Front Page Titles (by Subject) THE SECOND PART OF THE MAIN TRANSCENDENTAL PROBLEM. How is pure Natural Science possible? - Kant’s Prolegomena and Metaphysical Foundations of Natural Science.
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THE SECOND PART OF THE MAIN TRANSCENDENTAL PROBLEM. How is pure Natural Science possible? - Immanuel Kant, Kant’s Prolegomena and Metaphysical Foundations of Natural Science. 
Kant’s Prolegomena and Metaphysical Foundations of Natural Science, trans. with a Biography and Introduction by Ernest Belfort Bax (2nd revised edition) (London: George Bell and Sons, 1891).
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THE SECOND PART OF THE MAIN TRANSCENDENTAL PROBLEM.
|LOGICAL TABLE OF THE JUDGMENTS.|
|According to Quantity.||According to Quality|
|According to Relation.||According to Modality.|
|TRANSCENDENTAL TABLE OF THE CONCEPTIONS OF THE UNDERSTANDING.|
|According to Quantity.||According to Quality.|
|Unity (the measure).||Reality.|
|Plurality (the amount).||Negation.|
|Totality (the whole).||Limitation.|
|According to Relation.||According to Modality.|
|PURE PHYSIOLOGICAL TABLE OF THE UNIVERSAL PRINCIPLES OF NATURAL SCIENCE.|
|Axioms of Intuition.|
|Anticipations of Perception.||Analogies of Experience.|
|Postulates of Empirical Thought in general.|
In order to grasp the preceding in a single notion, it is necessary to remind the reader that we are not here speaking of the origin of experience, but of that which lies within it. The first belongs to empirical psychology, and would exist without the second, which belongs to the critique of cognition, and especially to that of the understanding, and can never be sufficiently developed.
Experience consists of intuitions, belonging to sensibility, and of judgments which are entirely the work of the understanding. But the judgments the understanding constructs merely out of sensuous intuitions, are not, by far, judgments of experience. For in the one case the judgment simply connects the perceptions, as they are given in sensuous intuition; but in the other, the judgments must say what experience generally contains, and not what the mere perception, the validity of which is purely subjective, contains. The judgment of experience must add something to a judgment, over and above the sensuous intuition, and the logical connection of the same (after it has been made universal by comparison), something that determines the synthetic judgment, as at once necessary and thereby universally valid; and this can be nothing else but that conception which presents the intuition as determined in itself, in respect to one form of judgment rather than another, i.e., a conception of that synthetic unity of intuitions, which can only be presented through a given logical function of the judgment.
The sum of the above is this: the business of the senses is to intuite, that of the understanding to think. But to think is to unite presentations in a consciousness. This union is either merely relative to the subject, and is contingent and subjective, or is given unconditionally, and is necessary or objective. The union of presentations in a consciousness is judgment. Thinking, then, is the same as judging, or referring presentations to judgments in general. Hence judgments are either entirely subjective when presentations are solely referred to a consciousness in one subject, and are therein united, or they are objective when they are united in a consciousness in general, that is, are necessarily united therein. The logical momenta of all judgments are so many possible modes of uniting presentations in a consciousness. But if they serve as conceptions, they are conceptions of the necessary union of the same in a consciousness, and therefore principles of objectively valid judgments. This union in a consciousness is either analytic by identity, or synthetic by the combination and addition of different presentations to one another. Experience consists in the synthetic connection of phenomena (perceptions) in a consciousness, in so far as this is necessary. Hence pure conceptions of the understanding are those under which all perceptions must be previously subsumed, before they can serve as judgments of experience, in which the synthetic unity of perceptions is presented as necessary and universal.1
Judgments, considered merely as the union of given presentations in a consciousness, are rules. These rules, in so far as they present the union as necessary, are rules à priori, and in so far as there are none beyond them from which they can be derived, they are axioms. Since, then, in respect of the possibility of all experience, when viewed as the mere form of thought, there are no conditions of the judgments of experience beyond those which bring the phenomena in the various forms of their intuition under the pure conceptions of the understanding which make the empirical judgment objectively valid, these must be the à priori axioms of all possible experience.
The axioms of possible experience are at the same time the universal laws of Nature as known à priori. And thus the problem contained in our present second question—How is pure natural science possible? is solved. For the systematic character required by the form of a science is met with here in completeness, since beyond the above-named formal conditions of all judgments in general, that is, of all the general rules to be found in logic, there are none possible, and these constitute a logical system; while the conceptions founded upon them, containing the conditions à priori of all synthetic and necessary judgments, [constitute] in the same way a transcendental system, and finally the axioms, by means of which all phenomena are subsumed under these conceptions, [constitute] a physiological1 system, i.e., a system of nature, preceding all empirical knowledge of nature, rendering this in the first place possible, and therefore to be properly termed the universal and pure natural science.
