Hegel’s Science of Logic
§ 1732
The universal must particularise itself; so far, the necessity for division lies in the universal. But since definition itself already begins with the particular, its necessity for passing over into division lies in the particular, that by itself points to another particular. Conversely, it is precisely in the act of holding fast to the determinateness in the need to distinguish it from its other, that the particular separates itself off from the universal; consequently the universal is presupposed for division. The procedure is, therefore, that the individual content of cognition ascends through particularity to the extreme of universality; but now the latter must be regarded as the objective basis, and with this as the starting point, division presents itself as disjunction of the universal as the prius.
§ 1733
This has introduced a transition which, since it takes place from the universal to the particular, is determined by the form of the Notion. Definition by itself is something individual; a plurality of definitions goes with the plurality of objects. The progress, proper to the Notion, from universal to particular, is the basis and the possibility of a synthetic science, of a system and of systematic cognition.
§ 1734
The first requisite for this is, as we have shown, that the beginning be made with the subject matter in the form of a universal. In the sphere of actuality, whether of nature or spirit, it is the concrete individuality that is given to subjective, natural cognition as the prius; but in cognition that is a comprehension, at least to the extent that it has the form of the Notion for basis, the prius must be on the contrary something simple, something abstracted from the concrete, because in this form alone has the subject-matter the form of the self-related universal or of an immediate based on the Notion.
§ 1735
It might perhaps be objected to this procedure in the scientific sphere that, because intuition is easier than cognition, the object of intuition, that is, concrete actuality, should be made the beginning of science, and that this procedure is more natural than that which proceeds in the opposite direction to its particularisation and concrete individualisation. But the fact that the aim is to cognise, implies that the question of a comparison with intuition is already settled and done with; there can only be a question of what is to be the first and what is to be the nature of the sequel within the process of cognition; it is no longer a natural method, but a method appropriate to cognition that is demanded. If it is merely a question of easiness, then it is self-evident besides, that it is easier for cognition to grasp the abstract simple thought determination than the concrete subject matter, which is a manifold connection of such thought determinations and their relationships; and it is in this manner that we have now to apprehend the concrete, and not as it is in intuition. The universal is in and for itself the first moment of the Notion because it is the simple moment, and the particular is only subsequent to it because it is the mediated moment; and conversely the simple is the more universal, and the concrete, as in itself differentiated and so mediated, is that which already presupposes the transition from a first. This remark applies not only to the order of procedure in the specific forms of definitions, divisions, and propositions, but also to the order of cognition as a whole and simply with respect to the difference of abstract and concrete in general. Hence in learning to read, for example, the rational way is not to begin with reading of whole words or even syllables, but with elements of the words and syllables, and the signs of abstract sounds: in written characters, the analysis of the concrete word into its abstract sounds and their signs is already accomplished; for this very reason, the process of learning to read is a primary occupation with abstract objects. In geometry, a beginning has to be made not with a concrete spatial figure but with the point and the line, and then plane figures, and among the latter not with polygons, but with the triangle, and among curves, with the circle.
§ 1736
In physics the individual natural properties or matters have to be freed from their manifold complications in which they are found in concrete actuality, and presented with their simple necessary conditions; they too, like spatial figures, are objects of intuition; but first the way for their intuition must be prepared so that they appear and are maintained free from all modifications by circumstances extraneous to their own specific character. Magnetism, electricity, the various gases, and so forth, are objects the specific character of which is ascertained by cognition only by apprehending them in isolation from the concrete conditions in which they appear in the actual world, Experiment, it is true, presents them to intuition in a concrete case; but for one thing experiment must, in order to be scientific, take only the conditions necessary for the purpose; and for another, it must multiply itself in order to show that the inseparable concretisation of these conditions is unessential, and this it does by exhibiting the things in another concrete shape and again in another, so that for cognition nothing remains but their abstract form.
§ 1737
To mention one more example, it might seem natural and intelligent to consider colour first, in the concrete manifestation of the animal's subjective sense, next, as a spectral phenomenon suspended outside the subject, and finally as fixed in objects in the actual external world. But for cognition, the universal and therefore truly primary form is the middle one of the above-named, in which colour hovers between subjectivity and objectivity as the familiar spectrum, completely unentangled as yet with subjective and objective circumstances. The latter above all merely disturb the pure consideration of the nature of this subject matter because they behave as active causes and therefore make it uncertain whether the specific alterations, transitions, and relationships of colour are founded in its own specific nature, or are rather to be attributed to the pathological specific constitution of those circumstances, to the healthy and the morbid particular affections and effects of the organs of the subject, or to the chemical, vegetable, and animal forces of the objects. Numerous other examples might be adduced from the cognition of organic nature and of the world of spirit; everywhere the abstract must constitute the starting point and the element in which and from which spread the particularities and rich formations of the concrete.
