It merely says that so far as observation has gone there is no exception to this rule. If, therefore, a judgment is thought with strict universality so that there can be no possible exception to it, it is not derived from experience, but is absolutely à priori. "Necessity and universality, therefore, are the sure criteria of à priori knowledge."
But, again, a further distinction must be made. All judgments are of two kinds—Analytic and Synthetic. Analytic are those in which the predicate is already contained in the subject, which, therefore, in being stated, does not add anything to our knowledge; as, for example, 'all bodies are extended.'
Synthetic Judgments, on the other hand, are those in which the predicate lies wholly outside the subject and is only added to it, and thereby contributes to our knowledge; as, for example, 'all bodies are heavy.' Now, of these two forms of judgment, Analytic are wholly à priori. Synthetic may be partly à posteriori and partly à priori, i.e. partly drawn from experience and partly from the mind itself.
The object, therefore, which Kant sets himself at the outset is to answer the question as to the possibility of an à priori knowledge, i.e. knowledge independent of experience: or, as he puts it, the question as to the possibility of a science of metaphysics. By metaphysics Kant understands in general the science of Pure Reason, the science which deals with the à priori forms of the mind. And, in particular, he distinguishes between metaphysics and two other à priori sciences—Mathematics and Physics. He, therefore, proceeds to ask the threefold question, as to the possibility of Pure Mathematics, of Natural Science, and of Metaphysics. His answer is that these sciences are possible if in relation to the objects with which they deal, synthetic judgments, or universal and necessary judgments are possible, i.e. if we can form conclusions in them without the help of sense experience.
Pure mathematics is possible because we have pure or à priori intuitions—(space and time)—and natural science is possible because the mind possesses à priori notions, viz., the categories and the principles of pure reason. Metaphysics, as the pretended science of the supersensible, can only be regarded as a futile effort, inasmuch as the ideas with which it is occupied reach out beyond experience and give an appearance of reality to the objects with which they deal. As a real science it is not possible, because the categories only permit of being applied within the domain of experience; whereas objects conceived by means of ideas, in so far as they are not received through the senses, involve the mind in indissoluble contradictions. On the other hand, the science, which teaches the proper use of the categories (as applicable only to phenomena), and of the ideas (as applicable to our knowledge of objects), and therefore determines the source as well as the limits of our cognition, is not only possible but necessary. Hence, with regard to metaphysics (knowledge springing from pure reason), the answer of Kant in effect is: It is not possible as a metaphysics of things in themselves; it is possible as a metaphysics of nature (within the domain of phenomena) and as a metaphysics of cognition. In other words, we must reject the science which professes to deal with things beyond experience while we recognise the science which confines itself to the province of possible experience.
The problem, then, which Kant has to discuss involves a theory of knowledge. The two factors of all knowledge are obviously—Sense and Understanding. What does each contribute? Sense is the receptive faculty in cognition; Understanding the active and spontaneous factor. By means of sense, objects are given; through the understanding they are thought. The former receives the raw material; the latter transmutes it into knowledge. "Notions," so runs the famous dictum of Kant, "without intuitions are empty: intuitions without notions are blind." It is the union of these two—the perceptions of sensibility and the notions of the understanding—which constitutes knowledge.
In reference to sensibility or the faculty of receiving the manifold objects of sense, there must be certain forms of intuition supplied by the mind itself, which make perceptions possible. And in regard to the understanding, there must also be certain mental processes by which our perceptions are rationalized and clothed with intelligibility. When, therefore, we inquire as to the à priori conditions of experience a twofold question arises:
(1) What are the à priori intuitions, lying ready in the mind,—the principles of our sensuous faculty?
(2) What are the à priori notions,—the principles of our thinking faculty?
The first question is considered in the Transcendental Aesthetic (aesthetic being used in its literal acceptation, as the science of the à priori principles of Sense, and not to denote the doctrine of taste). The second question is treated in the Transcendental Analytic and Dialectic.
1. Transcendental Aesthetic. What, asks Kant, are the à priori principles of our sensuous faculty? What are those forms of the mind which, in the first instance, make our sensations possible to the intelligence? In every act of perception there are two elements—the matter and the form. The matter is what is perceived: the form is that which reduces the manifoldness of appearance to order. But that which gives order to our sensations cannot belong to the phenomena themselves, but must be the pure forms which, belonging to the mind, receive the matter and afford a basis of unity.
Kant assumes that the forms of sense-perceptions are Space and Time. Space is an intuition which, without doubt, belongs inherently to the mind, whose function is to present to us objects outside of us. In the same way, time is also a pure à priori intuition. We can abstract all that belongs to the matter of sensation and yet there remain, Space and Time.