The first of the above physiological2 axioms subsumes all phenomena, as intuitions in space and time, under the conception of quantity, and is so far a principle of the application of mathematics to experience. The second subsumes the properly empirical, namely, the feeling, which denotes the reality of intuitions, not precisely under the conception of quantity, because feeling is no intuition, contained in space and time, although it places its corresponding object in both. But between reality (presentation of feeling) and zero, i.e., the complete emptiness of intuition in time, there is a difference which has a quantity. For between each given degree of light and darkness, between each degree of heat, and complete coldness, each degree of weight and of absolute lightness, each degree of the containing of space and of totally empty space, progressively smaller degrees can be thought of, and similarly between consciousness and complete unconsciousness (psychological darkness) continually smaller [degrees] exist. Hence no perception is possible that would prove an absolute void; for instance, no psychological darkness that could be viewed otherwise than as a consciousness, which is but surpassed by another stronger consciousness, and the same in all cases of feeling. In this way the understanding can even anticipate feelings which constitute the proper quality of empirical presentations (phenomena), by means of the axiom that they all (that is, the real of every phenomenon) have a degree, and this is the second application of mathematics (mathesis intensorum) to natural science.
As regards the relation of phenomena, and indeed simply as to their existence, the determination of this relation is not mathematic but dynamic, and can never be valid objectively, and therefore adequate to an experience, if it be not subordinated to principles à priori rendering the cognition of experience regarding them in the first place possible. Hence phenomena must be subsumed under the conception of substance, which lies at the foundation of all determination of existence as a conception of the thing itself; or secondly, in so far as a succession, that is, an event, is met with among the phenomena, under the conception of an effect in reference to cause; or in so far as co-existence is to be cognised objectively, that is, through a judgment of experience, under the conception of community (reciprocal action); and these principles à priori lie at the foundation of objectively valid although empirical judgments, that is, the possibility of experience in so far as it is to connect the existence of objects in Nature. These principles are the particular laws of Nature, which may be termed dynamic.
There belongs, finally, to the judgments of experience the cognition of the agreement and connection, not so much of phenomena among one another in experience, as of their relation to experience generally, which unites either their agreement with the formal conditions cognised by the understanding or their coherence with the material of sense and of perception, or both, in one conception, and consequently contains possibility, reality and necessity, according to universal natural laws, thereby constituting the physiological doctrine of method, the distinction between truth and hypotheses, and the limits of the reliability of the latter.
Although the third table of the principles drawn from the nature of the understanding on the critical method, shows a completeness in itself, which raises it far above every other that has been vainly attempted or may be attempted in the future [to be drawn] from the nature of the thing itself, in a dogmatic way, inasmuch as therein all synthetic axioms à priori have been produced in accordance with a principle, that is, the possibility of judgment in general, which constitutes the essence of experience, in reference to the understanding, in such a manner that one may be certain there are no more such axioms (a satisfaction never to be obtained from the dogmatic method)—yet this is by far not its greatest service.
Attention must be paid to the ground of proof, which discovers the possibility of this knowledge à priori, and limits at the same time all such axioms by a condition, that must never be overlooked, if they are not to be misunderstood, and extended farther in use than the original sense attached to them by the understanding will admit of: namely, that they only contain the conditions of possible experience in general, in so far as it is subordinated to laws à priori. Thus I do not say that things in themselves contain a quantity, their reality, a degree, their existence, connection of accidents in a substance, &c.; for this no one can prove, because such a synthetic connection is simply impossible out of mere conceptions, where all reference to sensuous intuition on the one hand, and all connection of the same in a possible experience on the other, is wanting. The essential limitation of conceptions in these axioms is, therefore, that all things only stand under the above-mentioned conditions à priori as objects of experience.
From this there follows, in the second place, a special and peculiar mode of proof of the foregoing: that the axioms in question do not refer directly to phenomena and their relation, but to the possibility of experience of which phenomena constitute the matter but not the form, i.e., to objective and universally valid synthetic propositions, wherein judgments of experience are distinguished from mere judgments of perception. This happens in that the phenomena as mere intuitions, taking in a portion of space and time, are subordinated to the conception of quantity, which unites the manifold in the same synthetically in accordance with à priori rules; and that in so far as the perception contains feeling as well as intuition, between which and zero, namely, its total disappearance, a progression by diminution always takes place, the real of the phenomena must have a basis, seeing that in itself it takes in no portion of space or time.1 But this progression towards it [viz., reality] from empty time or space, is only possible in time. Consequently, although feeling as the quality of empirical intuition can never be known à priori in respect of that wherein it is specifically distinguished from other feelings, it can nevertheless be distinguished in a possible experience generally, as quantity of perception intensively [distinct] from every other of the same kind; which means the application of mathematics to Nature in respect of the sensuous intuition, by which the former is given us, and by which it becomes in the first place possible and definite.
