De Mundi Sensibilis atque Intelligibilis Forma et Principiis
Dissertation on the Form and Principles of the Sensible and the Intelligible World
ON THE IDEA OF A WORLD IN GENERAL
As the analysis of a substantial composite terminates only in a part which is not a whole, that is, in a simple part, so synthesis terminates only in a whole which is not a part, that is, the world.
In this exposition of the underlying concept I have had regard not only to the marks pertaining to the distinct cognition of the object, but somewhat also to the two-fold genesis of the concept from the nature of the mind, which, being serviceable to a method of deeper metaphysical insight, by way of example appears to me not a little commendable. For it is one thing, the parts being given, to conceive the composition of the whole by an abstract notion of the intellect, and another thing to follow out this general notion considered as a problem of the reason by the cognitive sensuous faculty, that is, to represent it to one’s self in the concrete by a distinct intuition. The former is done through the class concept by composition, as several things are contained either under it or mutually, and hence by intellectual and universal ideas. The latter rests on the conditions of time, inasmuch as the concept of a composite is possible genetically, that is by synthesis, by the successive union of part to part, and falls under the laws of intuition. Similarly, a substantial composite being given, we easily attain to the idea of the simple parts by the general removal of the intellectual notion of composition; for what remains after the removal of conjunction are the simple parts. But according to the laws of intuitive cognition this is not done, that is, all composition is not removed, except by a regress from the given whole to any possible parts whatsoever—in other words, by an analysis again resting on the condition of time. But since in order to a composite a multiplicity, in order to a whole, the allness, of parts is required, neither the analysis nor the synthesis will be complete; hence neither by the former will the concept of the simple part emerge, nor by the latter the concept of the whole, unless either can be gone through within a time that is finite and assignable.
But since in a continuous quantity the regress from the whole to assignable parts, and in an infinite quantity the progress from the parts to the given whole are endless, complete analysis in the one and complete synthesis in the other direction are impossible; hence neither the whole in the first case as to composition, nor the composite in the latter case as to totality can be thought completely in accordance with the laws of intuition. Unthinkable and impossible being vulgarly deemed to have the same meaning, it is plain why the concepts of the continuous as well as that of the infinite are rejected by most men as concepts whose representation according to the laws of intuitive cognition is impossible. Although I do not here champion these notions, especially not the first, which are considered exploded by many schools, still the following reminder is of the greatest moment. Those who use so perverse an argumentation have fallen into a grave error. For whatever is repugnant to the laws of the intellect and reason is of course impossible, but that which being the object of pure reason does merely not fall under the laws of intuitive cognition is not so. For here the disagreement between the sensuous and the intellectual faculties, whose natures I shall presently explain, indicates nothing except that the abstract ideas which the mind has received from the intellect can often not be followed out in the concrete and converted into intuitions. This subjective difficulty generally feigns some objective repugnance and easily deceives the incautious, the limits by which the human mind is circumscribed being taken for those by which the essence of things themselves is contained.
Furthermore, as the argument from intellectual reasonings easily shows that substantial composites being given, whether by the testimony of the senses or otherwise, the simple parts and the world are also given, so does our definition point out causes contained in the nature of the subject why the notion of a world should not seem merely arbitrary and made up, as in mathematics, only for the sake of the deducible consequences. The mind intent upon resolving as well as compounding the concept of a composite demands and presumes boundaries in which it may acquiesce in the former as well as in the latter direction.
In defining the World the following points require attention:
I. Matter (in the transcendental sense), that is, the parts which are here assumed to be substances. We might plainly be regardless of coincidence between our definition and the meaning of the common word, the question being, so to speak, of a problem arising in accordance with the laws of reasoning, namely, how several substances may coalesce into one, and on what condition rests this one’s being no part of another. But the force of the word World, as commonly used, of itself falls in with us. For no one will attribute accidents to the World as parts, but as determinations, states; hence the so-called world of the ego, unrestrained by the single substance and its accidents, is not very appositely called a World, unless, perhaps, an imaginary one. For the same reason it is not permissible to refer the successive series—namely, of states—as a part to the mundane whole; for modifications are not parts, but consequences of the subject. Finally, as to the nature of the substances constituting the world, I have not here called into debate whether they be contingent or necessary, nor do I hide such a determination unproved in the definition in order subsequently, as is sometimes done, to draw it thence by some specious argumentation. But I shall show further on that their contingency can be amply concluded from the conditions here posited.
