FIRST SECTION

Of concepts

The concept in general and its distinction from intuition

All cognitions, that is, all representations related with consciousness to an object, are either intuitions or concepts. An intuition is a singular representation (repraesentatio singularis), a concept a universal (repraesentatio per notas communes) or reflected representation (repraesentatio discursiva).

Cognition through concepts is called thought (cognitio discursivd).

1. Note 1. A concept is opposed to intuition, for it is a universal representation, or a representation of what is common to several objects, hence a representation insofar as it can be contained in various ones.

2. 2. It is a mere tautology to speak of universal or common concepts – a mistake that is grounded in an incorrect division of concepts into universal, particular, and singular. Concepts themselves cannot be so divided, but only their use.

Matter and form of concepts

With every concept we are to distinguish matter and form. The matter of concepts is the object, their form universality.

Empirical and pure concept

A concept is either an empirical or a pure concept (vel empiricus vel intellectualis). A pure concept is one that is not abstracted from experience but arises rather from the understanding even as to content.

An idea is a concept of reason whose object simply cannot be met with in experience.

§3

Sensibility is the receptivity of a subject in virtue of which it is possible for the subject's own representative state to be affected in a definite way by the presence of some object. Intelligence (rationality) is the faculty of a subject in virtue of which it has the power to represent things which cannot by their own quality come before the senses of that subject. The object of sensibility is the sensible; that which contains nothing but what is to be cognised through the intelligence is intelligible. In the schools of the ancients, the former was called a phenomenon and the latter a noumenon. Cognition, in so far as it is subject to the laws of sensibility, is sensitive, and, in so far as it is subject to the laws of intelligence, it is intellectual or rational.

§4

In this way, whatever in cognition is sensitive is dependent upon the special character of the subject in so far as the subject is capable of this or that modification by the presence of objects: these modifications may differ in different cases, according to the variations in the subjects. But whatever cognition is exempt from such subjective conditions relates only to the object. It is thus clear that things which are thought sensitively are representations of things as they appear, while things which are intellectual are representations of things as they are. In a representation of sense there is, first of all, something which you might call the matter, namely, the sensation, and there is also something which may be called the form, the aspect namely of sensible things which arises according as the various things which affect the senses are co-ordinated by a certain natural law of the mind.

THE IMPORTANCE OF KANT'S LOGIC LECTURES

Kant's views about the nature of logic, and about various points of logical theory as well, figure prominently in his Critical works. This is especially true in the first and most fundamental of those works, the Critique of Pure Reason. Indeed, Kant characterizes the Critique – or the major portion of it, at least – as an essay in transcendental logic. This means, on the one hand, that the work is to be understood as containing something different from logic, something that does not deal merely with the canons of all thought, but with the concepts and principles governing knowledge of objects in space and time. It also means, however, that both in the broad sweep of its architectonic and in the detail of much of its argument the Critique assumes familiarity with Kant's views on logic; for transcendental logic, though different from logic proper, is supposed to build upon the latter. In dividing transcendental logic into an Analytic and a Dialectic, in deriving the table of categories, in classifying the dialectical inferences of pure reason, and in numerous other instances as well, Kant simply assumes that his readers are familiar with his views on logic.

I. THE PRINCIPLE OF SUCCESSION

Proposition XII. No change can happen to substances except in so far as they are connected with other substances; their reciprocal dependency on each other determines their reciprocal changes of state.

Hence, a simple substance, which is free from every external connection and which is thus abandoned to itself and left in isolation, is completely immutable in itself.

Furthermore, even were this simple substance to be included in a connection with other substances, if this relation did not change, no change could occur in it, not even a change of its inner state. Thus, in a world which was free from all motion (for motion is the appearance of a changed connection), nothing at all in the nature of succession would be found even in the inner states of substances.

Hence, if the connection of substances were cancelled altogether, succession and time would likewise disappear.

