Chapter 15

[1]Cf. p. 90.

[2]Augustin.Soliloq.i. 7. 'Deum et animam scire cupio. Nihilne plus? Nihil omnino.'

[3]'A Principle,' says Herbart (Psychologie als Wissenschaft,Einl.) 'should have the double property of having originally a certainty of its own, and of generating other certainty. The way and manner in which the second comes about is the Method.'

The antithesis between thought and being, between idea and actuality, between notion and object, is almost a commonplace of criticism. Between the ideas of the subject and objectivity a great gulf seems to yawn fixed and impassable. Thinkers, like Anselm and Descartes, have (it is asserted) attempted by a trick which cheated themselves to get from the notion to the object. But—as Kant is supposed to have for ever shown—thesedecepti deceptoresare now universally discredited.[1]Yet the same Kant had shown that the 'things' of ordinary experience are only ideas or appearances in consciousness. These latter ideas, however, were verified by the necessity of interdependence in which they stood, as given by sense. From the notions which Anselm and Descartes proposed to invest with objectivity, there was absent the feature of sense-perception. They were not limited and real ideas, but synthetic laws, general and abstract aspects of reality, modes of conception. They were not definite and individualised things, but terms or conditions for all concepts and realities. They were forms,—forms essential to the explication of reality—and never mere parts of reality.

With such 'forms' or 'thought-terms,' such abstractions, Logic (à la mode de Hegel) has to deal. And in dealing with them it has to counteract this popular distinction (which Kant inclines toward) which sets up an insuperable division between thought and being, between reality and syllogism, between is and is known. Certain of these denominators which thinking employs to describe reality the popular mind wholly identifies with reality. That being is a thought, that force and thing are only modes of conception, sounds to the untrained intellect only a verbal quibble. Things, beings, are there—out there, it says: force is 'ultimate reality.' It is perhaps ready to allow thatsubstancesare only mental figments: but it is more doubtful about causes, and inclines to assume them to be in outside nature, and to generate a real necessity in things. On the other hand, it has little doubt that concepts and syllogism are only our ways of looking at reality,—the reality of substances and phenomena, with quality and quantity: that 'final cause' is a mere subjective principle of explanation: and that ideas and knowledge are altogether additions superinduced on a real world.

Now what the Logic shows is that, on one hand, all these terms are ideal and regulative; and on the other that they are real, because constitutive of reality. Showing—or shall we say, reminding us—that being is after all a form of thought, it shows us that knowledge, at the other end, contains or implies reality. It is the business of logic as a fundamental philosophy to dispel the illusion that sensations are fixed reality: that causes and effects are an absolutely real order; whereas concepts and sciences and still more aesthetic and moral principles are not. Its doctrine is that all Our thought-terms, the most vulgar and the most delicate, are, as we may put it, symbolical of reality:explications and manifestations of it. Absolutely real—if that means utterly unideal—none of them are. On the other hand, absolutely ideal,—if that means utterly unreal—none of them are either. If you call them real, their reality is that of thought. If you call them ideal, it is an ideality of a real. Being is not a fixed and solid substratum, a hard rock of reality, on which we may build our relations and further determinations. It also is a thought: it also lives in relation, and becomes more real by further determination.[2]But the habit comes natural to the majority to attribute essential and independent reality (total reality) to the thought-modes it is familiar with in practice: whereas the modes familiar to more advanced intelligence are put aside as merely ideal.

Thus in proportion as Logic insists on the reality of idea, it insists also on the ideality of being. Being is after all a thought: when separate from the relations of experience, a very poor thought. A 'supreme being' even is a thought. And the question of questions for Logic is what degree of reality, what amount of truth does each result of unification express. Is it self-consistent and complete, or does it imply further elements, and if so, in what direction does it suggest and receive completion? But at the best the reality of a logical term is an abstract or formal reality, and consists in its power to interpret, to expound, to define the Absolute. Its more concrete and material reality it has in Nature and in Mind. There however Philosophy has in a further measure to repeat its earlier lesson and show that Nature is not without its ideal aspect, and that Mind is founded on physical reality.