II. Form, which consists in the co-ordination of the substances, not in their subordination. For co-ordinates are to be regarded as mutual complements to a whole, subordinates as effect and cause, or generally, as principle and consequence. The former relation is reciprocal and homonymous, any correlate in respect to any other being considered as at once determining and determined. The latter is heteronymous; on the one hand dependence only, causality on the other. This co-ordination is conceived as real and objective, not as ideal, and resting in the mere pleasure of a subject making up a whole by the summation of any multiplicity whatever. For the grasping of several things can by no contrivance be made a whole of representation, nor, for that reason, a representation of the whole. Therefore, if there be any totals of substances connected by no bond, a grasping of them together, the mind forcing the multiplicity into ideal oneness, will be called nothing more than a plurality of worlds comprehended in a single thought. But the connection constituting the essential form of a world is looked upon as the principle of the possible influences of the substances composing that world. For an actual influence pertains not to essence but to state, and the transitive forces, the causes of the influences, suppose some principle by which it is possible that the states of several things in other respects existing independently of each other are mutually related as consequences, which principle being abandoned, the possibility of transitive force in a world is an illicit assumption. And, furthermore, this form essential to the world is on that account immutable, and exposed to no vicissitude whatever. It is so in the first place for a logical reason, since any change supposes the identity of the subject with determinations succeeding one another in turn. Hence the world, remaining the same world through all the states succeeding one another, preserves the same fundamental form. For it does not suffice to the identity of the whole that all the parts be identical, the identity of characteristic composition is required also. But it follows especially from a real cause. For the nature of the world, which is the primary inner principle of whatever variable determinations may pertain to its state, never by any possibility being opposite to itself, is naturally, that is, by itself, immutable; hence there is given in any world whatever some form ascribable to its nature, constant and invariable, as the perennial principle of any contingent and transitory form pertaining to the state of the world. They who hold this disquisition superfluous are confuted by the concepts of space and time, conditions, as it were, given by their very own selves and primitive, by whose aid, that is to say, without any other principle, it is not only possible but necessary for several actual things to be regarded as reciprocally parts constituting a whole. But I shall show presently that these are plainly not rational notions, nor the bonds which they form objective ideas, but phenomena; and that though they witness, to be sure, some principle which is the common universal bond, it is not set forth by them.
III. Universality, which is the absolute allness of the appertaining parts. For, regard being had to any given composite, though it may be besides a part of another, still there always obtains a certain comparative allness, namely, that of the parts belonging to it as a particular quantity. But in this case whatsoever things are regarded as mutually parts of whatsoever whole, are understood to be conjointly posited. This absolute totality, apparently an everyday and perfectly obvious concept, especially when, as happens in the definition, it is enunciated negatively, when canvassed thoroughly becomes the crucial test of the philosopher. For it is scarce conceivable how the inexhaustible series of the states of the universe succeeding one another eternally be reducible to a whole comprehending all changes whatsoever. Since it is necessary to very infinitude to be without end, and hence no successive series is given but what is the part of another, completeness or absolute totality is by parity of reasoning plainly excluded. For although the notion of a part can be taken in a universal sense, and although everything contained under this notion, if regarded as posited in the same series, constitutes unity, yet the concept of the whole appears to exact their all being taken simultaneously, which in the case given is impossible. For, although to the whole series nothing succeeds, there is given in the succession no posited series to which nothing succeeds, unless it be the last. There will, then, in eternity be something which is last, which is absurd. Perhaps some may think that the difficulty which besets a successive infinite is absent from a simultaneous infinite, for the reason that apparently simultaneity plainly professes to embrace all at the same time. But, if the simultaneous infinite be admitted, the successive infinite also will have to be conceded, and the negation of the latter cancels the former. For the simultaneous infinite offers matters everlastingly inexhaustible to a successive progress in infinitum through its innumerable parts, which numberless series actually being given in the simultaneous infinite, a series though inexhaustible by successive addition could be given as a whole. In solution of the perplexing problem note; that both the successive and the simultaneous co-ordination of several things, since they rest upon the concept of time, do not pertain to the intellectual concept of a whole, but only to the conditions of sensuous intuition; hence though not sensuously conceivable, they do not on that score cease being intellectual concepts. For in order to the latter it suffices that co-ordinates be given, no matter how, and that they be thought of as all pertaining to a unit.
