Real Measure

§ 742

Measure is now determined as a correlation of measures which constitute the quality of distinct self-subsistent somethings — or things. The relations of measure just considered concern abstract qualities like space and time; those now about to be considered are exemplified in specific gravity and later on in chemical properties, i.e. in determinations characteristic of material existence. Space and time are also moments of such measures but their relationship no longer depends simply on their own nature because they are now subordinated to further determinations.

Among the determining moments in sound, for example, there is the time in which a number of vibrations occur, and the spatial element of length and thickness of the vibrating body; but the magnitudes of those ideal moments are determined externally.

Space and time are no longer in a relation of powers but in the ordinary direct relation, harmony being reduced to a quite external simplicity of numbers whose relations can be grasped with the utmost ease and hence afford a satisfaction falling entirely within the element of sensation since there is an absence for spirit of figurate conception, fantasy, abstract thought, and the like.

In that the sides which now constitute the measure relation are themselves measures, but at the same time real somethings, their measures are, in the first place, immediate measures and as regards their relations, direct relations. It is the inter-relationship of such relations that is now to be considered in its progressive determination.

§ 743

Measure, as now real measure, is first, a self-subsistent measure of a material thing which is related to others and in this relation specifies them and with them their self-subsistent materiality. This specification as an external relating to a plurality of others in general, produces other relations and hence other measures; and the specific self-subsistence does not continue as a single direct relation but passes over into a specific determinateness which is a series of measures. Secondly, the direct relations thus produced are in themselves determinate and exclusive measures (elective affinities); but because the difference between them is also only quantitative, the progressive determination of the relations presents itself as in part a merely externally quantitative development which, however, is also interrupted by qualitative relationships and forms a nodal line of specific self-subsistent measure relations. Thirdly, however, in this development measure gives place to the measureless as such, and more specifically to the infinity of measure. In this, the self-exclusive and self-subsistent measures are one with each other, and the self-subsistent measure enters into a negative relation with itself.

A. THE RELATION OF SELF-SUBSISTENT MEASURES § 744

Measures now are no longer merely immediate but self-subsistent, because they have become in themselves relations of measures which are themselves specified; and thus in this being-for-self are physical somethings, in the first instance, material things. The whole, which is a relation of such measures is, however, (a) first, itself immediate; thus the two sides which are determined as such self-subsistent measures exist apart in particular things and their combination is effected externally; (b) but what the self-subsistent material things are qualitatively, they are only in virtue of their quantitative determination as measures; hence through this same quantitative connection with others they are determined as differently specified in regard to them (so-called affinity), namely, as members of a series of such quantitative relationships; (c) at the same time, this indifferent, manifold interrelationship finishes by converting itself into exclusive being-for-self-so-called elective affinity.

(a) Combination of Two Measures § 745

Something is immanently determined as a measure relation of quanta which also possess qualities and the something is the connection of these qualities. One of them is the being-within-self or inwardness of the something by virtue of which it is a real being-for-self, a material thing (such as, taken intensively, weight, or in its extensive aspect, the multiplicity of material parts); the other quality is the externality of this inwardness (the abstract, ideal element of space). These qualities are quantitatively determined and their correlation constitutes the qualitative nature of the material something — e.g. the ratio of weight to volume: specific gravity. The volume, the ideal aspect, is to be taken as unit, but the intensive aspect, which manifests quantitatively and in comparison with the former as an extensive magnitude, as a plurality of independent ones, is to be taken as amount. The purely qualitative relation of the two specific magnitudes, that is, as a ratio of powers, has vanished, because with the self-subsistence of the material thing immediacy has returned and in this the specific magnitude is an ordinary quantum whose relation to the other side is likewise determined as the ordinary exponent of a direct ratio.

§ 746

This exponent is the specific quantum of the something, but it is an immediate quantum and this is determined and with it the specific nature of such something — only in the comparison with other exponents of such ratios. The exponent constitutes the specific intrinsic determinedness, the inner characteristic measure of something; but because this its measure rests on a quantum, it too is only an external, indifferent determinateness, with the consequence that the something, in spite of its inner determination as a measure, is alterable. The other to which it can, as alterable, enter into relation is not a material plurality, quantum in general — this it can withstand through its specific intrinsic determinedness -but it is a quantum which is at the same time also an exponent of such a specific ratio. Two things with different internal measures stand in relation and enter into combination — such as two metals of different specific gravities (the combination in question would not be, for example, of a metal and water); but what other kind of homogeneity is required to make possible such a combination will not be considered here. Now on the one hand, each of the two measures, just because it is a measure, preserves itself in the alteration which it ought to suffer through the externality of the quantum, but on the other hand this self-preservation is itself a negative relation towards this quantum, a specification of it; and since the quantum is the exponent of the measure relation, the self-preservation is an alteration of the measure itself and moreover a reciprocal specification.