But the reader must give the greatest attention to the mode of proof of the principles coming under the name of analogies of experience. For inasmuch as these do not, like the principles of the application of mathematics to natural science generally, concern the generation of intuitions, but the connection of their existence in an experience, this can be nothing but the determination of existence in time according to necessary laws, under which alone they are objectively valid, and therefore experience. Thus the proof of synthetic unity does not turn on the connection of things in themselves, but of perceptions, and even of these, not in respect of their content but of their determination in time, and of the relation of existence thereto, according to universal laws. These universal laws contain, therefore, the necessity of the determination of existence in time generally (consequently, according to a rule of the understanding, à priori) when the empirical determination in the relative time is to be objectively valid, that is, experience. I cannot enter further into the matter here, in Prolegomena, than to recommend the reader who has been long accustomed to regard experience as a mere empirical aggregation of perceptions, and hence does not reflect that it greatly exceeds the sphere of these, that it gives, namely, to empirical judgments, universal validity, and that for this a pure unity of the understanding is necessary to precede à priori, [to recommend him] to give attention to this distinction of experience from a mere aggregrate of perceptions, and to judge the manner of proof from this point of view.
It is here the place to raze Hume’s doubt from its foundation. He maintained justly that we can in nowise discern through the Reason the possibility of causation, namely, the reference of the existence of one thing to the existence of some other thing posited by the former. I may add to this, that we can just as little discern the conception of subsistence, i.e., the necessity contained therein, that a subject must lie at the basis of the existence of a thing, and itself be no predicate of any other thing. [I would say even] that we can form no conception of the possibility of such a thing (though we can point out examples of its use in experience). In the same way this inconceivability attaches even to the community of things, since it is not discernible how, from the state of one thing, a consequence can be drawn as to the state of some totally different thing, external to it, and vice versâ; and how substances of which each has its own separate existence, are necessarily dependent on one another. At the same time, I am far from regarding these conceptions as merely borrowed from experience, and the necessity, that is presented in them, as fictitious and mere illusion, induced in us by long custom. I have, rather, sufficiently shown that both they and the axioms deduced from them, subsist à priori before all experience, and possess indubitable objective correctness, though unquestionably only in respect of experiences.
Although I cannot have the slightest notion of such a connection of things in themselves as of their existing as substances, working as causes, or being able to stand in community with other [substances] as parts of a real whole, I can still less conceive such properties in phenomena as phenomena, because these conceptions contain nothing that lies in the phenomena, but something the understanding alone can conceive. We have, then, from such a connection of presentations in our understanding, and, indeed, in judgments generally, a similar conception, namely, that presentations cohere in one kind of judgments, as subject with reference to predicate, in another as cause with reference to effect, in a third as parts together making up a complete possible cognition. Further, we cognise à priori, that without the presentation of an object, in respect of one or the other of these momenta, to be considered as something definite, we could have no cognition that could be valid of objects, and if we occupied ourselves with the object in itself, there would be no single mark possible, by which I could cognise whether it was determined in respect of one or of another cogitated moment, i.e., whether it cohered under the conception of substance, or of cause, or (in relation to other substances) of reciprocity, for of the possibility of such a connection of existence I should have no conception. But it is not the question, how things in themselves, but how cognition of experience of things in respect of cogitated momenta of judgments generally, is defined, that is, how things as objects of experience can and should be subsumed under the above conceptions of the understanding. And hence it is clear, that I fully recognise not only the possibility, but also the necessity, of subsuming all phenomena under these conceptions, namely, of using them as axioms of the possibility of experience.
Let us now attempt a solution of Hume’s problematical conception (his crux metaphysicorum), namely, the conception of Cause. Firstly, there is given me, à priori, by means of Logic, the form of a conditioned judgment generally, one cognition as antecedent and another as consequent. But it is possible that in the perception, a rule of the relation may be met with, which will say, that on [the occurrence of a] given phenomenon another always follows (though not conversely), and this would be a case in which to make use of the hypothetical judgment, and to say, for instance, if a body be illumined long enough by the sun, it will become warm. There is certainly no necessity of connection here, in other words, no conception of cause. But I continue: if the above proposition, which is a mere subjective connection of perception, is to be a proposition of experience, it must be regarded as necessary and universally valid; but such a proposition would run: Sun is through its light the cause of heat. The above empirical rule is now looked upon as law, and indeed, not alone as valid of phenomena, but valid of them in relation to a possible experience, which requires thoroughly, and therefore necessarily, valid rules. I perfectly understand, then, the conception of Cause, as a conception necessarily belonging to the mere form of experience, and its possibility as a synthetic union of perceptions, in a consciousness in general; but the possibility of a thing in general as a cause I do not understand, because the conception of cause does not refer at all to things, but only indicates the condition attaching to experience, namely, that this can be only an objectively valid knowledge of phenomena, and their sequence in time, in so far as the antecedent can be united to the consequent according to the rule of hypothetical judgments.
Hence the pure conceptions of the understanding have no meaning whatever, when they quit the objects of experience and refer to things in themselves (noumena). They serve, as it were, to spell out phenomena, that these may be able to be read as experience. The axioms arising from their relation to the world of sense, only serve our understanding for use in experience. Beyond this, are only arbitrary combinations, destitute of objective reality, and the possibility of which can neither be known à priori, nor their reference to objects be confirmed, or even made intelligible by an example, because all examples are borrowed from some possible experience, and consequently the objects of those conceptions are nothing but what may be met with in a possible experience.