ON THE DISTINCTION BETWEEN THE SENSIBLE AND THE INTELLIGIBLE GENERALLY
Sensibility is the receptivity of a subject by which it is possible for its representative state to be affected in a certain way by the presence of some object. Intelligence, rationality, is the faculty of a subject by which it is able to represent to itself what by its quality cannot enter the senses. The object of sensibility is sensuous; what contains nothing but what is knowable by the intellect is intelligible. In the older schools the former was called phenomenon, the latter noumenon. To the extent to which knowledge is subject to the laws of sensuousness it is sensuous; to the extent to which it is subject to the laws of intelligence it is intellectual or rational.
Since whatever is in sensuous knowledge depends upon the subject’s peculiar nature, as the latter is capable of receiving some modification or other from the presence of objects which on account of subjective variety may be different in different subjects, whilst whatever knowledge is exempt from such subjective condition regards the object only, it is plain that what is sensuously thought is the representation of things as they appear, while the intellectual presentations are the representations of things as they are. Now there is in sense representation something which may be called the matter, namely, the sensation, and in addition to this something which may be called the form, namely, the appearance of the sensible things, showing forth to what extent a natural law of the mind co-ordinates the variety of sensuous affections. Furthermore, as the sensation constituting the matter of sensuous representations argues, to be sure, the presence of something sensible, but depends as to quality on the nature of the subject, as the latter is modifiable by the object; exactly so does the form of that representation witness certainly some reference or relation among the sensuous percepts, but itself is not, as it were, the shadowing forth or outlining of the object, but only a certain law inherent in the mind for co-ordinating among themselves sensuous percepts arising from the presence of the object. For by form or appearance the objects do not strike the sense, hence in order that various sense-affecting objects may coalesce into some whole of representation, there is need of an inner principle of the mind by which, in accordance with stable and innate laws, that variety shall take on some appearance.
To sensual cognition then pertains both the matter which is sensation and by which the knowledge is said to be sensual, and the form by which, even though we find it without any sensation, the representations are called sensuous. On the other hand, as to intellectual concepts, it is above all to be well noted that the use of the intellect, or of the superior faculty of the soul, is two-fold. By the first use are given the very concepts both of things and relations. This is the real use. By the second use they, whencesoever given, are merely by common marks subordinated to one another, the lower to the higher, and compared among themselves according to the principle of contradiction. This is called the logical use. The logical use of the intellect is common to all the sciences; the real use is not. For a cognition given in any wise is regarded either as contained under or as opposed to a mark common to several cognitions, and this either by immediate apposition, as in judgments in order to distinct cognition, or mediately, as in reasoning, in order to adequate cognition. Thus sensuous knowledge being given, sensuous percepts are by the logical use of the intellect subordinated to other sensuous percepts, as to common concepts, and phenomena to the more general laws of phenomena. In this connection it is of the greatest moment to note that cognitions must continue to be regarded as sensuous, no matter how great may have been the logical use of the intellect upon them. For they are called sensuous on account of their origin, not of their collation by identity and opposition. Hence, empirical laws, though of the greatest generality, are, nevertheless, sensual, and the principles of sensuous form in geometry, the relations in determinate space, however much the intellect arguing according to logical rules from what is sensuously given, by pure intuition, be employed upon them, do not for that matter pass beyond the class of sense-percepts. That in sense-percepts and phenomena which precedes the logical use of the intellect is called appearance, while the reflex knowledge originating from several appearances compared by the intellect is called experience. Thus there is no way from appearance to experience except by reflection according to the logical use of the intellect. The common concepts of experience are termed empirical, its objects phenomena, and the laws as well of experience as of all sensuous cognition generally are called the laws of phenomena. Empirical concepts, then, are not by a reduction to greater universality rendered intellectual in the real sense and do not transcend the species of sensuous cognition, but, however high abstraction may carry them, remain indefinitely sensuous.