§ 1738
Now although the difference of the particular from the universal makes its appearance, strictly speaking, with division or the particular this universal is itself already determinate and consequently only a member of a division. Hence there is for it a higher universal, and for this again a higher, and so on, in the first instance, to infinity. For the cognition here considered there is no immanent limit, since it starts from the given, and the form of abstract universality is characteristic of its prius. Therefore any subject matter whatever that seems to possess an elementary universality is made the subject matter of a specific science, and is an absolute beginning to the extent that ordinary thought is presupposed to be acquainted with it and it is taken on its own account as requiring no derivation. Definition takes it as immediate.
§ 1739
The next step forward from this starting point is division. For this progress, only an immanent principle would be required, that is, a beginning from the universal and the Notion; but the cognition here considered lacks such a principle, for it only pursues the form determination of the Notion without its reflection-into-self, and therefore takes the determinateness of the content from what is given. For the particular that makes its appearance in division, there is no ground of its own available, either in regard to what is to constitute the basis of the division, or in regard to the specific relationship that the members of the disjunction are to have to one another. Consequently in this respect the business of cognition can only consist, partly, in setting in order the particular elements discovered in the empirical material, and partly, in finding the universal determinations of that particularity by comparison. These determinations are then accepted as grounds of division, and there may be a multiplicity of such grounds, as also a similar multiplicity of divisions based on them. The relationship between the members, the species, of a division, has only this general determination, that they are determined relatively to one another in accordance with the assumed ground of division; if their difference rested on a different consideration, they would not be coordinated on the same level with one another.
§ 1740
Because a principle of self-determination is lacking, the laws for this business of division can only consist of formal, empty rules that lead to nothing. Thus we see it laid down as a rule that division shall exhaust the notion; but as a matter of fact each individual member of the division must exhaust the notion. It is, however, really the determinateness of the notion that one means should be exhausted; but with the empirical multiplicity of species devoid of any immanent determination, it contributes nothing to the exhaustion of the notion whether more or fewer are found to exist; whether, for example, in addition to the sixty-seven species of parrots another dozen are found is for the exhaustion of the genus a matter of indifference. The demand for exhaustion can only mean the tautological proposition that all the species shall be presented in their completeness. Now with the extension of empirical knowledge it may very well happen that species are found which do not fit in with the adopted definition of the genus; for frequently the definition is adopted more on the basis of a vague conception of the entire habitus, rather than in accordance with a more or less individual mark that is expressly meant to serve for its definition. In such a case the genus would have to be modified and a justification would have to be found for regarding some other number of species as species of a new genus; in other words, the genus would be defined by what we group together in accordance with some principle or other that we choose to adopt as unity; and in this case the principle itself would be the basis of division. Conversely, if we hold to the determinateness originally adopted as characteristic of the genus, that material which we wished to group, as species, in a unity with the earlier species would be excluded. This unsystematic procedure, which sometimes adopts a determinateness as essential moment of the genus and then either subordinates the particulars to it or excludes them from it, and sometimes starts with the particular and in grouping it lets itself again be guided by some other determinateness, gives the appearance of the play of a caprice to which it is left to decide which part or which side of the concrete it will fix on and use as its principle of arrangement. Physical nature presents of itself such a contingency in the principles of division. By reason of its dependent external actuality it stands in a complex connectedness that for it likewise is given; accordingly there exists a crowd of principles to which it has to conform, and therefore in one series of its forms follows one principle, and in other series other principles, as well as producing hybrids that belong at the same time to different sides of the division. Thus it happens that in one series of natural objects marks stand out as very characteristic and essential that in others become inconspicuous and purposeless, so that it becomes impossible to adhere to a principle of division of this kind.
§ 1741
The general determinateness of empirical species can only consist in their being simply different from one another without being opposed. The disjunction of the Notion has been exhibited at an earlier stage in its determinateness; when particularity is assumed as immediate and given and without the negative unity of the Notion, the difference remains only at the stage of diversity as such, a form of reflection that we considered earlier. The externality in which the Notion chiefly exists in Nature brings with it the complete indifference of the difference; consequently, a frequent determination for division is taken from number.
§ 1742
Such is the contingency here of the particular in face of the universal and therefore of division generally, that it may be attributed to an instinct of reason when we find in this cognition grounds of division and divisions that, so far as sensuous properties permit, show themselves to be more adequate to the Notion. For example, in the case of animals, the instruments of eating, the teeth and claws, are employed in systems of classification as a broad radical ground of division; they are taken, in the first instance, merely as aspects in which the distinguishing marks for the subjective purposes of cognition can be more easily indicated. But as a matter of fact these organs do not merely imply a differentiation belonging to external reflection, but they are the vital point of animal individuality where it posits itself as a self-related individuality distinct from its other, from the nature that is external to it, and as an individuality that withdraws itself from continuity with the other. In the case of the plant, the fertilising organs constitute the highest point of vegetable life, by which the plant points to the transition into sex difference, and thereby into individual individuality. The system of botany has therefore rightly turned to this point for a principle of division that, if not adequate is far-reaching, and has thereby taken as its basis a determinateness that is not merely a determinateness for external reflection for purposes of comparison, but is in and for itself the highest of which the plant is capable.
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