§ 747

As purely quantitatively determined, the compound would be a mere addition of the two magnitudes of the one quality and the two magnitudes of the other, e.g., the sum of the two weights and of the two volumes in the case of a compound of two material substances of different specific gravities; thus not only the weight of the mixture would remain equal to the said sum, but also the space occupied by the mixture would be equal to the sum of the said spaces. But this is true only of the weight of the mixture, which is equal to the sum of the weights before the combination; addition applies to that quality which, as a real being-for-self, has acquired a fixed determinate being with a permanent immediate quantum — the weight of the material thing, or, what counts as the same from the quantitative point of view, the number or amount of material parts. The exponents however are subject to alteration since they are the expression of the qualitative aspect of the compound, of its being-for-self in the form of measure relations; and since the quantum as such suffers contingent external alteration by an increase which is summed, the being-for-self at the same time displays itself as negating this externality. Because this immanent determining of the quantitative element cannot, as we have seen, be manifested in the weight, it displays itself in the other quality which is the ideal side of the relation. From the point of view of sense perception it may appear remarkable that the mixing of two specifically different material substances should be followed by an alteration — usually a diminution-in the sum of the two volumes, for it is space itself which constitutes the subsistence of matter in its external separated existence. But this subsistence in face of the negativity immanent in the being-for-self lacks intrinsic being, it is subject to alteration. In this manner space is posited as what it truly is, an ideal being.

§ 748

Not only, then, is one of the qualitative sides posited as alterable but measure itself — and so too the qualitative nature of the something based on it — has shown that it is unstable in its own self and, like the quantum as such, has its determinateness in other measure relations.

(b) Measure as a Series of Measure Relations § 749

(1) If two things forming a compound body owed their respective specific natures only to a simple qualitative determination, they would only destroy each other when combined. But a thing which is an immanent measure relation is self-subsistent; it is therefore also capable of combining with another such thing. But in being reduced to an element of this unity, it preserves itself through the persistence of its indifferent, quantitative character and at the same time functions as a specifying moment of a new measure relation. Its quality is masked in the quantitative element and is thus also indifferent towards the other measure, continuing itself in it and in the newly formed measure. The exponent of the new measure is itself only some quantum or other, an external determinateness, and its indifference finds expression in the fact that the specifically determined thing effects, in association with other such measures, precisely similar neutralizations of the reciprocal measure relations; it is in only one measure relation formed by itself and another specifically determined thing that its specific peculiarity is not expressed.

§ 750

(2) This combination with a number of others which are likewise measures within themselves, yields different ratios which therefore have different exponents. The self-subsistent measure has the exponent of its intrinsic determinedness only in the comparison with others; its neutrality with the others, however, constitutes its real comparison with them; it is its comparison with them through its own self. But the exponents of these ratios differ and the qualitative exponent of the self-subsistent measure is thus represented as the series of these different amounts of which it is the unit, i.e. as a series whose members are in a specific relationship to others. The qualitative exponent, as one immediate quantum, expresses only one relation. The distinctive character of the self-subsistent measure finds its true expression in the characteristic series of exponents which it, taken as unit, forms with other such self-subsistent measures; for one of these measures when brought into relation with the rest of them and taken as unit forms another series. Now it is the interrelationship of the members of such a series that constitutes the qualitative aspect of the self-subsistent measure.

§ 751

At first, it seems that a self-subsistent measure which forms a series of exponents with a series of such measures, is distinguished from another measure — outside this series — with which it is compared, by the fact that this other measure forms another series of exponents with the members of the first series. But in this way these two measures would not be comparable, because each is thus regarded as unit with respect to its exponents, and between the two series arising from this relation there is no specified difference. The two measures which, as self-subsistent, are supposed to be compared are at first contra-distinguished only as quanta; in order to determine their relation, an independent unit common to them both is required. This specific unit is to be sought, as has been indicated, only in that feature which embodies the specific determinate being of the measures to be compared, i.e. in the ratio which the exponents of the ratios of the members of the series have to each other. This ratio of the exponents themselves is, however, such independent and actually specific unit only in so far as the members of the series together have it as a constant ratio to both measures; in that way it can be their common unit. It is this alone, therefore, which makes it possible to compare the two self-subsistent measures which were assumed to be not reciprocally neutralising measures, but indifferent to each other. Each of them taken separately and apart from the comparison is the unit of the ratio it forms with the opposite members, which are the amounts relatively to that unit and which thus represent the series of exponents. But conversely, this series is the unit for the two measures which when compared with each other are related as quanta; as such they are themselves different amounts of the unit just indicated.