That space and time are à priori Kant proves, first, directly from the nature of the notions themselves in that they are presupposed in all experience; and, secondly, indirectly—because unless these forms were à priori, the science of mathematics, whose propositions are based on the universality and necessity of these notions, would be impossible.
But, says Kant, we must remember that space and time are only intuitions or sense perceptions; they are not to be identified with notions of the understanding, for general notions contain their particulars under them and not as parts in them. Whereas all particular spaces and particular times are but parts of space and time generally.
Space and time, therefore, are the indispensable conditions of all our perceptions. Things can only be known to us through these forms. They afford the possibility of unity. They form "the warp of experience across which the shuttle of thought continually throws its woof and constructs its web of knowledge." The one is the form of all outer sense, the other of all inner experience. Every object in the world, every state of feeling, can only become a part of consciousness as it is either localized or timed.
Space and time being thus subjective forms in which all things are presented, it follows that we do not perceive things as they are in themselves, but only as they appear to us through the media of space and time. What the thing is in itself we can never know, for we can never get it apart from our sensuous perception of it. Kant does not, however, hold that the entire world is a mere semblance. Phenomena must have realities behind them; but we cannot get at the reality, for we cannot get outside of our own minds. Things as certainly exist as our own states within us, but we can never divest ourselves of those necessary conditions through which they are presented to us.
2. Transcendental Analytic. To constitute our knowledge, as we have seen, the mind must not only be able by means of its two forms, space and time, to receive outward objects, it must have a power of co-ordinating them and giving them intelligibility. This is the work of the understanding. The action of the understanding must come in to unify the objects of sense. That action is synthesis or correlation. A pure sensation would be a mere isolated occurrence in consciousness. Sentient life, if we had no unifying faculty, would be a mere series of blind pulses. In Kant's words, "perceptions without conceptions are blind." The string which gathers the isolated beads into a necklace—the glass which collects the beams of sentient life into one focus—is what we call intellect. Synthetic unity is the one function of thought which is required to bind our sensations into knowledge.
It is, therefore, the business of the Transcendental Analytic or Logic to exhibit the special form in which this general intellectual synthesis is exercised, and to show how the work of unification is accomplished. It falls into two parts; the first, called the Analytic of Conceptions, which is a classification of the ultimate forms of the understanding; and the second, the Analytic of Principles, which exhibits these forms in their application to the elements of sense.
(a) Analytic of Conceptions. The discovery and classification of the notions of the understanding is the first task of the Analytic. Here Kant does not give himself much trouble. He simply takes the classification of judgments of traditional logic—Quantity, Quality, Relation, and Modality, and from these, in a somewhat arbitrary manner, deduces twelve categories, which he sets forth in the following table:
Every judgment in reference to Quantity is, Universal, Particular or singular; as to Quality, Affirmative, Negative or infinite; as to Relation, Categorical, Hypothetical or disjunctive; as to Modality, Problematic, Assertive, or apodictic.
Hence to these judgments there correspond an equal number of categories from which all the other pure principles may be derived. These are, under Quantity—Unity, Plurality, Totality; under Quality—Reality, Negation, Limitation; under Relation—Substance and Accident, Cause and Effect, Action and Reaction; under Modality—Possibility and Impossibility, Existence and Non-existence, Necessity and Contingency.
These categories act necessarily upon the objects of experience, as by means of these alone can an object be thought at all. But in themselves they are simply empty forms, and only receive their contents through the perceptions.
But, now, the question arises, how can the categories be applied to things and take them up into themselves? How can these forms, so plainly mental, come into relation with the sensuous world? How can two such dissimilar powers as sensibility and understanding operate in conjunction? This is what Kant calls the "Deduction of the Categories," which means their justification or application, according to which we have the second condition (the condition of time and space being the first and the unity of consciousness, as we shall see, the third), by which experience becomes possible. This synthesis is the work of the imagination, whose function is to bring the sense perceptions and the notions of the understanding together, and the element in which they meet is the form of time. If we ask then, how can objects of sense be brought into connection with intelligible notions? the answer is, not directly, but by means of a third or intermediate factor, which, being at once sensuous and mental, shares the nature of both. Such a mediating principle is to be found in the formal element of all sense perceptions—viz., time. To this determination of time Kant gives the name "The Transcendental Schema." Being à priori, it is homogeneous with the categories; being a form of sensibility, it partakes also of the character of sensible objects. Thus sense and intellect, though so dissimilar, meet by means of this product of the imagination, which has the peculiar power of bringing an object, which is not actually present, before the mind and enabling it to be an object of thought. In other words, the categories cannot act directly on objects. They work through their schematic or semi-sensuous forms. "These schemata," says Kant, "are the true and only conditions for securing to the categories a bearing upon objects—of giving them, in short, import and meaning."
