reduced when the form reaches us but faintly- for in sound the hearing is concerned only about the form; magnitude is not discerned except incidentally.

Well, in hearing magnitude is known incidentally; but how? Touch conveys a direct impression of a visible object; what gives us the same direct impression of an object of hearing?

The magnitude of a sound is known not by actual quantity but by degree of impact, by intensity- and this in no indirect knowledge; the ear appreciates a certain degree of force, exactly as the palate perceives by no indirect knowledge, a certain degree of sweetness. But the true magnitude of a sound is its extension; this the hearing may define to itself incidentally by deduction from the degree of intensity but not to the point of precision. The intensity is merely the definite effect at a particular spot; the magnitude is a matter of totality, the sum of space occupied.

Still the colours seen from a distance are faint; but they are not small as the masses are.

True; but there is the common fact of diminution. There is colour with its diminution, faintness; there is magnitude with its diminution, smallness; and magnitude follows colour diminishing stage by stage with it.

But, the phenomenon is more easily explained by the example of things of wide variety. Take mountains dotted with houses, woods and other land-marks; the observation of each detail gives us the means of calculating, by the single objects noted, the total extent covered: but, where no such detail of form reaches us, our vision, which deals with detail, has not the means towards the knowledge of the whole by measurement of any one clearly discerned magnitude. This applies even to objects of vision close at hand: where there is variety and the eye sweeps over all at one glance so that the forms are not all caught, the total appears the less in proportion to the detail which has escaped the eye; observe each single point and then you can estimate the volume precisely. Again, magnitudes of one colour and unbroken form trick the sense of quantity: the vision can no longer estimate by the particular; it slips away, not finding the stand-by of the difference between part and part.

It was the detail that prevented a near object deceiving our sense of magnitude: in the case of the distant object, because the eye does not pass stage by stage through the stretch of intervening space so as to note its forms, therefore it cannot report the magnitude of that space.

(57) Timaeus: not merely a triangle of one definite size, but larger and smaller triangles of sizes as numerous as are the classes within the Kinds. Consequently, when these are combined amongst themselves and with one another they are infinite in their variety; and this variety must be kept in view by those who purpose to employ probable reasoning concerning Nature. Now, unless we can arrive at some agreed conclusion concerning Motion and Rest, as to how and under what conditions they come about,

(5) How then can a multitude of essential beings be really one?

Obviously either the one essence will be entire in all, or the many will rise from a one which remains unaltered and yet includes the one- many in virtue of giving itself, without self-abandonment, to its own multiplication.

It is competent thus to give and remain, because while it penetrates all things it can never itself be sundered: this is an identity in variety.

There is no reason for dismissing this explanation: we may think of a science with its constituents standing as one total, the source of all those various elements: again, there is the seed, a whole, producing those new parts in which it comes to its division; each of the new growths is a whole while the whole remains undiminished: only the material element is under the mode of part, and all the multiplicity remains an entire identity still.

It may be objected that in the case of science the constituents are not each the whole.

But even in the science, while the constituent selected for handling to meet a particular need is present actually and takes the lead, still all the other constituents accompany it in a potential presence, so that the whole is in every part: only in this sense is the whole science distinguished from the part: all, we may say, is here simultaneously effected: each part is at your disposal as you choose to take it; the part invites the immediate interest, but its value consists in its approach to the whole.

The detail cannot be considered as something separate from the entire body of speculation: so treated it would have no technical or scientific value; it would be childish divagation. The one detail, when it is a matter of science, potentially includes all. Grasping one such constituent of his science, the expert deduces the rest by force of sequence.

the geometrician, in his analysis, shows that the single proposition includes all the items that go to constitute it and all the propositions which can be developed from it.

It is our feebleness that leads to doubt in these matters; the body obscures the truth, but There all stands out clear and separate.

(9) Anaxagoras, again, in his assertion of a Mind pure and unmixed, affirms a simplex First and a sundered One, though writing long ago he failed in precision.