All science tends to carry us over the hard lines ofseparation which practical interests treat as if ultimate disruptions. The sciences of Nature, for instance, in their completed circle must carry us from the inorganic to the organic: must in some way make a path from the lifeless to the alive. The science of thought has a corresponding task. It has to show that the incommensurability between thought and being, or between the idea and actuality, disappears on closer examination. When we trace the development of thought sufficiently far, we see that Being is an imperfect or inadequate thought,—certainly not adequate to the Idea, but not for that reason generically differing from it. The fixity of Being as more than, and superior to, mere Thought is a habit of mind, due to the same worldly-minded immobility as leads us all to believe (and, within the limited practical range, to believe rightly) that the earth is solidly at rest, notwithstanding all the demonstrations of the Copernicans. But Thought has not deposited all its burden, or uttered all its meaning in Being. Being is the veriest abstraction,—the very rudiment of thought—meagre as meagre can be. It is on one side the bare position or affirmation of thought: on the other hand it is the very negation of thought,—if thought be only possible under difference. For a mere 'Is' is a mere indescribable without-difference. There is no such thing as mere Being: or mere Being is mere nothing:mereBeing is not.

The first category of Ontology is that of Being. It is the merest simplicity and meagreness, with nothing definite in it at all: and for that very reason constantly liable to be confused with categories of more concrete burden. It denotes all things, and connotes next to nothing. It does not however mean something which has being; it does not mean definite being: still lessdoes it mean permanent and substantial being. Ordinary language certainly uses being in all these senses. But if we are to be logical, we must not mix up categories with one another: we must take terms at their precise value. Mere Being then is the mere 'Is,' which can give no explanation or analysis of itself: which indescribable in itself: which is an 'Is' and nothing more. The simplest answer to those who invest Being with so much signification, is to ask them to consider the logicalcopula. 'Every school-boy knows' that the 'Is' of the copula disappears in several languages: that it is far from indispensable in Latin: that in Greek e. g. the demonstrative article serves the same purpose. In Hebrew too the pronouns officiate for the so-called substantive verb: and the same verb probably does not exist in the Polynesian family of languages, where its place is supplied by what we call the demonstrative pronoun.[3]In the copula, which according to M. Laromiguiere, as quoted by Mr. Mill, expresses only 'un rapport spécial entre le sujet et l'attribut,' we encounter the mere undeveloped and unexplained unifying of thought, the very abstraction of relativity[4].

In the beginning, then, there is nothing and yet that nothing is. Such is the fundamental antithesis of thought: or the discrepancy which makes itself felt between each several term of thought and the whole Idea of which they are the expression. Being is the term emphasised as absolute by understanding: then the dialectical power, or the consciousness of the whole, steps in to counteract the one-sided element. In other words, thought, the total thought, asks what is Being, mere and simple; and answers mere nothing.[5]The one aspect of the point is as justifiable as the other. In other words the two aspects are indissoluble: they are in one. The term 'Unity,' applied to the relation of Being and Not, may perhaps mislead: and it is therefore better to say that the two points of view are (as Mr. Spencer puts it) at once 'antithetical and inseparable,' An unrelated being, an 'absolute' (i. e. separate and transcendent) reality is an Unknowable, i. e. an ineffable, an unspeakable of which we can legitimately predicate a not- , leaving imagination to fill up the blank after the hyphen. A mere Not, with no substratum which it negatives, is mere Being: and a mere Being, which has no substratum, is a mere Not. The movement upward and the movement downward are here illustrated: and it is evident that they are the same movement[6],—the sameunrest, only differentiated as up and down by sometermininot yet explicitly brought into view. Each—Is and Not—as it seeks to differentiate itself, to make itself clear, passes into the other. In fact, the very vocation, calling, or notion of Being and Nothing, is not Being and Nothing, but the tendency of each to pass into the other. Their truth, in short, is not in themselves, but in their process,—and that process by which the one passes into the other is 'To become.' Try to get at mere Being and you are left with Nought: of mere Nought you can only say it is. The two abstractions have no truth except in the passage into one another: and this passage or transition is 'To become.' Take reality apart from what it leads on to, and from what it has come from, apart from its end or purpose and from its cause, take it as mere being: then this being in its supposed singleness and self-subsistence is really annihilated:stat magni nominis umbra: but it is the name of nothing. True being is always on the way to or from being: to stop is fatal.