Thus we have presented to us the three acts of synthesis by which intellectual knowledge takes place. First, the manifold representations are unified by the application of the à priori forms of time and space: next the intuitions resulting from this application are unified by the determining schema of the imagination. Finally, above all there is the "unity of self-consciousness." The dynamical unification of the imagination thus carries us back to a statical unity—"the standing and abiding ego"—the third and primary synthesis—"the original synthetic unity of apperception," as Kant calls it. It is the 'I think' which accompanies all our perceptions and makes them objects of knowledge for us.
The "Deduction of the categories" consists then in showing that experience presupposes a formal unity of consciousness, and that the categories express the special rules under which this primal unity presents itself for the guidance of the imagination.
Each category has a corresponding schema or time-element of its own, through which the matter of sensation is taken up and transformed into thought. The relation of time that constitutes the schema of quantity is series in time or number—the succession of units. That of quality is the contents of time. Real is what fills time; Negative is empty time. That of relation is, order of time; a determinate relation suggests a determinate order of things. Substantiality is conceived as permanence in time. Causality, as sequence in time. Reciprocity, as co-existence in time. The categories of Modality take as their schema the relation of objects to time as a whole. Possibility is the agreement with the conditions of time generally; actuality, existence in a particular time; necessity, existence in all time.
(1) The Axioms of Intuition unite in the general principle that an object of perception is always recognisable as an extensive magnitude, and is known by its quantity.
(2) The Anticipations of Perception are based upon the view that every sensation, though it has no parts out of parts, is an intensive magnitude, or is known by its quality. These are called anticipations of sensation, because they precede all sensation and prescribe its character.
These two principles, which relate to quantity and quality, are based on mathematical elements, in the one case, elements which can be placed side by side, in the other, elements which appear as degrees of quality. They show that every object of perception, whether it be physical or mental, must be thought in terms of number or degree.
(3) The third class of principles—Analogies of Experience—relate not to mathematical but to physical science; not to the internal structure of objects, but to their order and relations in actual existence. They are termed analogies, because they represent the relation of things after the analogy of the relation of thought. Just as in a judgment there is the antecedent and consequent, so in our experience of things there is the physical cause and the physical effect. But it is only an analogy, not an identity. Under this head Kant treats of substance, causality, and simultaneity. Hence we have these rules—(a) With regard to substance; in all changes of phenomena the substance is permanent. Unless thought supplied this persistent background it would be impossible for us to realize the relations of succession and simultaneity, (b) With regard to Causality, we reach this conclusion, that every event is connected with or follows after another event. In other words, all changes take place according to the law of cause and effect. The justification of this law depends on a fixity in the order of time, (c) What the second analogy does for succession in time the mind does for simultaneity. The objective co-existence of things is only conceivable on the assumption that as parts of a community they act and react on each other. The rule then here is, that all substances as perceived in space and time exist in complete reciprocity.
(4) The Postulates of Experiential Thought, which are the last class of synthetical principles, explain the use of the terms, possible, actual, and necessary, in the scientific world. That which agrees with the formal conditions of experience is possible. That which coheres with the material conditions of things is actual, and, lastly, an existence is said to be necessary in the sense that everything which occurs is regarded as determined by a cause which preceded it, and on which it must follow.
Under these four heads Kant defines the limits of human experience. These principles of the understanding can be applied only to the objects of perception. Our notions cannot extend to a knowledge of noumena—to things in themselves as existing outside of time and space and all causal connection. The attempt to know noumena in the same way as phenomena has led to all manner of contradictions. To prove this is the object of what Kant calls Transcendental Dialectic.
3. Transcendental Dialectic. We can only know how things appear to us; we can never know what they are in themselves. But it is just this unknown and unknowable with which all so-called metaphysics concerns itself. In so far, then, as Kant limits our knowledge to experience he declares the impossibility of metaphysics. But the strange thing is that the mind is not content to remain within the confines of the known. Thought, in other words, has two sides or functions, a real and an ideal. There is a higher form of the mind which Kant distinguishes from understanding by the name Reason. And as the understanding has its conceptions, so the Reason has its ideas. The object then of the Transcendental Dialectic is to examine and criticise the Ideas.
Reason is the faculty of drawing conclusions from certain given ideas—and its function is to gain the most general principles that the mind is capable of. While the understanding has experience assigned to it, reason has only to do with itself, and is exclusively occupied in perfecting our subjective consciousness. Reason, therefore, is only a purely formal logical faculty of reflection. Taken generally, it expresses the effort to find, in respect to the knowledge that is given through the understanding, those principles by which completion and unity may be reached. But just here lies the danger of reason. It is not content to rest in the finite, but is continually pressing onwards beyond its legitimate data. It can only operate with the notions of the understanding. It must not strain those notions beyond their legitimate bounds and exalt its conclusions into objects of knowledge. We must not, in other words, apply our ideas to the unconditioned, to that which is beyond the limits of experience, We must remember that the ideas of reason are mere ideas yielding no real knowledge. They are not constitutive principles through which objects of knowledge are produced, but only regulative principles, whose real use is to enable us to arrange our knowledge and bring it under certain working conceptions.