Now as to strictly intellectual concepts in which the use of the intellect is real. Such concepts both of objects and relations are given by the very nature of the intellect, are not abstracted from any use of the senses, and do not contain any form of sensuous knowledge as such. It is needful here to take note of the extreme ambiguity of the word abstract, which, in order not to confuse our disquisition on intellectual concepts, must be removed to begin with, for properly we should say abstract from some things, not abstract something. The former denotes that in a concept we give no attention to other matters in whatsoever way they may be connected with it; but the latter, that it is not given but in the concrete and so as to be separated from what it is conjoined with. Hence an intellectual concept abstracts from everything sensuous, it is not abstracted from sensuous things, and perhaps would be more correctly called abstracting than abstract. Intellectual concepts it is more cautious, therefore, to call pure ideas, and concepts given only empirically, abstract ideas.
From the foregoing it will be seen that it is badly to expound the sensuous to call it the more confusedly known, and the intellectual the distinctly known. For these are only logical distinctions and plainly do not touch the data underlying all logical comparison. The sensuous may be exceedingly distinct, while intellectual concepts are extremely confused. The former we observe in the prototype of sensuous knowledge, geometry; the latter, in the organon of all intellectual concepts, metaphysics. It is evident how much toil the latter is expending to dispel the fogs of confusion darkening the common intellect, though not always with the happy success of the former science. Nevertheless, any cognition retains the marks of its origin, the former, however distinct, being called by genesis sensuous; the latter, no matter how confused, remaining intellectual, as for instance, the moral concepts, which are known not experientially but by the pure intellect itself. The writer fears that Wolf by the distinction between the sensuous and the intellectual, which to him is only logical, checked, perhaps wholly, and to the great detriment of philosophy, that noble enterprise of antiquity of discussing the nature of phenomena and noumena, turning us from the investigation of these to what are frequently but logical trifles.
The primary philosophy containing the principles of the use of pure intellect is metaphysics. But there is a science propaedeutical to it, showing the distinction of sensuous cognition from intellectual, a specimen of which we present in this dissertation. Empirical principles not being found in metaphysics, the concepts to be met with in it are not then to be sought for in the senses, but in the very nature of pure intellect; not as connate notions, but as abstracted from laws whose seat is in the mind, by attending to the actions of the mind on the occasion of experience, and hence as acquired. Of this species are possibility, existence, necessity, substance, cause, etc., with their opposites and correlates, which, never entering as parts into any sensual representation, can by no means have been abstracted thence.
The purpose of intellectual concepts is mainly twofold; in the first place refutative, by which they are of negative use, when, shutting off sensuous concepts from noumena, though not advancing science a hair’s breadth, they maintain however its immunity from the contagion of error. In the second place dogmatic, following which the general principles of pure intellect, such as are set forth in ontology or rational psychology, go forth into an exemplar inconceivable except by pure intellect, and the common measure of all other things considered as realities, namely, noumenal perfection. The latter is such either in the theoretical or in the practical sense. In the former it is the highest being, God. In the latter sense, it is moral perfection. Moral philosophy, then, inasmuch as supplying the first principles of judgment, is not cognized except by pure intellect, and itself belongs to pure philosophy, and Epicurus reducing its criteria to deduction from the sense of pleasure or pain is rightly reprehended, together with some moderns following him a certain distance from afar, as Shaftesbury and his adherents. In any class of things having variable quantity the maximum is the common measure and the principle of cognition. Now the maximum of perfection is called ideal, by Plato, Idea—for instance, his Idea of a Republic—and is the principle of all that is contained under the general notion of any perfection, inasmuch as the lesser grades are not thought determinable but by limiting the maximum. But God, the Ideal of perfection, and hence the principle of cognition, is also, as existing really, the principle of the creation of all perfection.
