Abstract rational knowledge

There are 2 processes of knowledge leads to concepts and direct knowledge.

1. One that belongs to the reason, rational knowledge, concepts

2. One that is purely sensuous, mathematical intuition or perception, and apprehension by the understanding

This remarkable relation of our kinds of knowledge led us almost inevitably to give, in passing, explanations of feeling and of laughter, but from all this we now turn back to the further consideration of science as the third great benefit which reason confers on man, the other two being speech and deliberate action.

The general discussion of science which now devolves upon us, will be concerned partly with its form, partly with the foundation of its judgments, and lastly with its content.

We have seen that, with the exception of the basis of pure logic, rational knowledge in general has not its source in the reason itself; but having been otherwise obtained as knowledge of perception, it is stored up in the reason, for through reason it has entirely changed its character, and has become abstract knowledge. All rational knowledge, that is, knowledge that has been raised to consciousness in the abstract, is related to science strictly so called, as a fragment to the whole.

Every one has gained a rational knowledge of many different things through experience, through consideration of the individual objects presented to him, but only he who sets himself the task of acquiring a complete knowledge in the abstract of a particular class of objects, strives after science. This class can only be marked off by means of a [081] concept; therefore, at the beginning of every science there stands a concept, and by means of it the class of objects concerning which this science promises a complete knowledge in the abstract, is separated in thought from the whole world of things. For example, the concept of space-relations, or of the action of unorganised bodies upon each other, or of the nature of plants, or of animals, or of the successive changes of the surface of the globe, or of the changes of the human race as a whole, or of the construction of a language, and so forth. If science sought to obtain the knowledge of its object, by investigating each individual thing that is thought through the concept, till by degrees it had learned the whole, no human memory would be equal to the task, and no certainty of completeness would be obtainable.

Therefore, it makes use of that property of concept-spheres explained above, that they include each other, and it concerns itself mainly with the wider spheres which lie within the concept of its object in general. When the relations of these spheres to each other have been determined, all that is thought in them is also generally determined, and can now be more and more accurately determined by the separation of smaller and smaller concept-spheres.

In this way it is possible for a science to comprehend its object completely. This path which it follows to knowledge, the path from the general to the particular, distinguishes it from ordinary rational knowledge; therefore, systematic form is an essential and characteristic feature of science. The combination of the most general concept-spheres of every science, that is, the knowledge of its first principles, is the indispensable condition of mastering it; how far we advance from these to the more special propositions is a matter of choice, and does not increase the thoroughness but only the extent of our knowledge of the science. The number of the first principles to which all the rest are subordinated, varies greatly in the different sciences, so that in[082] some there is more subordination, in others more co-ordination; and in this respect, the former make greater claims upon the judgment, the latter upon the memory.

It was known to the schoolmen,19 that, as the syllogism requires two premises, no science can proceed from a single first principle which cannot be the subject of further deduction, but must have several, at least two. The specially classifying sciences: Zoology, Botany, and also Physics and Chemistry, inasmuch as they refer all inorganic action to a few fundamental forces, have most subordination; history, on the other hand, has really none at all; for the general in it consists merely in the survey of the principal periods, from which, however, the particular events cannot be deduced, and are only subordinated to them according to time, but according to the concept are co-ordinate with them. Therefore, history, strictly speaking, is certainly rational knowledge, but is not science. In mathematics, according to Euclid’s treatment, the axioms alone are indemonstrable first principles, and all demonstrations are in gradation strictly subordinated to them. But this method of treatment is not essential to mathematics, and in fact each proposition introduces quite a new space construction, which in itself is independent of those which precede it, and indeed can be completely comprehended from itself, quite independently of them, in the pure intuition or perception of space, in which the most complicated construction is just as directly evident as the axiom; but of this more fully hereafter. Meanwhile every mathematical proposition remains always a universal truth, which is valid for innumerable particular cases; and a graduated process from the simple to the complicated propositions which are to be deduced from them, is also essential to mathematics; therefore, in every respect mathematics is a science. The completeness of a science as such, that is, in respect of form, consists in there being as much subordination and as little co-ordination of the principles [083] as possible. Scientific talent in general is, therefore, the faculty of subordinating the concept-spheres according to their different determinations, so that, as Plato repeatedly counsels, a science shall not be constituted by a general concept and an indefinite multiplicity immediately under it, but that knowledge shall descend by degrees from the general to the particular, through intermediate concepts and divisions, according to closer and closer definitions. In Kantian language this is called satisfying equally the law of homogeneity and that of specification. It arises from this peculiar nature of scientific completeness, that the aim of science is not greater certainty—for certainty may be possessed in just as high a degree by the most disconnected particular knowledge—but its aim is rather the facilitating of rational knowledge by means of its form, and the possibility of the completeness of rational knowledge which this form affords. It is therefore a very prevalent but perverted opinion that the scientific character of knowledge consists in its greater certainty, and just as false is the conclusion following from this, that, strictly speaking, the only sciences are mathematics and logic, because only in them, on account of their purely a priori character, is there unassailable certainty of knowledge. This advantage cannot be denied them, but it gives them no special claim to be regarded as sciences; for the special characteristic of science does not lie in certainty but in the systematic form of knowledge, based on the gradual descent from the general to the particular. The process of knowledge from the general to the particular, which is peculiar to the sciences, involves the necessity that in the sciences much should be established by deduction from preceding propositions, that is to say, by demonstration; and this has given rise to the old mistake that only what has been demonstrated is absolutely true, and that every truth requires a demonstration; whereas, on the contrary, every demonstration requires an undemonstrated truth,[084] which ultimately supports it, or it may be, its own demonstration. Therefore a directly established truth is as much to be preferred to a truth established by demonstration as water from the spring is to water from the aqueduct. Perception, partly pure a priori, as it forms the basis of mathematics, partly empirical a posteriori, as it forms the basis of all the other sciences, is the source of all truth and the foundation of all science. (Logic alone is to be excepted, which is not founded upon perception but yet upon direct knowledge by the reason of its own laws.) Not the demonstrated judgments nor their demonstrations, but judgments which are created directly out of perception, and founded upon it rather than on any demonstrations, are to science what the sun is to the world; for all light proceeds from them, and lighted by their light the others give light also. To establish the truth of such primary judgments directly from perception, to raise such strongholds of science from the innumerable multitude of real objects, that is the work of the faculty of judgment, which consists in the power of rightly and accurately carrying over into abstract consciousness what is known in perception, and judgment is consequently the mediator between understanding and reason. Only extraordinary and exceptional strength of judgment in the individual can actually advance science; but every one who is possessed of a healthy reason is able to deduce propositions from propositions, to demonstrate, to draw conclusions.

