The subject of the Prolegomena is also dealt with by Dr. Vaihinger in his invaluable and exhaustive Commentary to the Critique, at pp. 38, 141, 145, 163, 280, 298, 303–4, 318, 335, 340–350, 380, 412, 442, c., of Vol. I.
This friendship, as remarked by Schubert, is proved by letters to have begun long previously to the American War of Independence—probably during the early part of the decade 1760–70; so that the conversation quoted in the text must have reference to some earlier phase of the Anglo-American question.
Vaihinger, Commentar, pp. 9, 10.
Compare note to p. 97 (Prolegomena).
This apparently refers to a passage in the eighth book of ‘Paradise Lost.’
The change to the ordinary pronoun of polite address is in the original.
The original completely ignores the canons of orthography and punctuation. Two subsequent letters of Maria von Herbert to Kant are extant. The letter is unsigned, but the name and address are given at the top.
I give the instance of the latter adduced by Wasianski in German as it is untranslatable:—
The stress is characteristically laid by Marat on the initiative and legislative authority of the popular voice and on the ultimate dependence of the executive on the popular will—by Kant, on the independence of the executive in applying laws once given.
Even when compelled, as rector of the university, to lead a procession of the senate to the cathedral, he would not enter, himself, but turned aside at the door.
Berkeleyan idealism and French materialism may be regarded equally as antithetical dogmatic offshoots of English Empiricism.
When the word ‘Critique’ is used alone throughout the present introduction, the ‘Critique of the Pure Reason’ is to be understood.
A view diametrically opposed to the one before mentioned, which makes space and the categories the conditions of external reality in the only intelligible sense of the word.
The most emphatic utterances on the realistic side, in a cosmological sense, are contained in the remarks appended to the first division of the Prolegomena.
It is in virtue of these possibilities introduced by Kant that respectable persons in the present day can ward off the charge of Atheism, by sheltering themselves under the ægis of Agnosticism.
To put this somewhat differently: the conscious ego is only the formal determination of in -ness in time. The fact of in -ness, or existence in and for itself, is implied in this very fact of conscious egoition —or, as Kant has it, the transcendental unity of apperception—from which the notion of objective reality itself is ultimately deducible. (See section on “Deduction of Categories,” ‘Critique,’ first ed.)
For a detailed statement of the, perhaps not very happily designated, “mind-stuff” theory, see the essay “On the nature of things-in-themselves.”
Even empirical psychology, which traces the unfolding of experience in the individual, presupposes experience in general as already given. Psychology is the anatomisation—the mechanical dissection—of experience; “Theory of Knowledge,” or Transcendental Philosophy, its chemical analysis.
The italics are my own.
Schopenhauer ought to have excepted Spinoza from this accusation.
“Rusticus expectat, dum defluat amnis, at ille Labitur et labetur in omne volubilis ævum.” ( Horat. ) “The peasant waits till the river has flowed past, but it flows, and will continue to flow, to all eternity.”
At the same time, Hume called this destructive philosophy itself metaphysics, and attached a high value to it. “Metaphysics and morals,” he says (Essays, Part IV.), “are the most important branches of science; mathematics and natural philosophy have not half the same value.” But the acute man considered here only the negative uses, that the moderation of the exaggerated claims of the speculative reason would have, in putting an end to the many endless and vexatious disputes that perplex mankind; but at the same time he lost sight of the positive evils that would ensue from the removal of the most important expectations of the Reason, which it can alone place before the will as the highest goal of all its strivings.
Kant’s expression “erkenntnism” I have variously translated “knowledge” and “cognition,” according to circumstances and the usages of the English language.—Tr.—
It is impossible to avoid certain expressions become classical, and which have originated in the infancy of science, being found inadequate and unsuitable as knowledge gradually progresses, and a newer and more appropriate terminology from standing in some danger of confusion with the older. Analytic method, in so far as it is opposed to synthetic, is something quite distinct from a complex of analytic propositions. The former merely means that we start from what is sought as if it were given, and ascend to the conditions under which it is alone possible. Upon this method we often use none but synthetic propositions, of which mathematical analysis affords an instance, and it might perhaps with more propriety be termed the regressive method, in contradistinction to the synthetic or progressive. A main department of logic is known as analytic, moreover, which means the logic of truth in contrast to dialectic, without any special reference to the analytic or synthetic character of the cognitions belonging to it.