This unity or inseparability of opposite elements in a truth or real notion is the stumbling-block to the incipient Hegelian. The respectable citizens of Germany were amazed, says Heine, at the shamelessness of J. G. Fichte, when he proclaimed that the Ego produced the world, as if that had cast doubts on their reality; and the ladies were curious to know whether Madame Fichte was included in the general denial of substantial existence[7]. If easy-going critics treated Fichte in this way, they had even better source for amusement in Hegel. That Being and Nothing is the same was a perpetual fund for jokes, too tempting to be missed.Now, in the baldness, and occasionally paradoxical style, of Hegel's statements, there is some excuse for such exaggerations. Being and Nothing are not merely the same: they are also different: they at least tend to pass into each other. In the technical language of logicians, the question is not what being denotes, but what it connotes. The word 'is' had, it may be, originally a 'demonstrative' meaning, a 'pronominal' force, which in course of time passed from a local or sensuous meaning to express a thought. No doubt 'is' and 'is not' are wide enough apart in our application of them as copula of a proposition: but if we subtract the two terms and leave only the copula standing, the difference of the two becomes inexpressible and unanalysable. In both there is the same statement of immediacy or face-to-faceness: that two things are brought to confront each other,—united, as it were, without producing any real or specific sort of union. If Thought be unifying, Being is the minimum of unification: if Thought be relating, Being is the most abstract of relations. So abstract, indeed, that its relativity is completely lost sight of: so utterly one, that it vanishes in a point. And just because itis(as it seems) out of relations, it must be nothing. No doubt, between the two terms Being and not-Being a difference is meant; when they are employed, a difference is thrown into them; and then they are not the same: but if we keep out of sight what is meant, and stick to the ultimate point which is said, we shall find that mere being and mere nothing are alike inapprehensible by themselves, and that to institute a difference we must go out of and beyond them. Perhaps some approach to the right point of comprehension may be made, if we note that when two people quarrel and can give no reason or further development to theiropposite assertions, the one person's 'is' is exactly equal (apart from subsequent explanations) to the other's 'is not.' The mere 'Is' and 'Is not' have precisely the same amount of content: a mere affirmation or assertion, which is mere nothing,—because connecting, where there is nothing to connect.

The truth of 'is' then turns out 'become': nothingis: all things are coming to be and passing out of being. This illustrates the meaning of the word 'truth' in Hegel. It is partly synonymous with 'concrete,' partly with the 'notion.' With concrete: because to get at the truth, we must take into account a new element, kept out of sight in the mere affirmation of being. With notion: because if we wish to comprehend being, we must grasp it as 'becoming.' For truth lies in transcending the first or merely given. We have to go forward, and to go backward, as it were: forward from being, backward to being: we look before and after. The attempt to isolate the mere point of being is impossible in thought: it would only lead to the 'representation' of being,—i. e. the notion of being would be arrested in its development, and identified probably with a sensible thing, i. e. withsomething, and some concrete thing said to be.

If being, however, is truly apprehended as a passage from the unknown to the known, or as emergence from bare vacuity, then it implies a definiteness, which we missed before. Somewhat has become: or the indeterminate being has been invested with definiteness and distinct character. Mere being (mereIs)is nothing: to be something is must be not something else. The second step in the process to self-realisation therefore is reached: Being has become Somewhat; which is more, because it professes less. The fluid unity or movement from 'is' to 'is not,' andvice versa,has crystallised: and 'There is' is the still imperfectly unified result precipitated. By this term we imply thefinitudeof being,—imply that a portion has been cut off from the vague, and contrasted with something else. In the ordinary application of the word, Being is especially employed to denote this stage of definite being[8]. Thus we speak of bringing something into being: by which we mean, not mere being, but a definite being, or, in short, reality. Reality is determinateness, as opposite to mere vagueness. To be real, it is necessary to be somewhat,—to limit and define. Whatever is anything or is real, iseo factofinite. Even an infinite therefore to be real must submit to self-limitation. This is the necessity of finitude: in order to be anything more and higher, there must come, first of all, a determinate being and reality. But reality, as we have seen, implies negation: it implies limiting, distinction, and dependence. Everything finite, every 'somewhat,' has somewhat else to counteract, narrow, and thwart it. To be somewhat(esse aliquid)is an object of ambition, as Juvenal implies: but it is only an unsatisfactory goal after all. For somewhat always implies something else, by which it is limited: whereas mere being, just because it is nothing, is free from the check of an other.