To lay down and make permanent for reflection, in suitable concepts, what is known through perception, so that, on the one hand, what is common to many real objects is thought through one concept, and, on the other hand, their points of difference are each thought through one concept, so that the different shall be known and thought as different in spite of a partial agreement, and the identical shall be known and thought as identical in spite of a partial difference, all in accordance with the end and intention which in each case is in view; all this [085] is done by the faculty of judgment. Deficiency in judgment is silliness. The silly man fails to grasp, now the partial or relative difference of concepts which in one aspect are identical, now the identity of concepts which are relatively or partially different. To this explanation of the faculty of judgment, moreover, Kant’s division of it into reflecting and subsuming judgment may be applied, according as it passes from the perceived objects to the concepts, or from the latter to the former; in both cases always mediating between empirical knowledge of the understanding and the reflective knowledge of the reason.

There can be no truth which could be brought out by means of syllogisms alone; and the necessity of establishing truth by means of syllogisms is merely relative, indeed subjective. Since all demonstration is syllogistic, in the case of a new truth we must first seek, not for a demonstration, but for direct evidence, and only in the absence of such evidence is a demonstration to be temporarily made use of. No science is susceptible of demonstration throughout any more than a building can stand in the air; all its demonstrations must ultimately rest upon what is perceived, and consequently cannot be demonstrated, for the whole world of reflection rests upon and is rooted in the world of perception. All primal, that is, original, evidence is a perception, as the word itself indicates. Therefore it is either empirical or founded upon the perception a priori of the conditions of possible experience. In both cases it affords only immanent, not transcendent knowledge. Every concept has its worth and its existence only in its relation, sometimes very indirect, to an idea of perception; what is true of the concepts is also true of the judgments constructed out of them, and of all science. Therefore it must in some way be possible to know directly without demonstrations or syllogisms every truth that is arrived at through syllogisms and communicated by demonstrations. This is most difficult in the case of certain[086] complicated mathematical propositions at which we only arrive by chains of syllogisms; for example, the calculation of the chords and tangents to all arcs by deduction from the proposition of Pythagoras. But even such a truth as this cannot essentially and solely rest upon abstract principles, and the space-relations which lie at its foundation also must be capable of being so presented a priori in pure intuition or perception that the truth of their abstract expression is directly established. But of mathematical demonstration we shall speak more fully shortly. It is true we often hear men speak in a lofty strain of sciences which rest entirely upon correct conclusions drawn from sure premises, and which are consequently unassailable. But through pure logical reasoning, however true the premises may be, we shall never receive more than an articulate expression and exposition of what lies already complete in the premises; thus we shall only explicitly expound what was already implicitly understood. The esteemed sciences referred to are, however, specially the mathematical sciences, particularly astronomy.