Demonstration. Suppose that some simple substance, the connection of which with other substances had been cancelled, were to exist in isolation. I maintain that it could undergo no change of its inner state. The inner determinations, which already belong to the substance, are posited in virtue of inner grounds which exclude the opposite. Accordingly, if you want another determination to follow, you must also posit another ground. But since the opposite of this ground is internal to the substance, and since, in virtue of what we have presupposed, no external ground is added to it, it is patently obvious that the new determination cannot be introduced into the being.

The same differently. It is necessary that whatever is posited by a determining ground be posited simultaneously with that determining ground. For, having posited the determining ground, it would be absurd if that which was determined by the determining ground were not posited as well. Thus, whatever determining factors exist in some state of a simple substance, it is necessary that all factors whatever which are determined should exist simultaneously with those determining factors.

The celebrated Leibniz possessed many genuine insights, and by their means he enriched the sciences. But he also entertained projects which were of still greater importance. The world, however, was to wait in vain for their realisation. It is not my purpose here to decide what the reason for this failure may have been. Leibniz may have regarded his efforts as too imperfect – a reservation which is typical of men of great merit, and one which has constantly deprived learning of many valuable fragments. Or it may have been with him, as Boerhaave supposed that it was with great chemists: they often claimed to possess the ability to perform certain feats as if they had already executed them, whereas in fact they merely possessed the conviction and the assurance that they could do so, and that they could not fail in the undertaking if only they set their minds to the performance. At any rate, it looks as if a certain mathematical discipline, which Leibniz called analysis situs, and the loss of which was lamented by Buffon among others when he was considering the foldings together of nature in the seeds' – it looks as if this discipline was never more than a thought in Leibniz's mind. I do not know exactly to what extent the object which I propose examining here is related to what the great Leibniz had in mind. But to judge by the meaning of the term, what I am seeking to determine philosophically here is the ultimate ground of the possibility of that of which Leibniz was intending to determine the magnitudes mathematically. For the positions of the parts of space in reference to each other presuppose the direction in which they are ordered in such a relation. In the most abstract sense of the term, direction does not consist in the reference of one thing in space to another – that is really the concept of position – but in the relation of the system of these positions to the absolute space of the universe.

WARNING: Since I am particularly concerned to be brief in this treatise, I think it better here not to copy out afresh the definitions and axioms which are firmly established in ordinary knowledge and which are consonant with right reason. Nor do I think it a good idea to follow the example, by imitating their practice, of those who, slavishly bound by I know not what method, only deem themselves to have proceeded in a rational fashion if they have scrutinised from beginning to end whatever they find on the bookshelves of philosophers. I have thought it good to warn the reader of this in advance, lest he take for a fault that which I have done deliberately.

Proposition I. There is no UNIQUE, absolutely first, universal principle of all truths.

A first and truly unique principle must necessarily be a simple proposition; if it covertly embraced a number of propositions it would merely present the deceptive semblance of a unique principle. If, therefore, a proposition is truly simple, it must be either affirmative or negative. But I maintain that if it is one or the other, it cannot be universal and subsume under itself all truths whatever. For, if you say that it is affirmative, it cannot be the absolutely first principle of all negative truths; and if you say that it is negative it cannot take command of the positive truths.

Let us suppose, namely, that the proposition is negative. Who is there who does not see that, since the logical derivation of all truths from their principles is either direct or indirect, it is not possible, firstly, to deduce anything from a negative principle by the direct method of inference except negative conclusions? If you then go on to insist that affirmative propositions flow from that negative principle indirectly, then you will acknowledge that this can only happen by means of the following proposition: everything of which the opposite is false, is true.