This, then, is the price to be paid for rising into reality, and coming to be somewhat: there is always somewhat else to be minded. The very point which makes a 'somewhat,' as above a mere 'nothing,' is its determinateness: and determinateness, as at first determinateness from outside, a given and passive determinateness, is also a negation and limit. Now the limit of a thing is that point where it begins to be somewhat else: where it passes out of itself and yieldsto another. Accordingly in the very act of being determined, somewhat is passing over into another: it is altering, and becoming somewhat else. Thus a some-thing' implies for its being the being of somewhat else: its being is as it were only to be beside something else,—it is finite, and alterable, athiswith athatalways in the neighbourhood. Such is the character of determinate being. It leads to an endless series from some to an other, and so onad infinitum:everything as a somewhat, as a determinate being, in reality, presupposes a something else, and that again has some third thing; and so the chain is extended with its everlastingAnd,And, And, (as in the children's way of telling a story). Somewhat-ness is always vexed by the fact that it is not somewhat else: and for that very reason, ceasing to be the primary object, it becomes somewhat else itself; and the other term becomes the somewhat. And so the same story is repeated in endless progression, till one gets wearied with the repetition of finitude which is held out as infinite.

Thus in determinate being as in mere being we see the apparent fixity resolved into a double movement—the alteration from some to somewhat else, andvice versa.But a movement like this implies after all that there is a something which alters: which is alterable, but which alters into somewhat. This somewhat which alters into somewhat, and thus retains itself, is a being which has risen above alteration, which is independent of it because including it: which isfor itself,and not for somewhat else. Thus in order to advance a step further from determinate and alterable being, we have only to keep a firm grasp on both sides of the process, and not suffer the one to slip away from the other. We must not merelysay,but energise the unity of the two 'antithetical yet inseparable' elements we arenaturally disposed to take and leave only as Oneandan Other. Something becomes something else: in short, the one side passes on to the other side of the antithesis, and the limitation is absorbed. The new result is somethinginsomething else: the limit is taken up within: and this being which results is its own limit, i. e. no restrictive limit at all, but self-imposed characteristic and definiteness. It is Being-for-self:—the third step in the process of thought under the general category of Being. The range of Being which began in a vague nebula, and passed into a series of points, is now reduced to a single point, self-complete and whole.

This Being-for-self is a kind of true infinite, which results by absorption of the finite. The false infinite, which has already come before us, is the endless range of finitude, passing from one finite to another, from somewhat to somewhat else, untilsatietysets in with weariness. The true infinite issatisfaction,—the inclusion of the other being into self, so that it is no longer a limit, but a constituent part in the being. Such inclusion in the unity of an idea, of elements which are realistically separate, is termed 'ideality.' The antithesis is reduced to become an organic and dependent part. It still exists, but as no longer outside and independent. Thus in determinate being the determinateness is found in somewhat else: in being-for-self the determinateness is self-realisation. Being-for-self may be shortly expressed by 'one' or 'each': as determinate being a, or an, or by 'some': and Being simple has no nominal equivalent. As 'some' is always fractional or partial, 'each' is always a whole or unit. Mere Being has not the consistency of any noun or pronoun: it is the bare (impersonal) verb.