§ 752

But further, those measures which together with the two, or rather indefinitely many self-subsistent measures of the first series — measures which are compared only with each other — yield a series of exponents of the ratios between the members of that series, are similarly in themselves self-subsistent measures, each being a specific something with its own intrinsic measure ratio. Each of these then is similarly to be taken as unit so that they have a series of exponents in the two, or rather indefinitely many members of the first series which are compared merely among themselves, and these exponents are the numbers resulting from comparison among themselves of the measures just named; and conversely, the comparative numbers of the measures which are now also to be taken singly as self-subsistent are the series of exponents for the members of the first series. In this way, both sides are series in which each number is firstly simply a unit to the opposite series in which it has its self-determined character as a series of exponents; secondly, each number is itself one of the exponents for each member of the opposite series; and thirdly, it is a comparative number for the other numbers of its series and as such amount, which belongs to it also as an exponent, it has its own specifically determined unit in the opposite series.

§ 753

3. In this form of relationship there is a return to the particular kind of way in which quantum is posited as self-determined, i.e., as degree: namely, it is simple or unitary, but it has its quantitative determinateness in a quantum existing outside it, which is a circle of quanta. In measure, however, this external aspect is not merely a quantum and a circle of quanta, but a series of numerical ratios and it is in the entirety of these that the self-determinedness of measure lies. As is the case in the being-for-self of quantum as degree, the nature of the self-subsistent measure is converted into this externality of itself. Its self-relation is in the first place an immediate relation and therefore its indifference to an other consists only in the quantum. It is into this externality therefore that its qualitative side falls and its relationship to its other becomes that quantitative mode of relationship which constitutes the specific determination of this self-subsistent measure, a mode which is determined just as much by the other as by the measure itself; and this other is a series of quanta and the measure is reciprocally a quantum. But this relation in which two specific measures specify themselves in a third something, the exponent, also implies that the one has not passed into the other; that therefore there is not only one negation, but that both are posited as negative in the relation, and since in this each preserves itself as indifferent towards the other its negation is also in turn negated. This their qualitative unity is thus a self-subsistent exclusive unit. It is only as exclusive that the exponents, which are primarily comparative numbers of the members of the series, have in them their genuinely specific determinateness relatively to one another, and their difference thus acquires a qualitative nature. But this difference has a quantitative basis: first, the self-subsistent measure is related to a plurality of its qualitatively other side only because in this relationship it is, at the same time, indifferent; secondly, the neutral relationship, in virtue of its quantitative aspect, is now not simply an alteration but is posited as a negation of the negation and as an exclusive unit. Consequently, the affinity of a self-subsistent measure with the measures of the other side is no longer an indifferent relationship but an elective affinity.

(c) Elective Affinity § 754

The expression elective affinity used here and the terms neutrality and affinity employed in the preceding paragraphs, refer to the chemical relationship. For a chemical substance has its specific determinateness essentially in its relation to its other and exists only as this difference from it. Furthermore, this specific relation is bound up with quantity and is at the same time the relation, not only to a single other but to a series of specifically different others opposed to it. The combinations with this series are based on a so-called affinity with every member of the series; but along with this indifference each member is at the same time exclusive towards the others and it is this correlation of opposed determinations which we have still to consider. It is, however, not only in the sphere of chemistry that the specific relation is represented in a circle of combinations; the individual note, too, only has meaning in relationship and combination with another note and with a series of others. The harmony or disharmony in such a circle of combinations constitutes its qualitative nature which is at the same time based on quantitative ratios; these form a series of exponents and are the ratios of the two specific ratios which each of the combined notes is in its own self. The individual note is the key of a system, but again it is equally an individual member in the system of every other key. The harmonies are exclusive elective affinities whose characteristic quality is equally dissolved again in the externality of a merely quantitative progression. What it is, however, that constitutes the principle of a measure for those affinities which (whether chemical or musical or what else) are elective affinities between and in opposition to the others, will be the subject of a further Remark in connection with chemical affinity; but this higher question is very closely bound up with the specific nature of the strictly qualitative aspect and belongs to the particular concrete natural sciences.

