But 'each for self' expresses the sentiment of an armed neutrality with implicit leanings to universal war,—the bellum 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. They are 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 mere universal. Second, it appears a specialised and differentiated being of some and other: a mere particular, limited by other particulars, and so finite. Third, as a combination of the two earlier stages: as wholeness with determinateness, as unity; and so an individual which is the true or complete and authentic character of all being. In the metaphysics of Being these three elements follow, one after another: but in the logic of 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 of mere identity: 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 terms setzen: aufheben: an sich: für sich: Idealität: Realität. Thus Determinate Being or somewhat is an sich or 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 partly this, and partly that, now one, and now an other, which limits and is limited, determinate being is Realität. 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 the privilege, 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 of a, some, and each is to be reduced. The qualitative differences 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 the Is not clings to the Is: 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 which the 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 being normal 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 of all 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.