Among the curiosities of literature may be counted Richardson’s translation of the above passage, as “snails wound round contrary to all sense.”—Tr.
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.
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.
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.
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.
Or, as we should now term it, physical. —Tr.
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.
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.
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.
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, 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.)
Oppositum; Prius; Simul; Motus; Habere. (Opposition; Priority; Simultaneity; Motion; Possession.
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.
Critique, p. 190 et seq.
If it be said that a science is at least real in the idea of all men when it is constituted; that the problems leading to it are put forward by the nature of the human reason in all men, and consequently that many, if faulty, attempts at its solution are at all times unavoidable, we must then say, metaphysics is subjectively (and necessarily) real, and hence we ask with justice, How is it (objectively) possible?
In disjunctive judgments we consider all possibility as divided in relation to a particular conception. The ontological principle of the thorough determination of a thing generally (that of all possible opposite predicates one must attach to each thing), which is at the same time the principle of all disjunctive judgments, is based on the content ( Inbegriff ) of all possibility, in which the possibility of a thing in general is regarded as determined. This serves as a slight explanation of the above proposition, that the act of Reason, in disjunctive conclusions of the Reason, is the same, as regards form, as that whereby it attains to the idea of a content of all reality, embracing in itself the positive of all mutually opposing predicates.
Were the presentation of the apperception, the ego, a conception whereby anything whatever was thought, it could also be used as predicate of other things, or it would contain such predicates. It is, really, nothing more than the feeling of a reality without the least conception, but only presentation of that to which all thought stands in relation ( relatione accidentis ).
It is indeed very remarkable that the metaphysicians of all times should have so carelessly passed over the permanence of substances without ever attempting a demonstration of it, doubtless because they saw themselves forsaken by all proofs as soon as they began [to deal] with the conception of substance. Common sense, well aware that without this assumption no union of perceptions in an experience is possible, supplied this deficiency by a postulate; for from experience itself it could never have drawn this axiom; partly because it could not pursue the matters (substances) in all their changes and dissolutions far enough to find the matter for ever undiminished; partly because it contained the axiom of necessity, which is always the sign of an à priori principle. Now they composedly applied this axiom to the conception of the soul as a substance, and inferred its necessary continuance after the death of man, especially as the simplicity of this substance, deduced from the indivisibility of consciousness, assured it against destruction by dissolution. Had they found the real source of this axiom, which, however, demanded much deeper investigations than they were disposed to give to it, they would have seen that the above law, of the permanence of substances, only obtains for the sake of experience, and for things in so far as they are to be cognised and connected with others in experience, and that it can never be valid of things, irrespective of all possible experience, such as the soul after death.
Hence I am anxious that the critical reader should especially occupy himself with this antinomy, because Nature herself seems to have set it up, in order to make the Reason stagger in its pretensions, and to force it into self-examination. Each proof that I have given, as well for the thesis as the antithesis, I undertake to guarantee, and thereby to exhibit the certainty of this unavoidable antinomy of the Reason. If the reader is only brought by this singular phenomenon to go back to the examination of the assumption at its foundation, he will feel himself compelled to investigate more deeply with me the primary foundation of all cognition of the pure Reason.
The idea of freedom finds a place solely in the relations of the intellectual as cause to the phenomenon as effect. Hence we cannot attribute freedom to matter with regard to the ceaseless action with which it fills its space, although this action results from an internal principle. Just as little can we find any conception of freedom suited to pure essences of the understanding; as, for instance, God, in so far as His action, is immanent; for His action, although independent of external determining causes, is nevertheless determined in His eternal Reason, that is, in the divine nature. Only if an action is to commence something, in other words, if the effect is to be met with in the time-series, and consequently in the sense-world (e.g., the beginning of the world), only then does the question arise whether the causality of the cause itself must commence, or whether the cause can give rise to an effect without its causality itself commencing. In the first case the conception of this causality is a conception of necessity, in the second, of freedom. The reader will see from the above that in explaining freedom to be the faculty of beginning an event spontaneously, I exactly hit the conception constituting the problem of metaphysics.