This complete solution of Hume’s problem, although it turns out to be contrary to the opinion of its originator, preserves for the pure conceptions of the understanding their origin à priori, and for the universal laws of Nature their validity as laws of the understanding, but in such a manner that their use is limited to experience, because their possibility has its basis, solely, in the reference of the understanding to experience; not because they are derived from experience, but because experience is derived from them, which completely reversed mode of connection never occurred to Hume.
The following result of all previous researches follows from the above investigations: “All synthetic axioms à priori are nothing more than principles of possible experience,” and can never be referred to things in themselves, but only to phenomena as objects of experience. Hence pure mathematics no less than pure natural science can never refer to anything more than mere phenomena, and only present that which either makes experience in general possible, or which, inasmuch as it is derived from these principles, must always be able to be presented in some possible experience.
And thus we have at last something definite to hold by in all metaphysical undertakings, which hitherto, bold enough, but always blind, have pursued all things without distinction. Dogmatic thinkers have never let it occur to them, that the goal of their endeavours should be extended such a short way from them, and even those most confident in their imagined common sense have started with conceptions and principles of the mere Reason, legitimate and natural, it is true, but intended merely for use in experience, [in search of] spheres of knowledge, for which they neither knew nor could know of any definite boundaries, because they had neither reflected nor could reflect on the nature or even the possibility of any such pure understanding.
Many a naturalist of the pure Reason (by which I understand he who ventures to decide in questions of metaphysics, without any science) might well profess that what has been here put forward with so much preparation, or if he will have it so, with tediously pedantic pomp, he has long ago not merely conjectured but known and penetrated, by the prophetic spirit of his common sense, namely, “that with all our Reason, we can never pass beyond the field of experiences.” But he must confess, notwithstanding, when questioned seriatim as to his principles of Reason, that amongst these there are many to be found not drawn from experience, and therefore valid, independently thereof, and à priori. How then, and on what grounds, will he hold the dogmatist and himself in limits, who use these conceptions and principles outside all possible experience, simply because they are recognised as independent of it? And even this adept of common sense, in spite of all his pretended, cheaply acquired, wisdom, is not proof against wandering, unobserved, beyond the objects of experience into the field of chimeras. He is, indeed, in the ordinary way, deeply enough involved therein, although by the use of popular language, by putting everything forward as probability, reasonable supposition or analogy, he gives some colour to his groundless assumptions.
From the earliest ages of philosophy, investigators of the pure Reason have postulated, beyond the sensible essences (phenomena) which constitute the world of sense, special essences of the understanding (noumena) which are supposed to constitute a world of understanding; and since they held appearance and illusion [Erscheinung und Schein] for the same thing, which in an undeveloped epoch is to be excused, ascribed reality to the intelligible essence alone.
In fact, when we regard the objects of sense, as is correct, as mere appearances, we thereby at the same time confess that a thing in itself lies at their foundation, although we do not know it, as it is constituted in itself, but only its appearance, that is, the manner in which our senses are affected by this unknown something. The understanding then, by accepting appearances, admits also the existence of things in themselves, and we may even say that the presentation of such essences as lie at the basis of appearances, in short, mere essences of the understanding, is not only admissible, but unavoidable.
Our critical deduction does not by any means exclude such things (noumena), but rather limits the principles of æsthetic, in so far that these should not be extended to all things, whereby everything would be changed into mere appearance, but that they should only be valid of objects of a possible experience. Essences of the understanding are hereby admitted only by the emphasising of this rule, which admits of no exception, that we know nothing definite whatever of these pure essences of the understanding, neither can we know anything of them, because our pure conceptions of the understanding no less than our pure intuitions, concern nothing but objects of a possible experience, in short, mere essences of sense, and as soon as we leave these, the above conceptions have not the least significance remaining.
There is indeed something seductive about our pure conceptions of the understanding, as regards temptation to a transcendent use; for so I name that which transcends all possible experience. Not only do our conceptions of substance, force, action, reality, &c., which are entirely independent of experience containing no phenomenon of sense, really seem to concern things in themselves (noumena); but what strengthens this supposition is, that they contain a necessity of determination in themselves, to which experience can never approach. The conception of cause contains a rule, according to which from one state another follows in a necessary manner; but experience only teaches us that often, or at most usually, one state of a thing follows upon another, and can therefore acquire neither strict universality nor necessity.
Hence these conceptions of the understanding seem to have far too much significance and content for mere use in experience to exhaust their entire determination, and the understanding builds in consequence, unobserved, by the side of the house of experience, a much more imposing wing, which it fills with sheer essences of thought, without even noticing that it has overstepped the legitimate bounds of its otherwise correct conceptions.