But 'each for self' expresses the sentiment of an armed neutrality with implicit leanings to universalwar,—thebellum omnium contra omnes.Each is self-centred, independent, resting upon self, and not minding anything else,—which is now thrown out as indifferent into the background. Each is centripetal; anything else is for it a matter of no moment. If determinate being was something to be explained by something other, this is or professed to be self-explanatory, and rests upon itself. It seems purely affirmative, and promises to give a definite unity. But we cannot free thought from negation in this sphere, any more than in the earlier. We may, if we like, assert the absolute self-sufficingness, primariness, and unalterability of each; but a very little reflection shows the opposite to be true. The very notion of each is exclusiveness towards the rest: a negative and, as it were, polemical attitude towards others is the very basis of Being-for-self. One after one, they each rise to confront each, each excluding each, until their self-importance is reduced to be a mere point in a series of points, one amongst many. When that is clearly seen, their qualitative character has disappeared: and there is left only their quantity.[9]The negative attitude of each to each forms a sort of bond connecting them. If to the reference which connects we give the name of attraction, then we may say that the repulsion of each against each is exactly equal to their mutual attraction. And thus, in the language of Hobbes, the universal quarrel is only the other side of the general union in the great Leviathan: repulsion, in the shape of mutual fear, is the principle of attraction. Thus each for self is repeated endlessly: instead of the atom or unit we have a multitude, utterly indifferent to what each is for itself. The mere fact that it is, entitles it to count, and so constitutes quantity.Here we may shortly recapitulate the categories of Quality or Being Proper. It forms three steps or grades: those of indeterminate being: determinate being: self-determined being: or if we speak of them as processes, we have becoming: alteration: attraction and repulsion[10]. From the extreme of abstraction and concentration thought, under the form of Being, passes on to greater determinateness and development. The fixity of mere Being is seen to imply a distinction of elements, and a dependence of one upon the other: where the 'is' and 'is not' part from each other sufficiently to let us distinguish them. This is the stage of finitude: when we say that there is somewhat, but there are others, and imply that any one has an end, a limit, a negation in its nature. These words describe the finite scene,—a fragmentary being which makes an advance upon indeterminateness, but loses its wholeness and is always and necessarily leading on to something else. It is the revulsion from the vague and yet unspecified universal to definite and limited particulars. In the third stage the limit is uplifted and included in the particular, which now contains its negation in itself,—is (by accepting its dependence) independent, is its own ground, and may be called an individual. But an individual, again, implies an aggregate of ones, or a multitude. This being-for-self is an individual or atom: it is the basis of those higher developments known as subjectivity and personality. These are, as it were, higher multiples of it.

This first sphere of thought, apparently so abstruse and unreal in its abstractions, had to be thus narrowly discussed because it presents all the difficulties and peculiarities of Hegel in their elementary form. Theyare clearly the fundamental problems of ancient Greek philosophy—of that first or fundamental philosophy which discusses Being and its intrinsic attributes or accidents. Modern superficiality has sometimes reproached these old thinkers (who, forsooth, 'knew no language but their own') for their tiresome insistence on this problem of Is and Is not. Compared, indeed, with what are called topics of interest, e. g. the Soul and the Hereafter, or the origins of the Cosmic process, tiresome such inquiry is. But it is the bitter lesson of experience that till such fundamentals are at least critically surveyed, the interesting topics will still (and in more than one sense) belong to the Unknowable. Herbart not less than Hegel sees it is the prime business of philosophical criticism (i. e. of philosophy) to examine thoroughly those primary notions on which the whole structure of thought rests. It is on the comprehension of the radical limitations latent in the seemingly simplest terms of thought, that the profoundest problems of human interest ultimately turn.

Thus, in the first place, the process of Being, as seen in the light of the whole system of Logic, shows that reality is truly known only as a trinity,—or perhaps rather as a duality in unity. This is the 'Notion' or 'Grasp' of Being. First, reality seems an unspecialised and self-centred being,—and that by itself is mere nothing: a mereuniversal.Second, it appears a specialised and differentiated being of some and other: a mereparticular, limited by other particulars, and so finite. Third, as a combination of the two earlier stages: as wholeness with determinateness, as unity; and so anindividualwhich is thetrueor complete and authentic character of all being. In themetaphysicsof Being these three elements follow, one after another: but in thelogicof the notion they interpenetrate,and each of them is the others and the total. The truth or the notion of being takes it in Being-for-self as a universalised particular or as an individual.—In the second place: the sphere of mere Being is that ofmereidentity: that of determinate being is the sphere of otherness, difference: that of self-determined being is the sphere of well-grounded existence.—Thirdly: the first sphere may be illustrated by the freedom of indeterminateness, expressed by the word 'may': the second by necessity or determinateness, expressed by the word 'must': and the third, by the freedom which even in its determinateness is self-determining, expressed by the word 'will.'—Fourthly: these steps illustrate the meaning of the Hegelian technical termssetzen:aufheben: an sich:für sich:Idealität: Realität.Thus Determinate Being or somewhat isan sichor implicitly (by implication) somewhat else: and the process of determinate being is to lay it down or express (setzen) it as such. When this explicitly-stated 'other' or limit is included in the Being, and reduced into a unity with somewhat in each Being-for-self, it is said to be 'aufgehoben'—uplifted, as it were, so that it is no longer a separate existent, but is still an efficient element. As being partlythis,and partlythat,nowone,and now another,which limits and is limited, determinate being isRealität.The characteristic of reality is externality of its parts, which are thus left side by side quasi-independent: that of ideality is unity and solidarity of function. When the mutual dependence of elements is tightened till it becomes equivalent to unity and totality, these elements are seen in their Ideality (Idealität). Such a total has the others in it as elements (Momente); they are there ideally (ideëller Weise,) as it were (in the loose analogical use of that term) organically: that is, they are denied theprivilege, which their total has, of being-for-themselves. They do not enjoy the benefit of their own being, though their presence is felt.—Fifthly: Being-for-self is absolute negativity; i.e. the negation of negation. Determinate being was a negation of Being mere and simple: Being-for-self is the negation of this, and so a return to true affirmation, as including the element of negation.