Herr Plattner in his Aphorisms says with acuteness, §§ 728, 729: “If the Reason be a criterion no conception can be possible which is incomprehensible to the human Reason. In the real alone is incomprehensibility to be found. Here the incomprehensibility arises from the insufficiency of the ideas acquired.” It, therefore, only sounds paradoxical and is really not strange to say that in Nature there is much that is incomprehensible (for instance, the faculty of procreation), but that when we rise higher and pass beyond Nature all is again comprehensible; for we then quit the objects that can be given us, and occupy ourselves merely with ideas, by which we may well comprehend the law wherewith the Reason prescribes to the Understanding its use in experience, because it is its own product.
Of this nature is an analogy between the juridical relations of human actions and the mechanical relations of moving forces: I can do nothing to another without giving that other the right, under the same conditions, to do the same to me; just as no body can act upon another body with its moving force without causing thereby that other body to react upon itself to the same extent. Here right and moving force are quite dissimilar things, but in their relation there is complete resemblance. Hence, by means of such an analogy as this, I can give a relational conception of things absolutely unknown to me. For instance, how the promotion of the happiness of children is related (= a ), to the love of parents (= b ), to the welfare of the human race (= c ), to the unknown [quality] in God (= x ), which we term love, not as though it had the least resemblance to any human affection, but because we can conceive its relation to the world as similar to that which things of the world have among one another. But the relational conception is here a mere category, namely, the conception of cause, which has nothing to do with sensibility.
I should say, the causality of the supreme Cause is, in respect of the world, what human Reason is in respect of art-works. The nature of the supreme Cause itself remains unknown throughout. I only compare its effect known to me (the order of the world) and its accordance with Reason, with the known workings of human Reason, and hence call the former a Reason, without thereby attributing to it as its characteristics, what I understand by this expression in men or anything else known to me.
It has been my constant design throughout the Critique to omit nothing that could render the investigation into the nature of the pure Reason complete, however deeply hidden it might be. Every one is at liberty afterwards to carry his researches as far as he likes, if it has been only indicated to him what yet remains to be done; for this may be reasonably expected of any one who has made it his business to survey this whole field, in order afterwards to consign it to others for future cultivation and allotment. To this department belong also both the scholia, which by their dryness will scarcely recommend themselves to amateurs, and hence have only been added for specialists.
Not certainly higher. High towers, and metaphysically-great men resembling them, round both of which there is commonly much wind, are not for me. My place is the fruitful bathos of experience; and the word transcendental, the meaning of which is so often elucidated by me, but not once grasped by my critic (so carelessly has he regarded everything), does not signify something passing beyond all experience, but something that indeed precedes it à priori, but that is intended simply to make cognition of experience possible. If these conceptions overstep experience, their employment is termed transcendent, which is distinguished from their immanent [employment], that is, their employment as limited to experience. All misunderstandings of this kind have been sufficiently guarded against in the work itself, but the critic found his advantage in misunderstanding.
Idealism proper always has a mystical tendency, and can have no other, but mine is solely designed for the understanding of the possibility of our cognition à priori of objects of experience, which is a problem never hitherto solved or even suggested. In this way the whole mystical idealism falls to the ground, for (as may be seen already in Plato) it inferred from our cognitions à priori (even from those of geometry) another intuition to that of the senses (namely, an intellectual intuition), because it never occured to [philosophers] that the senses themselves might intuite à priori.
The critic often fights with his own shadow. When I oppose the truth of experience to dream, he never thinks that I am here speaking simply of the well-known somnio objective sumto of the Wolffian philosophy, which is merely formal, and with which the distinction between sleeping and waking is in no way concerned, and in a transcendental philosophy indeed can have no place. For the rest, he calls my deduction of the categories and table of the principles of the understanding, “common well-known axioms of logic and ontology, expressed in an idealistic manner.” The reader need only consult these Prolegomena upon this, to convince himself that a more miserable and historically incorrect, judgment, could hardly be made.