There were two important, and indeed altogether indispensable, although exceedingly dry investigations necessary, that have been undertaken in the Critique (p. 107), in the first of which it was shown that the senses do not furnish the pure conceptions of the understanding in concreto, but only the schema for their use, and that the object which conforms to it is only to be met with in experience as the [common] product of the understanding, and the materials of sense. In the second investigation (Critique, p. 178) it is shown, that—notwithstanding the independence of our pure conceptions of the understanding and principles of experience, even to the apparently greater range of their use—nothing whatever could be conceived through them outside the field of experience, because they can do nothing but determine the merely logical form of judgment in respect of given intuitions. But since, beyond the field of sensibility, no intuition is given, these pure conceptions become totally void of meaning, masmuch as they can in no way be presented in concreto. Consequently, all these noumena together with their sum-total, an intelligible world,1 are nothing but presentations of a problem, the subject of which in itself is indeed possible, but the solution of which is, by the nature of our understanding, utterly impossible, since our understanding is no faculty of intuition, but is merely the connection of given intuitions in an experience, and must comprise therefore all objects for our conceptions; but apart from these, all conceptions which cannot be supported by an intuition, must be without meaning.
The imagination may perhaps be forgiven, if it sometimes dreams, and fails to keep itself carefully within the limits of experience; for certainly it is invigorated and strengthened by a free flight like this, and it is always easier to moderate its boldness than to stimulate its languor. But for the understanding, which ought to think, to dream instead, can never be forgiven, as it is our only support in setting bounds to the fantasies of the imagination, where this is necessary.
It begins, however, very innocently and modestly. First of all, it reduces the elementary cognitions inhering in it before all experience, but having their application, notwithstanding, in experience, to their pure state. Gradually it lets fall these limits; and what is there then to hinder it, seeing that the understanding has taken its principles quite freely from itself? First of all, it is led to newly invented powers in Nature, soon after to essences outside Nature, in a word, to a world for whose fitting-up we can never fail in material, because by a fruitful imagination this will always be richly procured, and although not substantiated by experience, will yet never be confuted by it. This is the reason why young thinkers are so fond of metaphysics, treated in a genuinely dogmatic manner, and sacrifice to it their time and talents which might be otherwise useful.
But it is of no avail attempting to moderate these fruitless attempts of the pure Reason, by all manner of cautions as to the difficulty of the solution of such deeply-hidden questions, lamentations over the limits of our Reason, and by lowering assertions to mere conjectures. For if their impossibility be not clearly shown, and the self-knowledge of the Reason be not [raised to] a true science, in which the field of its right use is separated from that of its nugatory and fruitless use, so to speak, with geometrical certainty, these vain endeavours will never be completely laid aside.
How is Nature itself possible?
This question, which is the highest point the transcendental philosophy can ever touch, and to which it must also, as its boundary and completion, be directed, properly comprises two questions.
Firstly: How is Nature, in its material signification, namely, as intuition, as the sum-total of phenomena—how is space, time, and that which fills them both, namely, the object of feeling in general—possible? The answer is, by means of the construction of our sensibility, in accordance with which, it is affected in a special manner by objects, in themselves unknown and entirely distinct from these appearances. This answer has been given in the book itself in the Transcendental Æsthetic, but in these Prolegomena in the solution of the first general question.
Secondly: How is Nature in its formal signification—as the sum-total of the rules to which all phenomena must be subordinated, if they are to be thought of as connected in an experience—possible? The answer cannot but be: It is only possible by means of the construction of our understanding, in accordance with which all the above presentations of sensibility are necessarily referred to a consciousness, and whereby the special manner of our thought (namely, by rules), and by means of these, experience (which is to be wholly distinguished from a knowledge of things in themselves) is possible. This answer has been given in the book itself in the Transcendental Logic, but in these Prolegomena in the course of the solution of the second general question.
But how this special property of our sensibility itself, or of our understanding together with the necessary apperception lying at its basis, and at that of all thought, is possible, will not admit of any further solution or answer, because we invariably require it for all answers and for all thought of objects.
There are many laws of Nature that we can only know by means of experience, but regularity in the connection of phenomena, i.e., Nature in general, we can never learn through experience, because experience itself requires such laws, and these lie at the foundation of its possibility à priori. The possibility of experience in general is at once the universal law of Nature, and the axioms of the one are at the same time the laws of the other. For we know nothing of Nature otherwise than as the sum-total of phenomena, namely, of presentations in us, and hence can derive the law of their connection in no other way than from the principles of the same connection in ourselves; in other words, from the conditions of necessary union in a consciousness, which constitutes the possibility of experience.
Even the main proposition, worked out through the whole of this section, that universal natural laws are to be known à priori, of itself leads to the further proposition, that the highest legislation of Nature must lie in ourselves, namely, in our understanding, and that we must seek its universal laws, not in Nature, by means of experience; but conversely, must seek Nature, as to its universal regularity, solely in the conditions of the possibility of experience lying in our sensibility and understanding. For how would it otherwise be possible to know these laws à priori if they be not rules of analytic knowledge, but actually synthetic extensions of the same? Such a necessary agreement of the principles of possible experience with the laws of the possibility of Nature can only occur from one of two causes; either the laws are borrowed from Nature by means of experience, or conversely, Nature is derived from the laws of the possibility of experience generally, and is entirely the same thing as the purely formal regularity of the latter. The first supposition contradicts itself, for the universal laws of Nature can and must be known à priori (i.e., independently of all experience), and be posited as the basis of the empirical use of the understanding; so that only the second [hypothesis] remains to us.1
But we must distinguish the empirical laws of Nature, which always presuppose particular perceptions, from the pure or universal natural laws, which without any particular perceptions at their foundation, merely contain the conditions of their necessary union in an experience; and in respect of the last, Nature and possible experience are the same thing. Hence, as in this, the legitimacy rests on the necessary connection of phenomena in an experience, in other words, on the original laws of the understanding (without which we could cognise no object of the sensuous world whatever), it sounds at first singular, but is none the less certain, when I say in respect of the latter: The understanding draws its laws (à priori) not from Nature, but prescribes them to it.