Being seemed to describe a complete reality. But its latent limitation has become explicit. It only retains itself by a self-assertion which leaves it a mere abstract unit, or atom,—a unit with nothing in it to be united,-and where it matters not whether it be somewhat or other. The quality of Being, in which all qualitative attributes are lost and sunk, is Quantity: the characteristic of which is to be a matter of no importance to Being, as it originally presents itself. In other words, whilst Quality is identical with Being,—while Being means qualitativeness, and the Being of a thing means its quality, or constitution; Quantity is external to Being, and a thing is, while its quantity undergoes all sorts of variation. At least this is true within certain limits: for quantity is not an ultimate category any more than quality. But for the present the truth of quality is quantity; or, in other words, if a thing is to be anything definite it must ultimately rest on a solid atom: must be a unit and amenable to measurement. First come qualities, such as sweet, green, and the like: these seem to be truth and reality to the senses and the natural mind: and in their universality are represented by the abstract terms of qualitative being. The first step in the progress of knowledge consists in seeing that quality presupposes quantity. Number, in short, is the proximate truth to which the vague qualitative distinction ofa, some,andeachis to be reduced. The qualitativedifferences of sounds are reduced to relations or ratios of number: and so are the other data of sensation. We see this truth recognised in the Atomic School, which may be taken to represent the summing-up of that period of thought which begins with the 'Being' of Parmenides, and the 'Becoming' of Heraclitus. When Democritus says that, although bitter and sweet are conventional distinctions, yet in reality there is only atoms and void[11], he is introducing a distinction between real and apparent. But again the irregular and sporadic appearances of species of quality are replaced by a gradual and regular series of quantities. With mere Being you have a conception quite unfit for describing the manifold reality. But by breaking up the whole Being into a countless number of atoms of being, you get the means of establishing an equation between a given sensible and some multiple of the atomic unit. Thus Atomism, with its many bits of being and its interfluent non-being in which they can unite, replaces the total and complete universe of being and its attendant shadow of unreality, the world of opinion. Still theIs notclings to theIs: if each atom seems complete, they are subject to a necessity which forces them by negation, i. e. by the void (as Atomism figuratively calls the repulsion of the atoms) to meet each other and form apparent unities. Before a step could be made to higher problems, it was necessary to see that the proximate truth of the qualitative world,—or world of sense proper (ἰδία αἴσθησις) is in its simplest terms a quantitative world, or world of common sensibles (κοινὰ αἴσθητα), universalised sensibles, number and quantity.

The sphere of quantity need only be briefly sketched.It has its three heads: (1) quantity in general,—the universal and vague notion of quantitativeness, the mere conception of reality as the Great and the Little, or the More and Less[12]: (2) Quantum, or defined quantity, expressed in the shape of a number: and (3) the quantitative ratio or degree, which is the individualisation or self-determination of numbers, or their application to one another,—which gives the real meaning and value of numbers. The fundamental antithesis, which we found in quality, comes before us here more definitely as the opposition of many ones in one number. In every quantity there are the two elements: the 'one,' unity or solidarity, which renders a total number possible, and the 'many' or multiplicity, which gives it real body and character. By this quantitative law, reality must always be both Continuous and Discrete. Thus when I regard a line as consisting of a number of points I treat it as a discrete quantity: as many in one. When, on the other hand, I regard the line as the unity of these points, it becomes a continuous quantity. These distinctions are not so trivial as they may appear: they lie at the bases of paradoxes like those by which Zeno disproved the ordinary representations of motion, and when a M.P. informs the House of Commons that it is impossible to divide 73l. 1s. 6d. by 1l. 2s. 6d., he is, like Zeno, and perhaps more unconsciously, forgetting that these quantities are not merely continuous but discrete.