But reason is ever seeking to follow up the chain of phenomena beyond all possible experience. It aspires to complete and absolute unity. It furnishes ideas to which no perceptions can correspond. These ideas are not, however, valueless. They exist as demands, as à priori needs of the mind. Their function is to lead on the understanding and sustain it in its efforts to reach a more complete synthesis of phenomena. It is when reason attempts to do more than this that it falls into error. Reason, in other words, is the faculty of the absolute. It represents a need, an ideal of the mind. "Transcendental illusion" consists in our converting this mere subjective need into an objective reality.
The object of the Transcendental Dialectic is to expose this illusion.
Kant proceeds to trace the various forms of self-deception by which à priori reasoning imagines that it has gained a hold on truths outside the sphere of experience. And here, according to his wont, the procedure is designated by names borrowed from logic. Just as there are three forms of logical reasoning, so the absolute has these three forms: the Categorical, the Hypothetical, and the Disjunctive. Categorical reasoning presupposes a subject that is not itself an attribute—the soul or ego. Hypothetical reasoning implies a supposition that presupposes nothing further, and consequently embraces the whole of the conditions of phenomena—the Universe. Disjunctive reasoning, which embraces totality, assumes the ultimate ground of totality —viz., the Supreme Being, God.
The attempt to establish these ideas as existing outside of the mind gives rise to a series of contradictions which have vitiated all past systems of psychology, cosmology, and theology.
These three ideas give rise to three forms of dialectic reasoning, which Kant names: the Paralogisms of Pure Reason, the Antinomies of Pure Reason, and the Ideal of Pure Reason.
1. Psychology. With reference to the soul, with which he begins, Kant seeks to show that the Cartesian, "Cogito, I think," is made the basis for the assumption, without any support from experience, that the soul is a real object, immaterial, simple, personal, and immortal. The logical unity of consciousness is translated without any warrant into a real substance of mental life. The act of thought is falsely converted into a thing. What has never been given as a perception, but only as an idea, is treated as a real object. This Kant styles a paralogism.
2. Cosmology. In like manner when we attempt to form a conception of the world as a whole, we are involved in what he calls antinomies of cosmology, in which the thesis and the antithesis seem equally valid. With equal force we may say the world had a beginning in time and it had no beginning. We may assert that every compound consists of simple parts, and that there are no simple parts. Or, again, we may allege that there is such a thing as freedom, but we may also contend that nothing but necessity exists. Finally, we may allege that there exists an absolutely necessary Being and that there exists no such Being. The arguments on both sides are equally sound, and the fact that they contradict one another shows that we have entered a region where truth cannot be reached by the principles of mere logic.
3. Theology. And so finally with the ideas of God. In this section Kant attempts to destroy the cogency of the arguments hitherto adduced for the existence of the Deity. He combats the right of the ontological proof to infer existence from the conception alone. He shows that the cosmological argument involves a petitio principii, when it seeks the final cause of all contingent things in an absolutely necessary Being. Finally, he proves that the teleological proof, even when we grant the beauty, harmony, and design of the universe—leads only to the conception of a wise and good architect of the world.
But while these proofs are unsatisfactory from a logical point of view, the denial of God's existence, Kant holds, is equally incapable of proof. On the great questions of metaphysics,—immortality, freedom, God,— scientific knowledge is hopeless. "Both parties to the dispute beat the air; they worry their own shadow, for they pass beyond nature to a region where their dogmatic grips find nothing to lay hold of."
Are these ideas then pure delusions? If so, how is it that the human mind ever harks back to them and finds in them a perennial fascination? Kant admits that these ideas have a relative value. They stand as an ideal towards which the mind aspires. The ideas of reason, though involving the mind in contradiction if pursued to their ultimate logical conclusions, have a regulative and practical validity. We may regard them as postulates. They do not add to our knowledge, but they help us to systematize our manifold experience, and while incapable of logical justification, they possess a moral certainty. The existence of God, the freedom of the will, the immortality of the soul, are inexplicably bound up with our moral life. Metaphysics can no longer claim, indeed, to be the foundation-stone of religion and morality. "But if she cannot be the atlas who bears the moral heaven, she can furnish a magic defence. Around the ideas of religion she throws the bulwark of invisibility, and the sword of the sceptic and the battering ram of the materialist fall harmless on vacuity."