We will illustrate this apparently daring proposition by an instance, showing that laws, which we discover in objects of sensuous intuition, especially when they are cognised as necessary, are held by ourselves to be such as the understanding has placed them, although in all other respects they may resemble the natural laws we attribute to experience.
If we consider the properties of the circle, by which the figure unites in itself so many arbitrary determinations of space, in a universal rule, one cannot do otherwise than attribute a nature to this geometrical thing. Two lines, for instance, which intersect one another and the circle, it matters not how they may be drawn, are yet always so regular that the rectangle under the segments of the one line is equal to that under the segments of the other. Now I ask, “Does this law lie in the circle or in the understanding?” in other words, does this figure contain independently of the understanding the ground of this law in itself, or does the understanding impose the law that chords cut one another in geometrical proportion, upon it, inasmuch as it has itself constructed the figure according to its own conceptions, namely, the equality of radii? We soon perceive when we follow the proofs of this law, that it can only be derived from the condition the understanding places at the foundation of the construction of this figure, namely, the equality of radii. If we extend the conception, in order to pursue still farther the unity of the manifold properties of geometrical figure under common laws, and consider the circle as a conic section, subordinated to the same fundamental conditions of construction as other conic sections, we find that all chords that intersect within the ellipse (parabola and hyperbola) always intersect, so that the rectangles under their segments, though not indeed equal, yet stand in the same ratio to one another. If we proceed still farther, namely, to the fundamental doctrines of physical astronomy, a physical law of mutual attraction is seen extended over the whole of material nature, whose rule is, that it decreases inversely as the square of the distance from each attracting point, that is, as the spherical surfaces, in which this power diffuses itself, increase; and this seems to lie necessarily in the nature of things themselves, and therefore is usually enunciated as cognisable à priori. However simple the sources of this law may be, as they rest merely on the relations of spherical surfaces of different radii, the consequences are so valuable, as regards the manifold nature of its agreement and regularity, that not only all possible orbits of the heavenly bodies [are described] in conic sections, but such a relation of them among one another follows, that no law of attraction could be conceived as suitable for a world-system, other than that of the inverse square of the distance.
Here then is Nature resting on laws which the understanding cognises à priori, and indeed mainly on universal principles of the determination of space. Now I ask: Do these natural laws lie in space, and does the understanding learn them by merely seeking to investigate the abundant meaning contained therein, or do they lie in the understanding and in the manner in which this determines space according to the conditions of synthetic unity, on which all these conceptions hinge? Space is something so uniform, and as regards all particular properties so indefinite, that certainly no one will seek for any wealth of natural laws in it. On the other hand that which determines space to the circular form, to the figure of the cone or of the sphere, is the understanding in so far as it contains the ground of the unity of its construction. The mere universal form of intuition called space, is the substratum of all particular objects of definable intuitions, and in this certainly lies the condition of its possibility and variety. But the unity of objects is determined simply by the understanding, according to conditions that lie in its own nature, and the understanding is thus the source of the universal order of Nature, since it comprehends all phenomena under its own laws; and thereby it first constructs experience (according to its form) à priori, by means of which all that is to be known through experience becomes necessarily subordinated to its laws. For we have nothing to do with the nature of things in themselves, which is as independent of the conditions of our sensibility as of those of the understanding, but with Nature as the object of a possible experience; and the understanding, while making this possible, [insists] that the world of sense be either no object of experience at all, or else, a Nature.
APPENDIX TO PURE NATURAL SCIENCE.
Of the System of the Categories.
There can be nothing more desired by a philosopher than that the variety of conceptions or principles he had previously had presented to him in a scattered manner through the use he had made of them in concreto, should be deduced from one principle à priori, and should be all united in this manner in one cognition. Formerly he only believed that those things which remained over, after a certain abstraction, and which by comparison with one another seemed to constitute a particular kind of cognitions, were completely collected; but this was only an aggregate. Now he knows that exactly so many, neither more nor less, can constitute the mode of cognition, and sees the necessity of their division, which is a comprehension; and thus, for the first time, he has a system.
To search out conceptions from common cognitions, having no particular experience at their bases, and at the same time occurring in all cognition of experience, of which they constitute, as it were, the mere form of connection, presupposes no greater reflection or more insight than to search out in a language rules for the real use of words in general, and thus to get together the elements of a grammar. Indeed, both investigations are very nearly related, even if we are unable to give a reason why each language has precisely this and no other formal construction, and still less why exactly so many, neither more nor less, of such formal determinations of the same, generally, are to be found.