But the certainty of astronomy arises from the fact that it has for its basis the intuition or perception of space, which is given a priori, and is therefore infallible. All space-relations, however, follow from each other with a necessity (ground of being) which affords a priori certainty, and they can therefore be safely deduced from each other. To these mathematical properties we have only to add one force of nature, gravity, which acts precisely in relation to the masses and the square of the distance; and, lastly, the law of inertia, which follows from the law of causality and is therefore true a priori, and with it the empirical datum of the motion impressed, once for all, upon each of these masses. This is the whole material of astronomy, which both by its simplicity and its certainty leads to definite results, which are highly interesting on account of the vastness and importance [087] of the objects. For example, if I know the mass of a planet and the distance of its satellite from it, I can tell with certainty the period of the revolution of the latter according to Kepler’s second law. But the ground of this law is, that with this distance only this velocity will both chain the satellite to the planet and prevent it from falling into it. Thus it is only upon such a geometrical basis, that is, by means of an intuition or perception a priori, and also under the application of a law of nature, that much can be arrived at by means of syllogisms, for here they are merely like bridges from one sensuous apprehension to others; but it is not so with mere pure syllogistic reasoning in the exclusively logical method. The source of the first fundamental truths of astronomy is, however, properly induction, that is, the comprehension of what is given in many perceptions in one true and directly founded judgment. From this, hypotheses are afterwards constructed, and their confirmation by experience, as induction approaching to completeness, affords the proof of the first judgment. For example, the apparent motion of the planets is known empirically; after many false hypotheses with regard to the spacial connection of this motion (planetary course) the right one was at last found, then the laws which it obeyed (the laws of Kepler), and, lastly, the cause of these laws (universal gravitation), and the empirically known agreement of all observed cases with the whole of the hypotheses, and with their consequences, that is to say, induction, established them with complete certainty. The invention of the hypotheses was the work of the judgment, which rightly comprehended the given facts and expressed them accordingly; but induction, that is, a multitude of perceptions, confirmed their truth. But their truth could also be known directly, and by a single empirical perception, if we could pass freely through space and had telescopic eyes. Therefore, here also syllogisms are not the essential and only source of[088] knowledge, but really only a makeshift.

As a third example taken from a different sphere we may mention that the so-called metaphysical truths, that is, such truths as those to which Kant assigns the position of the metaphysical first principles of natural science, do not owe their evidence to demonstration. What is a priori certain we know directly; as the form of all knowledge, it is known to us with the most complete necessity. For example, that matter is permanent, that is, can neither come into being nor pass away, we know directly as negative truth; for our pure intuition or perception of space and time gives the possibility of motion; in the law of causality the understanding affords us the possibility of change of form and quality, but we lack powers of the imagination for conceiving the coming into being or passing away of matter. Therefore that truth has at all times been evident to all men everywhere, nor has it ever been seriously doubted; and this could not be the case if it had no other ground of knowledge than the abstruse and exceedingly subtle proof of Kant. But besides this, I have found Kant’s proof to be false (as is explained in the Appendix), and have shown above that the permanence of matter is to be deduced, not from the share which time has in the possibility of experience, but from the share which belongs to space. The true foundation of all truths which in this sense are called metaphysical, that is, abstract expressions of the necessary and universal forms of knowledge, cannot itself lie in abstract principles; but only in the immediate consciousness of the forms of the idea communicating itself in 107 apodictic assertions a priori, and fearing no refutation. But if we yet desire to give a proof of them, it can only consist in showing that what is to be proved is contained in some truth about which there is no doubt, either as a part of it or as a presupposition. Thus, for example, I have shown that all empirical perception implies the application of the law of causality, the knowledge [089] of which is hence a condition of all experience, and therefore cannot be first given and conditioned through experience as Hume thought. Demonstrations in general are not so much for those who wish to learn as for those who wish to dispute. Such persons stubbornly deny directly established insight; now only the truth can be consistent in all directions, and therefore we must show such persons that they admit under one form and indirectly, what they deny under another form and directly; that is, the logically necessary connection between what is denied and what is admitted.

It is also a consequence of the scientific form, the subordination of everything particular under a general, and so on always to what is more general, that the truth of many propositions is only logically proved,—that is, through their dependence upon other propositions, through syllogisms, which at the same time appear as proofs. But we must never forget that this whole form of science is merely a means of rendering knowledge more easy, not a means to greater certainty. It is easier to discover the nature of an animal, by means of the species to which it belongs, and so on through the genus, family, order, and class, than to examine on every occasion the animal presented to us: but the truth of all propositions arrived at syllogistically is always conditioned by and ultimately dependent upon some truth which rests not upon reasoning but upon perception. If this perception were always as much within our reach as a deduction through syllogisms, then it would be in every respect preferable.

For every deduction from concepts is exposed to great danger of error, on account of the fact we have considered above, that so many spheres lie partly within each other, and that their content is often vague or uncertain. This is illustrated by a multitude of demonstrations of false doctrines and sophisms of every kind. Syllogisms are indeed perfectly certain as regards form, but they are very uncertain on account of their matter, the concepts. For,[090] on the one hand, the spheres of these are not sufficiently sharply defined, and, on the other hand, they intersect each other in so many ways that one sphere is in part contained in many others, and we may pass at will from it to one or another of these, and from this sphere again to others, as we have already shown.

Or, in other words, the minor term and also the middle can always be subordinated to different concepts, from which we may choose at will the major and the middle, and the nature of the conclusion depends on this choice. Consequently immediate evidence is always much to be preferred to reasoned truth, and the latter is only to be accepted when the former is too remote, and not when it is as near or indeed nearer than the latter. Accordingly we saw above that, as a matter of fact, in the case of logic, in which the immediate knowledge in each individual case lies nearer to hand than deduced scientific knowledge, we always conduct our thought according to our immediate knowledge of the laws of thought, and leave logic unused.