Essence is the primal inner principle of all that belongs to the possibility of a thing. Hence one can only predicate an essence, but not a nature of geometrical figures (for nothing is contained in their conception expressive of an existence).
I find doubts expressed in the criticism of Professor Ulrich’s Institutiones Logicæ et Metaphysicæ, in the ‘Allgemeine Litteratur Zeitung’ (1785), No. 295, not indeed respecting this table of the pure conceptions of the understanding, but the conclusions drawn therefrom as to the limitation of the whole faculty of the pure Reason, and therefore of all metaphysics, in which the learned critic expresses himself at one with his no less accurate author; doubts which, because they are supposed to touch the foundation-stone of my system, as put forward in the Critique, should be reasons for thinking that the latter did not by far carry that apodictic necessity with it, in respect of its main object, which is indispensable in compelling an unqualified acceptance. This foundation-stone is said to be a deduction expounded partly there, and partly in the Prolegomena, of the pure conceptions of the understanding, which in that part of the Critique, that should have been the clearest, is said to be the most obscure, or indeed, to move in a circle, etc. I direct my answer to these objections, only to their chief point, namely, that without a completely clear and adequate deduction of the categories, the system of the Critique of pure Reason would totter to its foundations. I maintain, on the contrary, that for those who subscribe to my propositions as to the sensibility of all our intuition, and the sufficiency of the table of the categories, as determinations of our consciousness borrowed from the logical functions of judgment in general (as the Reviewer does) the system of the Critique must carry with it apodictic certainty because it is built on the proposition, that the whole speculative use of our Reason never reaches beyond objects of possible experience. For if it can be proved that the categories, of which the Reason must make use in all its cognition, can have no other employment whatever, except merely with reference to objects of experience (in such a way that only in them [viz. the categories] is the form of thought possible), the answer to the question, how they make such possible is indeed important enough, in order, as far as may be to complete this deduction, but in respect of the main object of the system, namely the determination of the boundary of the pure Reason in nowise necessary, but merely desirable. For in this respect, the deduction is already carried far enough, when it shows that the conceived categories are nothing but mere forms of the judgments, in so far as they are applied to intuitions (which are with us always sensuous), by which they first of all become objects and cognitions, because this already suffices to found the whole system of the Critique proper with complete certainty. Thus Newton’s system of universal gravitation is established, although it carries with it the inexplicable difficulty of how attraction at a distance is possible; but difficulties are not doubts. That the foundation remains even without the complete deduction of the categories being established, I can prove, from what is conceded, thus:
Conceded: that the table of the categories contains all the pure conceptions of the understanding complete, as well as all the formal operations of the understanding in judgments, from which they are deduced and differ in nothing, beyond that in the conception of the understanding an object is regarded as defined in respect of one or the other function of judgment (e.g., in the categorical judgment the stone is hard; the stone is employed as subject, and hard as predicate, so that it remains permissible to the understanding to turn the logical function of these conceptions round, and say, something hard is a stone: on the contrary, when I represent it to myself in the object as determined, that the stone (in every possible determination of an object, not of the mere conception) must be conceived only as subject, and the hardness only as predicate, the same logical functions become pure conceptions of the understanding of objects, namely, as substance and accident; )
2, Conceded: that the understanding, by its nature, carries with it synthetic principles à priori, by which it subordinates to the foregoing categories all objects that may be given it; and therefore that there must be also intuitions à priori, containing the requisite conditions for the application of the above pure conceptions of the understanding, because, without intuition there is no object in respect of which the logical function can be determined as category, and hence no cognition of any object; and that without pure intuition, no axiom defining it à priori in this respect can obtain;
3, Conceded: that these pure intuitions can never be anything but mere forms of the phenomena of the external or internal sense (space and time), and consequently only of the objects of possible experience:
It follows, that no employment of the pure Reason can ever refer to anything but objects of experience, and, as in axioms à priori, nothing empirical can be the condition, they can be nothing more than principles of the possibility of experience generally. This alone is the true and adequate foundation of the determination of the boundary of the pure Reason, but not the solution of the problem: how experience is possible by means of these categories and only by means of them. The last problem, although even without it the structure would be firm, has meanwhile great importance, and, as I now see, equally great facility, since it can be solved well-nigh by a single conclusion from the precisely determined definition of a judgment in general (an act by which the given presentations first become cognitions of an object). The obscurity which, in this portion of the deduction attaches to my previous operations, and which I do not disclaim, is attributable to the usual fortune of the understanding in research, the shortest way being commonly not the first it is aware of. I shall, therefore, take the earliest opportunity of supplying this defect (which more concerns the style of exposition than the ground of explanation, which is given correctly enough, even there) without placing my acute critic in the, doubtless, to himself, unpleasant necessity of taking refuge in a pre-established harmony, by reason of the unaccountable agreement of the phenomena with the laws of the understanding notwithstanding that the latter have sources quite distinct from the former—a remedy, by the way, far worse than the evil it is intended to cure, and against which it can really avail nothing at all. For the objective necessity in question, characterising the pure conceptions of the understanding (and the principles of their application to phenomena) cannot come out of this. For instance, in the conception of cause in connection with effect, everything remains merely subjectively necessary, but objectively simply chance combination, just as Hume has it, when he terms it mere illusion through custom. No system in the world can derive this necessity otherwise than from the pure à priori principles lying at the foundation of the possibility of thought itself, whereby alone the cognition of objects whose phenomenon is given us, that is, experience, is possible; and even supposing that the mode, how experience is thereby possible, were never adequately explained, it would remain indisputably certain that it is merely possible through these conceptions, and conversely that these conceptions are capable of no meaning or employment in any other reference than to objects of possible experience.
Gloria geometria, quod tam paucis principiis alicunde petitis tam multa praestet.— Newton, Princ. Phil. Nat. Math. Praefat.
See Prolegomena. —[ Tr. ]
This formula means: “Velocity ( Celeritas: C ) is related as the space passed over ( Spatium: S ) divided by the time consumed therein, ( Tempus: T ) or: the velocity increases in direct ratio to the space passed over, and in inverse ratio to the time consumed therein.” ( Kirchmann, Erläuterungen, p. 25).—[ Tr. ]
The verb is wanting to this sentence in the original.—[ Tr. ]
It is impossible to represent surfaces at given distances as wholly filled by the action of lines spreading out from a point in the form of rays, whether of luminosity or attraction. Thus, by such diverging rays of light, the inferior luminosity of a distant surface would merely rest on the fact that between the luminous there remain non luminous places, and these so much the larger the farther the surfaces are removed. Euler’s hypothesis avoids this inconvenience, but has certainly so much the greater difficulty in rendering the rectilinear motion of the light conceivable. But this difficulty arises from an easily avoidable mathematical conception of light-matter as a mass of globules, which according to their variously oblique arrangement, as regards the direction of the impact, would produce a lateral motion of light; whereas nothing prevents us from conceiving this matter as originally and in every sense fluid, instead of as divided into fixed globules. If the mathematician wishes to render intuitable the diminution of light by increasing distance, he makes use of rays spreading in a circle, in order to exhibit on the disc of its diffusion the size of the space, in which the same quantity of light is to be uniformly diffused between these circle-rays, in short, the diminution of the degree of luminosity; but he does not intend these rays to be regarded as the only [places of] luminosity, as though there were always places devoid of light, to be met with between them, these increasing with the distance. If one wishes to conceive each of these places as throughout luminous, the same quantity of luminosity which covers the smaller must be conceived as in equal proportion in the larger, and therefore, in order to indicate the rectilinear direction, they must be drawn from the surface and all its points to the luminous straight lines. The effect and its quantity must be previously fixed, and the cause indicated in accordance therewith. The same applies to rays of attraction, if one chooses to call them so, and indeed to all directions of forces, which are to fill a space, be it even a corporeal one, from a point.