§ 755

Inasmuch as the member of a series has its qualitative unity in its relation to all the members of an opposite series, whose members however are distinguished only by the quantum required for neutralising them with the member of the first series, the more specific determinateness in this multiple affinity is likewise only quantitative. In elective affinity as an exclusive, qualitative correlation, the relationship is rid of this quantitative difference. The next determination which offers itself is this; that in accordance with the difference of the amounts, that is, of extensive magnitude, of the substances of the one series required for the neutralisation of a substance in the other series, the elective affinity of the latter substance would also be directed towards the substances of the first series with all of which it has an affinity. The exclusion which would thereby be established in the form of a firmer holding together against other possibilities of combination, would appear, thus transformed, in a proportionately greater intensity in virtue of the previously demonstrated identity of the forms of extensive and intensive magnitude, the quantitative determinateness being one and the same in both forms. However, this sudden conversion of the one-sided form of extensive magnitude into its other, intensive form, makes no difference to the nature of the fundamental determination, which is one and the same quantum; consequently, no real exclusion would, in fact, result therefrom and there could take place equally well either only one combination, or a combination of an indefinite number of substances, provided that the portions of them entering into the combination corresponded to the required quantum in accordance with the ratios existing between them.

§ 756

The combination which we have also called neutralisation, however, is not only the form of intensity; the exponent is essentially a measure determination and therefore exclusive. In this aspect of exclusive relations, numbers have lost their continuity with one another and their fluid combinatory nature; the relationship is one of more or less, which acquires a negative character and the preference which one exponent has over another does not remain confined to the quantitative determinateness. But equally, too, there co-exists this other aspect which again makes it a matter of indifference that a substance receives the neutralising quantum from several substances of the opposed series and from each according to its specific ratio relatively to the others; the exclusive, negative relation is thus at the same time adversely affected by the quantitative aspect. The effect of this is an actual conversion of an indifferent, merely quantitative relationship into a qualitative one, and conversely, a transition from a specifically determined relation into a merely external one — a series of relations which are sometimes of a merely quantitative nature and sometimes are specific relations and measures.

Remark: Berthollet on Chemical Affinity and Berzelius’s Theory of it

§ 757

Chemical substances are the most characteristic examples of those measures which, as moments of a measure, are characterised solely by their relationship to other such measure moments. Acids and alkalis or bases generally, appear to be intrinsically determinate things just as they are; but the fact is that they are incomplete elements of bodies, constituents which strictly speaking do not exist for themselves but only as a tendency to get rid of their isolatedness by combining with another constituent. Further, the difference in virtue of which 1 they are self-subsistent, does not consist in this immediate quality but in the peculiar quantitative mode of the relationship. This, namely, is not restricted to the chemical opposition of acid and alkali or base in general, but is a specific measure of saturation and consists in the specific determinateness of the quantity of the substances which neutralise each other. This specific quantity required for saturation constitutes the qualitative nature of a substance; it makes it what it is on its own account and the number which expresses this is essentially one of several exponents for an opposed unit. A substance of this kind has a so-called affinity with another. If this connection remained of a purely qualitative nature, then, as in the case of the magnetic poles or positive and negative electricity, the one determinateness would be only the negative of the other and both sides would not at the same time show themselves to be indifferent towards each other. But because the connection has also a quantitative side, each of these substances is capable of neutralising itself with more than one and is not restricted only to the one to which it is opposed. It is not only an acid and an alkali or base which are in relation, but acids and alkalis or bases which are related to one another. They are specifically distinguished from each other primarily according to whether one acid, for example, requires a greater amount of an alkali for its saturation than another acid does. But the independent, self-determined character of the substances is displayed in the exclusiveness of the relation between the affinities, one having a preference over another in that one acid can by itself enter into combination with any alkali, and conversely. Thus the cardinal difference between two acids consists in one of them having a closer affinity to a base than the other, i.e., in a so-called elective affinity.

§ 758

The law of the chemical affinities of acids and alkalis has been discovered and it states that if two neutral solutions are mixed resulting in dissociation followed by two new compounds, these products, too, are neutral. From this it follows that the amounts of two alkaline bases required for the saturation of an acid must be in the same ratio to saturate another acid; and in general, when for one alkali, taken as unit, the series of numerical ratios has been determined in which the various acids saturate it, then this series is the same for any other alkali, though the different alkalis must be taken in different amounts relatively to one another-amounts which again on their part form a similar fixed series of exponents for each of the opposite acids since they are related to any one acid in the same ratio as to any other. Fischer was the first to extract these series in their simplicity from the works of Richter and Berthollet. Since that was written, our knowledge of the numerical ratios of mixtures of chemical elements has been greatly expanded in every direction and to consider it here would be a digression, all the more so because this empirical expansion which is in part only hypothetical remains confined within the same group of concepts. We may however add a few remarks on the categories employed here and also on the views about chemical elective affinity itself and its relation to the quantitative aspect as well as the attempt to base this on specific physical qualities.

