LITMIR.BIZ

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to elaborate in detail; it depends for its material on experience, or rather perception. Looked at in one light, it makes no difference that it has reference to foreign perceptions and their evidences; argumentation, that is to say, the exercise of understanding proper regarding the objective connection of circumstances and actions, makes these data into presuppositions and fundamental assumptions, just as its criticism of evidences has done in drawing its conclusions. But in so far as argument and criticism constitute the other essential side of historical proof, such proof treats its data as being the ideas of other people; the subjective element directly enters into the material, and the reasoning about and combination of that material is likewise subjective activity; so that the course and activity of knowledge has quite different ingredients from the course followed by the circumstances themselves. As regards the pointing things out in everyday experience, this is certainly concerned, in the first instance, with individual perceptions, observations, and so on, that is to say, with the kind of material which is only pointed out, but its interest is by so doing to prove further that there are in Nature and in Spirit such species and kinds, such laws, forces, faculties, and activities as are mentioned in the sciences. We pass by the metaphysical or common psychological reflections about that subjective element of ​sense, external and internal, which accompanies perception. But the material, however, in so far as it enters into the sciences, is not so left to itself as it is in the senses and in perception. On the contrary, the content of the sciences—the species, kinds, laws, forces, and so on—is built up out of that material, which is, perhaps, already called by the name of phenomena, by putting together through analysis what is common, the leaving aside of what is not essential, the retention of what is called essential, without any certain test having been applied to distinguish between what is to be regarded as non-essential and what as essential. It is admitted that what is perceived does not itself make these abstractions, does not compare its individuals (or individual positions, circumstances, and so on), or put what is common in them together; that therefore a great part of the activity of knowledge is a subjective affair, just as in the content which has been obtained a part of its definitions, as being logical forms, are the product of this subjective activity. The expression “predicate,” or mark (Merkmal), if people will still use this stupid expression, directly indicates a subjective purpose of isolating properties for our use in marking distinctions, while others, which likewise exist in the object, are put aside. This expression is to be called stupid, because the definitions of species and kinds directly pass for something essential and objective, and not as existing merely for us who mark distinctions. We may certainly also express ourselves by saying that the species leaves aside, in one kind, properties which it places in another, or that energy in one form of its manifestation leaves aside circumstances which are present in another, that these circumstances are thus shown by it to be unessential, and it of itself gives up the form of its manifestation, and withdraws itself into inactivity or self-containedness; that thus, for example, the law of the motion of the heavenly bodies penetrates to every single place and every moment in which the heavenly ​body occupies that place, and just by this continual abstraction shows itself to be a law. If we thus look on abstraction as objective activity, which it so far is, it is yet very different from subjective activity and its products. The former leaves the heavenly body to fall back again after abstraction from this particular place and this particular moment into the particular changing place and moment of time, just as the species may appear in the kind in other contingent or unessential forms and in the external particularity of individuals. On the other hand, subjective abstraction raises the law like the species into its universality as such, and makes it exist and preserves it in this form, in the mind.

      In these forms of the knowledge which progresses from mere indication to proof, from immediate objectivity to special products, the necessity may be felt of considering explicitly the method, the nature, and fashion of the subjective activity, in order to test its claims and procedure; for this method has its own characteristics and kind of progress which are quite different from the characteristics and process of the object in itself. And without entering more particularly into the nature of this method of knowledge, it becomes immediately apparent, from a single characteristic which we observe in it, that inasmuch as it is represented as being concerned with the object in accordance with subjective forms, it is only capable of apprehending relations of the object. It is therefore idle to start the question whether these relations are objective and real or only subjective and ideal, not to mention the fact that such expressions as subjectivity and objectivity, reality and ideality, are simply vague abstractions. The content, be it objective or merely subjective, real or ideal, remains always the same, an aggregate of relations, not something that is in-and-for-itself, the notion of the thing, or the infinite, with which knowledge must have to do. If that content of knowledge is taken by perverted sense as containing relations only, ​and these are understood to be phenomena or relations to a faculty of subjective knowledge, it must, so far as results are concerned, always be recognised as representing the great intellectual advance which modern philosophy has achieved, that the mode of thinking, proving, and knowing the infinite, which has been described, is proved incapable of reaching what is eternal and divine.

      What has been brought out in the preceding exposition regarding knowledge in general, and especially what relates to thinking knowledge (which is what alone concerns us), and to proof, the principal moment in that knowledge, we have looked at from the point of view from which it is seen to be a movement of the activity of thought which is outside the object and different from the development of the object itself. This definition may in part be taken to be sufficient for our purpose, but partly, too, it is to be taken as what is essential in opposition to the one-sidedness which lies in the reflections about the subjectivity of knowledge.

      In the opposition of the process of knowledge to the object to be known lies the finiteness of knowledge. But this opposition is not on that account to be regarded as itself infinite and absolute, and its products are not to be taken to be appearances only because of the mere abstraction of subjectivity; but in so far as they themselves are determined by that opposition, the content as such is affected by the externality referred to. This point of view has an effect upon the nature of the content, and yields a definite insight into it; while, on the contrary, the other way of looking at the question gives us nothing but the abstract category of the subjective, which is, moreover, taken to be absolute. What we thus get as the result of the way in which we look at the proof, for the otherwise quite general quality of the content, is, speaking generally, just this, that the content, inasmuch as it bears an external relation to knowledge, is itself determined as something external, or, to put it ​more definitely, consists of abstractions from finite properties. Mathematical content as such is essentially magnitude. Geometrical figures pertain to space, and have thus in themselves externality as their principle, since they are distinguished from real objects, and represent only the one-sided spatiality of these objects, as distinguished from their concrete filling up, through which they first became real. So number has the unit for its principle, and is the putting together of a multiplicity of units which are independent, and is thus a completely external combination. The knowledge which we have here before us can only attain its greatest perfection in this field, because that field contains only simple and definite qualities, and the dependence of these upon each other, the insight into the nature of which is proof, is thus stable, and ensures for proof the logical progress of necessity. This kind of knowledge is capable of exhausting the nature of its objects. The logical nature of the process of proof is not, however, confined to mathematical content, but enters into all departments of natural and spiritual material; but we may sum up what is logical in knowledge in connection with proof by saying that it depends on the rules of inference; the proofs of the existence of God are therefore essentially inferences. The express investigation of these forms belongs, however, partly to logic, and for the rest the nature of the fundamental defect must be ascertained in the course of the examination of these proofs which is about to be taken in hand. For the present it is enough to remark further, in connection with what has been said, that the rules of inference have a kind of foundation which is of the nature of mathematical calculation. The connection of propositions which are requisite to constitute a syllogistic conclusion depends on the relations of the sphere which each of them occupies as regards the other, and which is quite properly regarded as greater or smaller. The definite extent of such ​a sphere is what determines the correctness of the subsumption. The older logicians, such as Lambert and Ploucquet, have been

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