In Phoronomy, as the motion of a body in respect of its space, was considered as change of relation in the same, it was quite indifferent whether I sought to ascribe to the body in space—or instead thereof to the relative space—an equal but opposite motion. Both give fully the same phenomenon. The quantity of the motion of the space was merely the velocity, and hence that of the body was similarly nothing but its velocity (for which reason it could be conceived as a mere movable point). But in Mechanics, since a body is conceived as in motion toward another, respecting which it has a causal relation through its motion—namely that of moving itself, inasmuch as either by its approach by the force of impenetrability or its retreat by the force of attraction, it comes into community with it—then it is no longer indifferent, whether I seek to attribute to this body or to the space, an opposite motion. For now another conception of the quantity of motion comes into play, namely not only that merely conceived in respect of the space and only consisting in the velocity, but that whereby at the same time, the quantity of the substance (as moving cause) must be taken into consideration; and it is here no longer optional, but necessary, to assume both bodies as moved, and [moved] with an equal quantity of motion in an opposite direction; but when the one relative in respect of space is at rest, to attribute to it, together with the space, the requisite motion. For one cannot act on the other by its own motion, unless, through approach by means of repulsive force, or at a distance by means of attraction. As now both forces always act equally and reciprocally in opposite directions, no body can act by means of it, through its motion, on another, except precisely in so far as the other reacts with equal quantity of motion. Thus no body can impart motion through its motion to an absolutely resting [ body ], but this [latter] must be moved (together with the space) in an opposite direction to that which it is to maintain by the motion and in the direction of the former. The reader will easily perceive, that apart from the unusual [character] which this conception of the communication of motion has in itself, it admits of being placed in the clearest light, if one is not afraid of the diffuseness of the exposition.
The equality of the action with the, in this case, falsely-called reaction, appears just as much, when under the hypothesis of the transfusion of motions, from one body into the other, the moved body A is allowed to transmit its entire motion in one moment to the resting [body], so that it would rest after the impact, a case that would be inevitable, as soon as both bodies were conceived as absolutely hard (a property which must be distinguished from elasticity). But as this law of motion could not be made to coincide in its application either with experience or with itself, nothing else remained to be done but to deny the existence of absolutely hard bodies, which was equivalent to confessing the contingency of this law, inasmuch as it ought to rest on the special quality by which matters move one another. In our presentation of this law, on the other hand, it is quite the same whether bodies that strike one another are considered absolutely hard or not. But how the transfusionists of motion can explain the motion of elastic bodies by impact in their way is quite incomprehensible to me. For it is clear that resting bodies do not, as merely resting, acquire motion, which the striking body sacrifices, but that in the impact real force is exercised in the opposite direction against the striking [body], in order as it were to compress the springiness between both, which to this end from its side demands as much real motion (although in the opposite direction) as the moving body on its side.
Of this distinction of disjunctive and alternative opposition, more in the general observation to this division.
In logic the either or always denotes a disjunctive judgment; for if one be true, the other must be false. For instance, a body is either moved or not-moved, that is, at rest. For it is simply the relation of the cognition to the object which is there spoken of. In phenomenal doctrine, where the relation to the subject is referred to, in order therefrom to determine the relation to the object, it is otherwise. For there the proposition: the body is either moved and the space at rest, or conversely, is not a disjunctive proposition in an objective, but only a subjective connection, and both these judgments therein contained are alternatively valid. In the same phenomenology, where the motion is considered not merely phoronomically, but rather dynamically, on the contrary, the disjunctive proposition is to be taken in an objective signification, that is, in place of the turning of a body I cannot assume its rest and the opposite motion of the space. But even where the motion is regarded mechanically (as when a body rushes against another apparently resting) even then, the, as regards form, disjunctive judgment in respect of the object is to be employed distributively, so that the motion must not be attributed either to the one or to the other, but to each an equal share. This distinction of alternative, disjunctive and distributive determinations of a conception as regards mutually opposed predicates has its importance, but cannot be further discussed here.
He there says: Motus quidem veros corporum singulorum cognoscere et ab apparentibus actu discriminare difficillimum est; propterea quod partis spatii illius immobilis, in quo corpora vere moventur, non incurrunt in sensus. Causa tamen non est prorsa disparata. Thereupon he allows two spheres attached by a thread, to turn about their common centre of gravity in empty space, and shows how the reality of their motion, together with its direction, can nevertheless be found in experience. I have also sought to demonstrate this under somewhat altered circumstances from the earth as moved on its axis.