§ 759

It is well known that Berthollet modified the general conception of elective affinity by the concept of the activity of a chemical mass. This modification does not affect the quantitative ratios of the chemical laws of saturation themselves, but its effect on the qualitative moment of exclusive elective affinity as such is not only to weaken it but rather to eliminate it, and this is a point that must not be overlooked. If two acids act on an alkali and the one which has a greater affinity for it is also present in the requisite amount for saturating it, then according to the concept of elective affinity this is the only saturation which occurs; the other acid remains quite inactive and is excluded from the neutral combination. According to the concept of the activity of a chemical mass, on the other hand, each of the two acids is active in a proportion which is composed of the amounts of the acids present and their saturation capacity or so-called affinity. Berthollet’s investigations have indicated in greater detail the circumstances in which the activity of the chemical mass is nullified and one acid (the one with a stronger affinity) appears to expel and to exclude the action of the other acid (with a weaker affinity) that is, appears to be active in the sense of elective affinity. He has shown that this exclusion takes place in certain circumstances, such as strength of cohesion, or the insolubility in water of the salts formed, but the qualitative nature of the agents as such does not come into play; and the action of these circumstances can in turn be nullified by other circumstances, for example, by temperature. With the removal of these obstacles the chemical mass enters unimpeded into activity and what appeared as a purely qualitative exclusion, as an elective affinity, proves to depend only on external modifications.

§ 760

It is Berzelius principally who should be heard further on this subject although in his Textbook of Chemistry he does not put forward anything original or more specific on the matter. The views of Berthollet are taken up and repeated literally, only decked out in the metaphysics peculiar to an uncritical reflection, the categories of which are therefore all that offer themselves for a more detailed consideration. The theory goes beyond the limits of experience and, on the one hand, invents sensuous images such as are not given in experience and on the other hand, applies categories of thought, in both cases making itself a subject for logical criticism. We propose therefore to hear what he has to say about the theory in the Textbook itself. Now there we read ’that one must imagine that in a uniformly mixed liquid, each atom of the dissolved substance is surrounded by an equal number of atoms of the solvent; and if several substances are dissolved together they must share between them the interstices between the atoms of the solvent, so that with a uniform mixture of the liquid there is produced a symmetry in the arrangement of the atoms such that all the atoms of the individual substances are uniformly arranged in relation to the atoms of the other bodies; it could therefore be said that the solution is characterised by symmetry in the arrangement of the atoms, and the combination by the fixed proportions.’ This is then illustrated by an example of compounds formed when sulphuric acid is added to a solution of copper chloride; but the example certainly does not demonstrate that atoms exist; neither does it show that a number of atoms of the dissolved substances surround atoms of the fluid, nor that free atoms of the two acids arrange themselves around the atoms which remain combined (with the copper oxide), nor that there exists a symmetry in their position and arrangement, nor that interstices between the atoms exist — and least of all that the dissolved substances share among themselves the interstices between the atoms of the solvent. This would mean that the atoms of the dissolved substances take up their positions where the solvent is not — for the interstices between the atoms of the solvent are spaces empty of it — and hence that the dissolved substances are not present in the solvent, but rather are outside it, even if the solvent is arranged around them or they around it, and it is also certain therefore that they are not dissolved by it. One fails therefore to see why it is necessary to form such conceptions which are not empirically demonstrated, are in essence directly self-contradictory and are not corroborated in any other way. Corroboration could be provided only by a consideration of these conceptions themselves, i.e. by metaphysics, which is logic; but this cannot confirm them any more than experience can — on the contrary! For the rest, Berzelius admits what was also said above, that Berthollet’s propositions are not opposed to the theory of fixed proportions, although he does add that they are also not opposed to the views of the corpuscular theory, i.e. the ideas mentioned above of atoms, of the filling of the interstices of the solvent by the atoms of the solid substances, and so on; this latter baseless metaphysics however, has essentially nothing to do with the proportions of saturation as such.