Now that an appropriate concept of God has been formed, there is perhaps nothing more natural than the thought: if God chooses, he chooses only what is best. It was said of Alexander that he thought that he had done nothing as long as there was still something left for him to do. The same thing can be said with infinitely greater propriety about the most benevolent and most powerful being of all. Leibniz did not think that he was saying anything new when he maintained that this world was the best of all possible worlds, or, which amounts to the same thing, that the totality of all that God has created outside Himself, was the best which could possibly have been created. What was new was the employment to which Leibniz put this principle. He employed it, namely, to cut the knot, so difficult to untie, of the difficulties relating to the origin of evil. An idea which is so easy and so natural, and which is eventually repeated so often as to become a common platitude and a source of disgust to people of more refined taste, cannot continue an object of respect for long. Where is the honour in thinking like the common herd, or in maintaining a proposition which is so easy to prove? Subtle errors are a stimulus to one's self-love, which takes delight in the sense of its own strength. Obvious truths, on the other hand, are apprehended with such ease and with an understanding so common that in the end their fate is the fate of those songs which become intolerable as soon as they start to ring out from the mouths of the common masses. To put the matter briefly: it is often the case with some of the things we know that they are highly esteemed, not because they are right, but because they have been gained at a cost.

§13

The principle of the form of the universe is that which contains the ground of the universal connection, in virtue of which all substances and their states belong to the same whole which is called a world. The principle of the form of the sensible world is that which contains the ground of the universal connection of all things, in so far as they are phenomena. The form of the intelligible world recognises an objective principle, that is to say, some cause in virtue of which there is a combining together of the things which exist in themselves. But the world, in so far as it is regarded as phenomenon, that is to say, the world in relation to the sensibility of the human mind, does not recognise any other principle of form than a subjective one, that is to say, a fixed law of the mind, in virtue of which it is necessary that all the things which can be objects of the senses (through the qualities of those objects) are seen as necessarily belonging to the same whole. Accordingly, whatever the principle of the form of the sensible world may, in the end, be, its embrace is limited to actual things, in so far as they are thought capable of falling under the senses. Accordingly, it embraces neither immaterial substances, which are already as such, by definition, excluded from the outer senses, nor the cause of the world, for, since it is in virtue of that cause that mind itself exists and is active through all its senses, that cause cannot be an object of the senses. These formal principles of the phenomenal universe are absolutely primary and universal; they are, so to speak, the schemata and conditions of everything sensitive in human cognition. I shall now show that there are two such principles, namely, space and time.

FIRST REFLECTION: IN WHICH THE EXISTENCE OF GOD IS INFERRED A POSTERIORI FROM THE UNITY PERCEIVED IN THE ESSENCES OF THINGS

1. The unity in the manifold? of the essences of things is demonstrated by appeal to the properties of space

The necessary determinations of space afford the geometer a pleasure which is far from ordinary. They do so because of the certainty of their conviction, the exactitude of their execution, and the extensiveness of their application. The whole range of human knowledge has nothing to show which equals it, far less anything which exceeds it. But, for the present, I wish to examine this same object from an entirely different point of view. Looking at it with a philosophical eye, I come to notice that order and harmony, along with such necessary determinations, prevail throughout space, and that concord and unity prevail throughout its immense manifold. Let us suppose, for example, that I wish to produce a bounded space by moving a straight line around a fixed point. I have no difficulty at all in grasping that the result is a circle, the circumference of which is at all points equidistant from the aforementioned fixed point. But I have no reason at all to suppose that such a simple construction should conceal something highly complex which is itself subject, in virtue of that very construction, to major rules of order. And yet I discover that all the straight lines which intersect each other inside a circle at any given point, when they are extended to its circumference, are always divided in geometrical proportion. Likewise, I discover that all the straight lines which extend from a given point outside a circle so as to intersect its circumference are always divided into parts which are related to each other in inverse proportion to their wholes.

Metaphysics is nothing other than the philosophy of the fundamental principles of our cognition. Accordingly, what was established in the preceding reflection about mathematical cognition in comparison with philosophy will also apply to metaphysics. We have seen that the differences which are to be found between cognition in mathematics and cognition in philosophy are substantial and essential. And in this connection, one can say with Bishop Warburton that nothing has been more damaging to philosophy than mathematics, and in particular the imitation of its method in contexts where it cannot possibly be employed. The application of the mathematical method in those parts of philosophy involving cognition of magnitudes is something quite different, and its utility is immeasurable.