Heraclitus, with his sense of bodily forms as things of ceaseless process and passage, knows the One as eternal and intellectual.

In Empedocles, similarly, we have a dividing principle, "Strife," set against "Friendship"- which is The One and is to him bodiless, while the elements represent Matter.

Later there is Aristotle; he begins by making the First transcendent and intellective but cancels that primacy by supposing it to have self-intellection. Further he affirms a multitude of other intellective beings- as many indeed as there are orbs in the heavens; one such principle as in- over to every orb- and thus his account of the Intellectual Realm differs from Plato's and, failing reason, he brings in necessity; though whatever reasons he had alleged there would always have been the objection that it would be more reasonable that all the spheres, as contributory to one system, should look to a unity, to the First.

We are obliged also to ask whether to Aristotle's mind all Intellectual Beings spring from one, and that one their First; or whether the Principles in the Intellectual are many.

If from one, then clearly the Intellectual system will be analogous to that of the universe of sense-sphere encircling sphere, with one, the outermost, dominating all- the First will envelop the entire scheme and will be an Intellectual Kosmos; and as in our universe the spheres are not empty but the first sphere is thick with stars and none without them, so, in the Intellectual Kosmos, those principles of Movement will envelop a multitude of Beings, and that world will be the realm of the greater reality.

If on the contrary each is a principle, then the effective powers become a matter of chance; under what compulsion are they to hold together and act with one mind towards that work of unity, the harmony of the entire heavenly system? Again what can make it necessary that the material bodies of the heavenly system be equal in number to the Intellectual moving principles, and how can these incorporeal Beings be numerically many when there is no Matter to serve as the basis of difference?

For these reasons the ancient philosophers that ranged themselves most closely to the school of Pythagoras and of his later followers and to that of Pherekudes, have insisted upon this Nature, some developing the subject in their writings while others treated of it merely in unwritten discourses, some no doubt ignoring it entirely.

(8) What, then, is this Kind, this Matter, described as one stuff, continuous and without quality?

Clearly since it is without quality it is incorporeal; bodiliness would be quality.

It must be the basic stuff of all the entities of the sense-world and not merely base to some while being to others achieved form.

Clay, for example, is matter to the potter but is not Matter pure and simple. Nothing of this sort is our object: we are seeking the stuff which underlies all alike. We must therefore refuse to it all that we find in things of sense- not merely such attributes as colour, heat or cold, but weight or weightlessness, thickness or thinness, shape and therefore magnitude; though notice that to be present within magnitude and shape is very different from possessing these qualities.

It cannot be a compound, it must be a simplex, one distinct thing in its nature; only so can it be void of all quality. The Principle which gives it form gives this as something alien: so with magnitude and all really-existent things bestowed upon it. If, for example, it possessed a magnitude of its own, the Principle giving it form would be at the mercy of that magnitude and must produce not at will, but only within the limit of the Matter's capacity: to imagine that Will keeping step with its material is fantastic.

The Matter must be of later origin than the forming-power, and therefore must be at its disposition throughout, ready to become anything, ready therefore to any bulk; besides, if it possessed magnitude, it would necessarily possess shape also: it would be doubly inductile.

No: all that ever appears upon it is brought in by the Idea: the Idea alone possesses: to it belongs the magnitude and all else that goes with the Reason-Principle or follows upon it. Quantity is given with the Ideal-Form in all the particular species- man, bird, and particular kind of bird.

The imaging of Quantity upon Matter by an outside power is not more surprising than the imaging of Quality; Quality is no doubt a Reason-Principle, but Quantity also- being measure, number- is equally so.

(56) Timaeus: when taken singly each in its several kind, is seen by us, but when many are collected together their masses are seen. And, moreover, as regards the numerical proportions which govern their masses and motions and their other qualities, we must conceive that God realized these everywhere with exactness, in so far as the nature of Necessity submitted voluntarily or under persuasion, and thus ordered all in harmonious proportion. From all that we have hitherto said about these Kinds,