§ 761

Hence, what finds specific expression in the laws of saturation concerns only the amount of units themselves quantitative (not atoms), of a substance with which the quantitative unit (equally not an atom) of another substance chemically distinct from the first, is neutralised; the difference between them consists solely in these different proportions. When Berzelius, then, notwithstanding the fact that his theory of proportions is wholly and solely a determination of amounts, nevertheless also speaks of degrees of affinity’ in explaining Berthollet’s chemical mass as the sum of the degree of affinity, from the given quantity of the active substance — although Berthollet is more consistent for he uses the expression capacite de saturation — then he himself lapses into the form of intensive magnitude; but it is this form which is the characteristic feature of the so-called dynamic philosophy which earlier on he calls ’the speculative philosophy of certain German schools’,’ and emphatically rejects in favour of the excellent ‘corpuscular theory’. He there states of this dynamic philosophy that it assumes that the elements interpenetrate one another in their chemical combination, and that neutralization consists in this mutual interpenetration; this means nothing else than that the chemically different particles, which are interrelated as a plurality, collapse into the simplicity of an intensive magnitude, a fact which also finds expression as a diminution of volume. In the corpuscular theory, on the other hand, even the atoms which are chemically combined are supposed to be preserved in the interstices, i.e. outside one another (juxtaposition); in such a relationship which is one of merely extensive magnitude, of a perpetuated amount, a degree of affinity has no meaning. In the same place it is stated that for the dynamic view the phenomena of specific proportions came as something quite unforeseen; but this would be only an external, historical circumstance, apart from the fact that Richter’s stoechiometric series in Fischer’s compilation of them were already known to Berthollet and are quoted in the first edition of this Logic which proves the nullity of the categories on which the old, like the would-be new, corpuscular theory is based. But Berzelius is in error when he judges that if ’the dynamic view’ had prevailed, the phenomenaof specific proportions would have remained ‘for ever’ unknown-meaning that this view is incompatible with the determinateness of proportions. This is, in any case, only a determinateness of quantity, no matter whether in an extensive or an intensive form; so that even Berzelius, much as he adheres to the first of these forms, that of aggregate or amount [Menge], himself makes use of the conception of degrees of affinity.

§ 762

Since in this way affinity is reduced to a quantitative difference, it is sublated as elective affinity; but the exclusive factor which occurs in it is ascribed to circumstances, i.e. to determinations which appear as something external to the affinity, to cohesion, insolubility of the compounds formed, and so on. A partial comparison may be made between this conception and the manner of considering the effect of gravity on a moving pendulum. Through gravity the- pendulum necessarily passes into a state of rest; but this intrinsic effect of gravity itself is treated as a merely concomitant circumstance of the external resistance of the air, the thread and so on, and it is ascribed solely to friction instead of to gravity. Here it makes no difference to the nature of the qualitative element present in elective affinity whether this is manifested in the form of these circumstances taken as its conditions, and is so interpreted. With the qualitative aspect as such there begins a new order, the specifying of which is no longer only a matter of quantitative difference.

§ 763

Now although the chemical affinity in a series of quantitative ratios has thus been accurately distinguished from elective affinity which occurs as a qualitative determinateness whose behaviour in no way coincides with the order of that series, this distinction in turn gets utterly confused by the way in which electrical action has recently been coupled with chemical action; and the hope that this supposedly profounder principle would throw light on the most important relation, that of measure, has met with complete disappointment. We need not here consider more closely this theory in which the phenomena of electricity and chemistry are completely identified, since it concerns the physical nature of substances and not merely their measure relations and it calls for mention only in so far as the distinctive character of the determinations of measure is confused by it. The theory as such must be dubbed shallow, for shallowness consists in omitting the difference between distinct terms and then treating them as identical. As for affinity, chemical processes being thus identified with electrical, and also with the phenomena of fire and light, this is reduced ’to neutralisation of opposite electricities. It is almost comical to find the identification of electricity and chemical action expounded in the following manner: ‘it is true that electrical phenomena explain the action of bodies at a greater or lesser distance, their attraction before combination (i.e. a behaviour which is not yet chemical) and the fire(?) caused by this combination, but they throw no light on the cause of the combination which persists with such strength after the opposite electrical condition has been destroyed;’ that is to say, the theory tells us that electricity is the cause of the chemical action, but about the specifically chemical nature of the chemical process electricity tells us nothing. Chemical difference as such being thus reduced to the opposition of positive and negative electricity, the different affinities of the agents on either side are determined as the order of two series of electro-posit’ e and electro-negative substances. In identifying electricity and chemical action it is overlooked that the former generally (and its neutralisation) is transient and remains external to the quality of substances, whereas chemical action, especially in the process of neutralisation, embraces and alters the entire qualitative nature of substances. Equally transient within electricity is its opposition of positive and negative; this is so unstable that it is dependent on the most trivial outer circumstances and cannot be compared with the definiteness and fixity of the opposition between acids, for example, and metals, and so on.