In mathematics I begin with the definition of my object, for example, of a triangle, or a circle, or whatever. In metaphysics I may never begin with a definition. Far from being the first thing I know about the object, the definition is nearly always the last thing I come to know. In mathematics, namely, I have no concept of my object at all until it is furnished by the definition. In metaphysics I have a concept which is already given to me, although it is a confused one. My task is to search for the distinct, complete and determinate concept. How then am I to begin? Augustine said: ‘I know perfectly well what time is, but if someone asks me what it is I do not know.’ In such a case as this, many operations have to be performed in unfolding obscure ideas, in comparing them with each other, in subordinating them to each other and in limiting them by each other. And I would go as far as to say that, although much that is true and much that is penetrating has been said about time, nonetheless no real definition has ever been given of time.

What I have said so far merely amounts to a preliminary examination of an object? which is as important as it is difficult. In advancing to general principles from the examples which have been introduced and which are easy enough to understand, there are good grounds for extreme concern: in pursuing this untrodden path mistakes may be made which only come to be noticed as one advances. Accordingly, what I have yet to say on the matter is to be regarded as an experiment which is very imperfect. And yet it is my expectation that any attention, which may be paid to it, will be beneficial in a variety of different ways. I am fully aware that an admission of this kind is a very poor sort of recommendation to those who demand an assertive and dogmatic tone, if they are to permit themselves to be steered in the desired direction. I do not feel the least regret at losing this kind of acclaim. It seems to me, however, that, in a branch of knowledge as difficult to handle as metaphysics, it is much more appropriate that one's thought should first of all be presented to public examination in the guise of tentative experiments than that they should be announced from the beginning with all the adornments of pretended thoroughness and complete conviction. It commonly happens with that latter course that all improvement is rejected out of hand, and any weakness which may be found in what one has to say becomes incurable.

1. Anybody can easily understand why something does not exist, when the positive ground for its existence is lacking. But how that which exists should cease to be – that is not so easy to understand. There exists at this moment in my soul, for example, the representation of the sun, and it exists in virtue of the power of my imagination. The next moment, I cease to think of this object.

If one were to draw up a compendium of everything concerning spirits which is recited by schoolboys, related by the common people and demonstrated by philosophers, it would, it seems, constitute no small part of our knowledge. Notwithstanding, I would venture the following opinion. If it were to occur to someone to linger for a while over the question: What exactly is this thing which, under the name of spirit, people claim to understand so well, all the know-alls would be put in a very embarrassing position. The methodical gossip of the universities is frequently nothing but an agreement to exploit the instability of the meaning of words with a view to evading questions which are difficult to answer. And the reason for this evasiveness is the fact that the easy and generally reasonable answer ‘I do not know’ is frowned upon in the academies. Certain modern philosophers, as they like to be called, have no difficulty in disposing of this question. Their answer runs: A spirit is a being endowed with reason. No miraculous powers are needed, therefore, to see spirits; for, whoever sees human beings sees beings endowed with reason. But, the argument continues, this being, which in man is endowed with reason, is only a part of man, and this part of man, the part which animates him, is a spirit. Very well, then, before you go on to prove that only a spirit-being can be endowed with reason, please make sure that I have first of all understood what sort of concept I am to form for myself of a spirit-being. The self-deception in this case, though plain enough to be seen with half-opened eyes, nonetheless has an origin which can easily be understood. For that about which one knows a great deal early on in life as a child – of that, one can be sure, one will certainly know nothing later on in life when one has reached maturity. And the man of thoroughness will in the end at best be the sophist of his youthful delusions.

I do not, therefore, know whether spirits exist or not. And, what is more, I do not even know what the word ‘spirit’ means.