Aristotle collected ten such pure elementary cognitions under the name of categories.1 To these, which were also called predicaments, he saw himself, subsequently, obliged to add five post-predicaments,2 which yet lay partly in the former (as prius, simul, motus); but this rhapsody could but serve, and be admired, as a hint for future investigators, rather than be valid as a regularly developed idea; hence in more advanced [stages] of philosophy it has been rejected as altogether useless. On investigation of the pure elements (containing nothing empirical) of the human cognition, I first succeeded, after long reflection, in distinguishing and separating with confidence the elementary conceptions of sensibility (space and time) from those of the understanding, Under these circumstances, the 7th, 8th, and 9th categories were excluded from the list. The remainder could be of no use to me, because there was no principle at hand by which the understanding could be fully gauged, and all its functions, from which its pure conceptions arise, be defined completely and with precision.
In order to find out such a principle, I looked about me for an act of the understanding containing all the rest, and distinguishing itself, only through different modifications or momenta, in bringing the manifold of presentation under the unity of thought generally, and I then found this act of the understanding to consist in judgment. There lay already before me the entire, although not altogether faultless, work of the logicians, whereby I was placed in a position to present a complete table of the pure functions of the understanding that were indefinite as regards the whole object-world. I finally referred these functions of judgment to objects generally, or rather to the conditions determining judgments as objectively valid, and there arose pure conceptions of the understanding, respecting which I could be without doubt that they alone, and only so many of them, neither more nor less, could constitute our whole cognition of things from mere understanding. I called them, as was suitable, by their old name of categories; in doing which, however, I reserved to myself the right to add in their entirety, under the name of predicables, all conceptions to be derived from these—whether by connection with one another, or with the pure form of the phenomenon (space and time), or with their matter so far as it is not empirically determined (object of feeling, generally), as soon as a system of transcendental philosophy, in furtherance of which I was now occupied with a Critique of the Reason itself, should be constructed.
But that which is essential in this system of categories, and distinguishes it from the old rhapsody which proceeded without any principle, and that which alone entitles it to be counted as philosophy, consists in that by its means the true significance of the pure conceptions of the understanding and the conditions of their use can be clearly defined. For it is evident that they are only logical functions in themselves, and as such do not constitute the least conception of an object in themselves, but require sensuous intuition at their foundation. And hence they serve only to determine in respect of the same empirical judgments that are otherwise undetermined and indifferent as regards all functions of judgment; to procure for them thereby universality, and by means of them to make judgments of experience generally, possible.
Such an insight into the nature of the categories, at the same time limiting them to use in experience, never occurred either to their first originator or to any one after him. But without this insight (which exactly depends on their derivation or deduction) they are quite purposeless, and a miserable list of names without explanation or rule of use. Had anything of the kind ever entered into the minds of the ancients, without doubt the whole study of the cognition of the pure Reason, which under the name of metaphysics has through long centuries ruined many a good head, would have come down to us in quite a different form, and would have enlightened the human understanding instead of, as has actually happened, [causing it] to exhaust itself in obscure and vain subtleties, and making it unfruitful for true science.
This system of categories makes all treatment of any object of the pure Reason itself systematic, and affords an indubitable direction or clue how and to what point in the investigation every metaphysical consideration, if it is to be complete, must be reduced; for it exhausts all the momenta of the understanding, under which every other principle must be brought. It is thus that the table of conceptions has arisen, of whose completeness we can only be assured by means of the system of categories.1 And even in the division of these conceptions destined to transcend the physiological use of the understanding (Critique, pp. 207 and 257), it is always the same clue, which, because it must be always carried through the same fixed points, determined à priori in the human understanding, invariably forms a closed circle, leaving no doubt remaining that the object of a pure conception of the understanding or of the Reason, in so far as it is to be weighed philosophically and according to principles à priori, can be completely known in such a manner. I have not been able even to omit from this derivation, to make use of the most abstract of ontological divisions, namely, the manifold distinction of conceptions of something and nothing, and accordingly to construct a regular and necessary table (Critique, p. 207).
This system, like every true system based on a universal principle, shows its inestimable utility, in that all foreign conceptions, which might otherwise creep in between the above pure conceptions of the understanding, are excluded, and its place given to every cognition. Those conceptions which under the name of conceptions of reflection, I had reduced to a table, on the clue of the categories, mingle themselves, in an ontology without favour or just claim, under the pure conceptions of the understanding, although the latter are conceptions of the connection [of the object] and thereby of the object itself; but the former are the mere comparison of previously given conceptions, and have therefore an altogether different nature and use: by my legitimate division1 they are saved from this confusion. But the utility of the above separate table of the categories will be seen much more clearly, when, as we are now about to do, we separate the table of the transcendental conceptions of the Reason which are of quite a different nature and origin from the former conceptions of the understanding, and must consequently have a form other than the latter. This necessary separation has never yet taken place in any system of metaphysics, where ideas of the Reason and conceptions of the understanding intermingle, without distinction, as though they were members of one family—a state of confusion which in the absence of a special system of categories could never be avoided.