§ 764

The alterations which can be produced by chemical action under extremely powerful influences, e.g., of a raised temperature are not comparable with the superficial nature of the opposition in electricity. Also the further distinction within the series of each of the two sides, between a more or less positive-electrical or more or less negative-electrical disposition is quite uncertain and entirely unconfirmed. But it is on the basis of the ’electrical dispositions’ of these series of substances that ’the electro-chemical system is to be set up, which above all would be best fitted to provide an idea of chemistry’: these series are now quoted; but what their nature really is, is indicated in the remark ’that this is approximately the order of these substances, but so little investigation has been made into this matter, that as yet nothing really certain can be ascertained about this relative order. Both the numerical ratios of the series of affinities (first made by Richter) as well as the extremely interesting reduction by Berzelius of the combinations of two substances to the simplicity of a few quantitative ratios, are absolutely independent of that hypothetical electro-chemical hotchpotch. If the experimental method has been the correct guiding star in the theory of proportions and its universal expansion since Richter, then the mixing of these great discoveries with the so-called corpuscular theory, a desert lying away from the path of experience, forms all the greater contrast with it; only this beginning, the abandoning of the principle of experience, could be the reason for taking up again and developing that idea introduced earlier, especially by Ritter, namely, the setting up of fixed classifications of electro-positive and electronegative substances, which classifications were also supposed to have a chemical significance.

§ 765

Even if the opposition of electro-positive and electro-negative substances were more in keeping with the facts than it is, then the nullity of this assumed basis of chemical affinity soon shows itself even experimentally and this again leads to further inconsistencies. It is admitted that two so-called electro-negative substances such as sulphur and oxygen combine in a much more intimate way than, e.g. oxygen and copper, although the latter is electro-positive.2 Here therefore, the basis for the affinity founded on the general opposition of positive and negative electricity must give place to a mere more or less within one and the same series of electrical quality. From this it is now inferred that the degree of affinity of the substances depends therefore not only on their specific unipolarity (with what hypothesis this determination is connected is irrelevant here; it is significant here only for the ’either’ of the positive and the ‘or’ of the negative); the degree of affinity must be derived mainly from the intensity of their polarity generally. At this point then, the consideration of affinity passes on to the relationship of elective affinity which is our chief concern; let us see then what the result now is for this subject. It is at once admitted that the degree of this polarity, if this does not exist merely in our imagination, does not seem to be a constant quality but to depend very much on temperatures so that, after all, the result turns out to be not only that every chemical action is therefore at bottom an electrical phenomenon, but also that what seems to be an effect of so-called elective affinity is brought about only by an electrical polarity which in certain substances is present in greater strength than in others. The conclusion then after all this meandering in hypothetical conceptions, is that we are left with the category of greater intensity, which is the same formal determination as elective affinity in general; and since the latter is made to depend on a greater intensity of electrical polarity, it is not a whit nearer to being put on a physical basis than it was before. But even what is here supposed to be determined as a greater specific intensity is subsequently reduced to the modifications demonstrated by Berthollet which have already been cited.

§ 766

The merit and fame which Berzelius has earned by his theory of proportions, which has been extended to all chemical relations, ought not as such to be made a reason for not setting forth the weaknesses of this theory; but a more particular reason for doing so must be the circumstance that such merit in one aspect of a science, as with Newton, tends to become an authority for a baseless structure of spurious categories which is attached to it and that it is just this kind of metaphysics which is proclaimed and echoed too with the greatest pretension.

§ 767

Apart from the forms of measure relation connected with chemical and elective affinity, others too can be considered with respect to quantities which are specified into a system. Chemical substances form a system of relations with respect to saturation; saturation itself rests on the specific proportion in which the reciprocal amounts of two substances, each of which has a particular material existence, combine with each other. But there are also measure relations the moments of which are inseparable and cannot be displayed in a separate and distinct existence of their own. These are what we called earlier on, immediate self-subsistent measures and which are displayed in the specific gravity of substances. They are a ratio within the substances of weight to volume; the exponent of the ratio, which is the expression of the difference between one specific gravity and another, is a definite quantum only as a result of.comparison. This is a relationship external to the substances in an external reflection, and is not founded on the one substance’s own qualitative behaviour towards another contrasted substance. The problem would be to recognize the exponents of the ratios of the series of specific gravities as a system based on a rule which would specify a merely arithmetical plurality into a series of harmonic nodes. The same demand would apply to our knowledge of the series of chemical affinities already mentioned. But the accomplishment of this task still lies a long way ahead, as far ahead as the problem of grasping the numbers of the relative distances of the planets from the sun as elements in a system of measure.