The Pythagoreans, according to the tradition of antiquity, philosophised number. In it they found the reality, or the principle of things,—the characteristic feature which dominated existence, and by whichthe world in all its multiplicity could be made coherent and intelligible. They saw it composed of two elements: a limit or limiting, and an unlimited: the latter as it were a dark ground, measureless and endless, on which definiteness was gradually marked out. Such a limiting principle would be e. g. the unit of number. But the full definiteness of number only comes out when a numerical scale is fixed on, in which each number bears a definite ratio to what goes before and what comes after. Each number in such a scale is really a multiple of its unit: a product of its unity into its multeity, of the monad into the indefinite duad. It is this view of each number, as the product of its prime unit with the ratio, which comes explicitly to the fore in Degree, or quantitative ratio. Each so-called quantitative statement is thus a ratio between a given quantity in the object and an assumed standard or unit of number.

These implications latent in quantitative order or determination come out in mensuration. If quantitative or numerical precision is to have a real basis, it presupposes the existence of a qualitative atom or unit which shall be the Measure. Measure is therefore the truth and the unity of quantity and quality: each refers forward and backward to the other, and both lead up to or imply a modulus, or standard unit. Such a standard unit may seem, at first sight, to be a matter of arbitrary choice and imposition. There seems to be no ultimate reason for taking the foot or the cubit as unit of measurement: and if the original foot or cubit be the king's limb, it is easy to say that the whole thing is conventional and artificial. But it is evident on further reflection, first that the foot or the pace is the natural and primitive measurer of lengths of space for the human being, and secondly that the particular foot which is imposed as the measure is taken as beingnormal and typical. So too it is partly arbitrary choice which fixes upon the starting-point for the scale of temperatures: but here also the range from freezing-point to boiling-point of the commonest of liquids affords a sufficient standard from which naturally to carry on the scale above or below it.

What happens is therefore that what is the rule, the standard,—we may also say, the test of being, is the natural mean or average. The measure presents itself as the permanent and regular proportion of quantity and quality. It is the amount or quantity at which things settle down in equilibrium and produce the quality or characteristic feature of the object. To say that Measure is the supreme category or the truth of being—of that superficial being which merely is—of the mere fact of perception—is to say that the prime or governing feature of reality, its obviously dominant characteristic in this sphere, is a self-imposing harmony and proportion. It naturally arranges itself—defines and describes itself in rhythmic series, in regular scales, in symmetrical schemes. All things are in geometrical proportion, self-defined and uniformly graded. Such a conception and category of reality may be said to be peculiarly Greek. The doctrine of the Mean is well known as a principle of their popular Ethics. But the Mean is an average which is regarded as a Normal,—a regular and permanent mode of being which is equivalent to a standard. The rule is given by the logic of facts and of nature. There is in it an apparent optimism—a belief that what is predominant and fundamental is right: a doctrine of immanent symmetry and order. The mere habitual custom is as such held to be the right and good. It is true, no doubt, that Protagoras came to point out that this Measure was not inherent in things, but came from Man, the measure ofall things: and that the later philosophy had to show how the conception of reality should be re-construed, if the objectivity of Measure and symmetry in the universe were still to be maintained. Still even with this correction the belief remained down to the Stoic School that being is essentially self-ordering: that Nature is immanent proportion.