[1 ]I readily admit that these instances do not present judgments of perception that ever could become judgments of experience, even if a conception of the understanding were added to them, because they refer to mere feeling, which every one recognises to be merely subjective, and as such never predicable of the object, and thus never capable of becoming objective. I only desire at present to give an instance of a judgment subjectively valid, but containing in itself no ground of necessity, and thereby no reference to an object. An example of judgments of perception becoming judgments of experience by the addition of a conception of the understanding follows in the next remark.
[1 ]As a more readily comprehensible example, the following may be taken. When the sun shines on the stone it grows warm—this judgment is a mere judgment of perception and contains no necessity, no matter how often I or others have perceived it. The perceptions only find themselves usually so combined. If I say the sun warms the stone the conception of the understanding, cause, is superadded to the perception, which with the conception of sunshine necessarily connects that of warmth, when the synthetic judgment becomes of necessity universally valid, consequently objective, and thus a perception is transformed into experience.
[1 ]I prefer to call the judgments by this name, which are known in logic as particularia, for this expression implies the notion that they are not universal. When I commence at unity in singular judgments and proceed to universality, I must not introduce any reference to universality; I think merely of plurality without totality, not of its exception. This is necessary if the logical momenta are to be the basis of the pure conceptions of the understanding; in logical use the matter may be left as heretofore.
[1 ]But how does this proposition, that judgments of experience must contain necessity in the synthesis of perception, agree with the proposition above so much insisted upon, that experience as knowledge à posteriori can simply give contingent judgments? When I say experience teaches me something, I always mean the perception that lies in it, e.g., that heat invariably follows on the illumination of the stone by the sun, and the proposition of experience is so far always contingent. That this heating necessarily results from the illumination by the sun is indeed contained in the judgment of experience (by means of the conception of cause); yet I do not learn this from experience, but the reverse, experience being in the first instance generated by this addition of the conception of the understanding (that of cause) to the perception. As to how the perception came by this addition, the Critique may be consulted in the division respecting the transcendental faculty of judgment.
[1 ]Or, as we should now term it, physical.—Tr.
[2 ]The three following paragraphs will hardly be able to be understood without referring to what the Critique says on the axioms, but it may be useful to have a general view of them, and to fix the attention upon the main points.
[1 ]Heat, light, &c., are in a small space (so far as degree is concerned) as great as in a large one. In the same way inward presentations (Vorstellungen), as pain or consciousness in general, are not smaller in degree, whether they last a long or a short time; hence quantity is as great here in one point and in one moment as in any time or space, however large. Degrees then are quantities, not as to intuition but as to mere feeling, or [in other words] the quantity of the basis of an intuition can only be estimated as quantity through the relation of 1 to 0, that is, by each one passing by endless mediate degrees to disappearance, or by each one growing from zero through endless moments of increase to a definite feeling in a given time.
- (The quantity of quality is degree.)
[1 ]Not, as it is commonly expressed, Intellectual world; for cognitions, through the understanding, are intellectual, and these refer only to our world of sense; but objects are called intelligible, so far as they can be presented through the understanding, and to which none of our sensuous intuitions can have reference. But as every object must require some possible intuition, one would have to conceive an understanding that contemplated things immediately, but of such we have not the least conception, and just as little therefore of the essence of the understanding, to which it should have reference.
[1 ]Crusius alone thought of a compromise, namely, that a spirit who cannot err nor deceive may have implanted those natural laws in us originally; but, since deceptive principles often intrude themselves, of which the system of this man itself shows not a few examples, it looks dubious as to the use of such principles, owing to the want of certain criteria to distinguish those of genuine from those of ungenuine origin, for we can never know for certain what the Spirit of truth or the Father of lies may have instilled into us.
[1 ]1, Substantia; 2, Qualitas; 3, Quantitas; 4, Relatio; 5, Actio; 6, Passio; 7, Quando; 8, Ubi; 9, Situs; 10, Habitus (Substance; Property; Quantity; Relation; Action; Passion; When; Where; Position; State.)
[2 ]Oppositum; Prius; Simul; Motus; Habere. (Opposition; Priority; Simultaneity; Motion; Possession.
[1 ]On the table of the categories many ingenious observations may be made; as (1) that the third arises from the combination in one conception of the first and second; (2) that those of quantity and quality are merely a progression from unity to totality, or from something to nothing (for which purpose the categories of quality must stand thus: reality, limitation, complete negation) without correlata or opposita; while, on the other hand, those of relation and modality carry the latter with them; (3) that, as in logic, categorical judgments lie at the foundation of all others, so the category of substance does to all conceptions of real things; (4) that, as modality is no particular predicate in judgments, so also modal conceptions add no determination to things, &c. Such considerations are very useful. If, in addition, all the predicables are counted up, that can be drawn pretty completely from any good Ontology (e.g., Baumgarten’s), and are arranged in classes under the categories—whereby we must not omit, however, to add as complete a dissection of all these conceptions as possible—a purely analytic part of metaphysics will arise, containing, not a single synthetic proposition, which might precede the second (the synthetic), and by its definiteness and completeness be not only useful, but by virtue of its symmetrical character contain a certain beauty.
[1 ]Critique, p. 190 et seq.