§ 768

Although at first specific gravities do not seem to have any qualitative relationship to one another, yet they likewise enter into a qualitative relation. When substances are chemically combined, or even form only amalgams or synsomates, there occurs also a neutralisation of the specific gravities. We mentioned earlier on the fact that the volume of a mixture, even a mixture of substances remaining really indifferent chemically to each other, is not of the same magnitude as the sum of the volumes of the substances before mixing. There is a reciprocal modification in the mixture of the quantum of specific gravity with which the substances enter into the relation and in this way they indicate their qualitative behaviour towards each other. Here the quantum of specific gravity is expressed not merely as a fixed comparative number, but as a numerical ratio which can be varied; and the exponents of the mixtures give series of measures the specifying principle of which is other than the numerical ratios of the specific gravities of the substances in combination. The exponents of these ratios are not exclusive determinations of measure; their progress is continuous but it contains an immanent specifying law which is distinct from the formally progressive ratios in which the amounts are combined and makes the former progress incommensurable with the latter.

B. NODAL LINE OF MEASURE-RELATIONS § 769

The last determination of the measure relation was that being specific it is exclusive; the neutrality is exclusive because it is a negative unity of the distinct moments. For the relation of this self-subsistent unity, of the elective affinity to the other neutralities, no further principle of specification has offered itself; the specification resides only in the quantitative determination of affinity in general, according to which the amounts which neutralise themselves are specific and therefore stand opposed to other relative elective affinities of their moments. But further, because the fundamental determination is quantitative, the exclusive elective affinity also continues itself into the opposed neutralities; and this continuity is not only an external relation of the different ratios of the neutralities in the form of a comparison, but the neutrality is, as such, separable into the moments which united to produce it, since it is as self-subsistent somethings that these enter into relation indifferently with one or the other of the opposite series, although combining in different, specifically determined amounts. This measure, based on such a relation, is thus infected with its own indifference; it is in its own self something external and alterable in its relation to itself.

§ 770

The relation to itself of the measure relation is distinct from its externality and alterableness which represent its quantitative aspect. As related to itself in contrast to these, it is an affirmatively present [seiende], qualitative foundation — a permanent, material substrate which, as also the continuity of the measure with itself in its externality, must contain in its quality the principle of the specification of this externality referred to above.

§ 771

Now the exclusive measure as thus more precisely determined is external to itself in its being-for-self and hence repels itself from itself, positing itself both as another measure relation and also as another, merely quantitative, relation; it is determined as in itself a specifying unity which produces measure relations within itself. These relations differ from the affinities of the kind above-mentioned in which a self-subsistent measure relates itself to self-subsistent measures of a different quality and to a series of such. They take place in one and the same substrate within the same moments of the neutrality; the self-repelling measure develops other, merely quantitatively different relations which likewise form affinities and measures, alternating with those which remain only quantitatively different. They form in this way a nodal line of measures on a scale of more and less.

§ 772

Here we have a measure relation, a self-subsistent reality which is qualitatively distinguished from others. Such a being-for-self, because it is at the same time essentially a relation of quanta, is open to externality and to quantitative alteration; it has a range within which it remains indifferent to this alteration and does not change its quality. But there enters a point in this quantitative alteration at which the quality is changed and the quantum shows itself as specifying, so that the altered quantitative relation is converted into a measure, and thus into a new quality, a new something. The relation which has taken the place of the first is determined by this, partly according to the qualitative identity of the moments which are in affinity, and partly according to the quantitative continuity. But because the difference falls into this quantitative aspect, the relation between the new something and its predecessor is one of indifference; their difference is the external one of quantum. The new something has therefore not emerged from or developed out of its predecessor but directly from itself, that is, from the inner specifying unity which has not yet entered into existence. The new quality or new something is subjected to the same progressive alteration, and so on to infinity.

§ 773

Since the progress from one quality [to another] is in an uninterrupted continuity of the quantity, the ratios which approach a specifying point are, quantitatively considered, only distinguished by a more and a less. From this side, the alteration is gradual But the gradualness concerns merely the external side of the alteration, not its qualitative aspect; the preceding quantitative relation which is infinitely near the following one is still a different qualitative existence. On the qualitative side, therefore, the gradual, merely quantitative progress which is not in itself a limit, is absolutely interrupted; the new quality in its merely quantitative relationship is, relatively to the vanishing quality, an indifferent, indeterminate other, and the transition is therefore a leap; both are posited as completely external to each other. People fondly try to make an alteration comprehensible by means of the gradualness of the transition; but the truth is that gradualness is an alteration which is merely indifferent, the opposite of qualitative change. In gradualness too, the connection of the two realities, whether these are taken to be states or self-subsistent things, is eliminated; gradualness necessarily implies that neither of the two is the limit of the other but that each is completely external to the other. In this way there is eliminated the very factor which is necessary for an understanding of change, although little enough is required for that purpose.