The Measure thus emerging as the Mean, which stands out as the permanent background or recurrent same amidst varying extremes, is set against these divergencies and used to measure them. It has to serve as a denominator for all of these: or each of these differences has a definite ratio to it. For that purpose it must be so graded or present such a scale that the smallest difference from it that exists may be measured, estimated and defined in terms of it. It is here out of place to consider how this can be accomplished,—how mensuration in any case is solved as a problem of scientific determination. What is more important is to note the fact that appearances everywhere start up to testify to the incompatibility of the two elements in measure,—to their tendency to fly away from each other. It is only within certain ranges that quantity and quality change proportionately to each other. The colour spectrum, the scale of musical notes, the series of chemical combination, the order of the planets, all are found in experience up to some point to follow a symmetrical order, and exhibit a measure. But after that point is reached, a sudden change or transition occurs. There is a break in the continuity of being: without warning, a new series of physical manifestation, having a new rule or measure, emerges by a sort of catastrophe. So also, it is only to a certain portion of the process of physical order in the human body that psychical changes are found to correspond.Everywhere the correspondence or harmony or proportion of immediate fact has its breaks,—its sudden emergencies into a new range of being.

It is on the repeated evidence of this fact—the discontinuity of immediate being, the inexplicable gulfs which separate its ordered provinces from one another, that we rise to the distinction of two orders or grades of being: a double aspect of reality. The primitive consciousness is, we may suppose, confined to one level of being, one world. And so long as the facts remain within limits there is no need to go further. The measure is the rule. But the uniformity breaks down abruptly[13]: the rule has its inevitable exceptions: it is no law or principle, but only the factual majority within a fixed range. Thus the measure, to fulfil all that is expected of it, and be a full expression or definition of reality, must go beyond a mere measure: must become the essence, or rather give place to the essence. In order to explain the irregularity and want of measure which turns up if we exceed the narrow provinces of being, we are forced on the conception of a being, one permanent and the same, set in relation, antithetical but inseparable, to an other being, manifold, changing, and different. The undying rhythm, the ceaseless symmetry retreat into the further region—the world beyond: while the older surface-being, as set against it, comes to be a mere phenomenon or appearance, a derivative and dependent something, which has its roots of being in the underlying law and essential reality. But the two planes are still in intimate connexion, in a correlation which becomes more and more palpable as its implications are disclosed and realised.

This change from Measure to Essential Being is onewhich Greek philosophy seems to exhibit in the step from Pythagoreanism to Platonism. Plato himself has noted the passage from what have been called the mathematical to the metaphysical categories, and insisted on the essential and higher truth to which mathematics only point. Mathematical terms give the supreme definiteness to the world of being; they show it as in its several compartments a world immanently ordered and measured. As in Greek Art, all seems to be fully brought to the surface: as the image suggests no further and deeper meaning, but affords an absolute identity of aspect and purport; so the natural and semi-popular philosophy of Greece was satisfied for its ethics with the proportionate, the becoming, the beautiful. Plato however passes beyond the surface, and reflects the apparent fact on a deeper permanent reality behind. That reality is still, in name, only the 'form' or 'shape'— only the regular and permanent type—only the measure. But it is called the really real, theὄντως ὄν,—the being of being. In it the truth is clear, transparent, one and systematic, which in the sensible or immediate world is obscure, confused, multiple. It is the key to explain the difficulties and irregularities of the first and visible scene. Yet even Plato never for a moment forgets the essential correspondence of the two realms, however he may insist upon their separation, and however hard he may find it to explain how being can be duplicated, how the one can be many and yet not cease to be one, how appearance has part in reality.

This indeed is not a difficulty confined to Plato. It is, after all, the same antithesis as we found in the beginning: the Is which lapses into the Is not. It now becomes the play of positive and negative—of perpetual relativity: of a known dependent on an unknown, and an unknown interpreted by a known: an essenceguaranteed by its show or seeming and aScheinwhich supposes permanentSein.How can a thing be, and yet not be true? How can pleasures seem and not be real? Aristotle, taking up the Platonic antithesis of true and apparent being, carries it on into greater detail. Matter and form: possibility and actuality: are amongst his cardinal pairs of correlatives. But he is anxious to maintain their essential relativity: to show that reality only is and maintains itself as the unity of the two poles of universal and particular, reason and sense, or as a syllogism and a development. So far as he succeeds in doing this, Aristotle rises above the correlational view of reality into the comprehension of it as a unity, which carries itself through difference into self-realisation.

[1]What he did show was that these Ideas were not objects in the vulgar sense of reality, or things.

[2]Cf. the controversy between Schiller and Goethe as to idea and observation, quoted by Whewell,Scientific Ideas, i. 36.

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