To man, no intuition of intellectual concepts is given, only symbolical cognition, and intellection is granted us only by universal concepts in the abstract, not by the concrete singular. For all intuition is restricted by some principle of form under which alone anything can be discerned by the mind immediately or as singular, and not merely conceived discursively by general concepts. This formal principle of our intuition—space and time—is the condition under which something can be an object of our senses, and hence as a condition of sensuous knowledge is not a medium for intellectual intuition. Besides, all the material of our cognition is given only by the senses, but the noumenon, as such, is not conceivable by representations drawn from sensations; hence the intellectual concept, as such, is destitute of all data of human intuition. For the intuition of our mind is always passive, and therefore possible only to the extent to which something can affect our senses. But the divine intuition, the cause—not the consequence, of objects, being independent, is the archetype, and hence perfectly intellectual.
But although phenomena are properly the appearances of things, but not ideas, or express the inner and absolute quality of objects, their cognition is nevertheless of the truest. For in the first place, being apprehended sensual concepts, they, being consequences, witness the presence of the object, contrary to Idealism; and as regards judgments concerning that which is sensuously known, since truth in judging consists in the agreement of the predicate with the given subject, and since the concept of the subject as a phenomenon is given only by relation to the sensuous cognitive faculty, the sensuously observable predicates being given according to the same, it is plain that the representations of subject and predicate are made according to common laws, and hence give occasion for perfectly true cognition.
All sense-objects are phenomena, but that which, not touching our senses, contains the form only of sensuality, belongs to pure intuition, that is, an intuition devoid of sensations, but not on that account, intellectual. Phenomena of the external sense are examined and set forth in physics; those of the internal sense in empirical psychology. But pure human intuition is not a universal or logical concept under which, but a singular in which all sensible objects are thought, and hence contains concepts of space and time, which, since they determine nothing concerning sensible objects as to quality, are not the objects of science except as to quantity. Hence pure mathematics considers space in geometry and time in pure mechanics. To these is to be added a certain concept, intellectual to be sure in itself, but whose becoming actual in the concrete requires the auxiliary notions of time and space in the successive addition and simultaneous juxtaposition of separate units, which is the concept of number treated in arithmetic. Pure mathematics, then, expounding the form of our entire sensuous cognition, is the organon of all intuitive and distinct knowledge, and since its objects are not only the formal principles of all intuition, but themselves original intuitions, it confers cognition both perfectly true, and the model of the highest degree of clearness to others. There is given, therefore, a science of sensual things, though being phenomena there is not given a real intellection, but a logical one only; hence it is plain in what sense those borrowing from the Eleatic school are to be thought to have denied a science of phenomena.
ON THE PRINCIPLES OF THE FORM OF THE SENSIBLE WORLD
The principle of the form of a universe is that which contains the cause of the universal tie by means of which all substances and their states pertain to one which is called a world. The principle of the form of the sensible world is that which contains the cause of the universal tie of all things regarded as phenomena. The form of the intelligible world acknowledges an objective principle, that is, some cause by which it is the colligation of what exists in it. But the world regarded as phenomenon, that is, in respect to the sensibility of the human mind, acknowledges no principle of form but a subjective one, that is, a certain mental law by which it is necessary that all things qualified for being objects of the senses would seem to pertain necessarily to the same whole. Whatever be, therefore, the principle of the form of the sensible world, it will comprise only actual things in as far as thought of as possibly falling under sense-perception; hence neither immaterial substances, which as such are excluded by definition from the external senses altogether, nor the cause of the world, which, since by it the mind exists and has the power of sense-perception, cannot be the object of the senses. These formal principles of the phenomenal universe which are absolutely primary, universal, and, so to speak, the outlines and conditions of anything else whatsoever in human sensuous cognition, I shall now show to be two: time and space.
1. The idea of time does not originate in, but is presupposed by the senses. Whether things falling under sense-perception be simultaneous or in line of succession cannot be represented but by the idea of time; nor does succession beget the concept of time; it appeals to it. Hence the notion of time, though acquired by experience, is badly defined by a series of actual things existing one after another, for what the word after means I understand only by the previous concept of time. For those things are after one another which exist at different times, as those are simultaneous which exist at the same time.
2. The idea of time is singular, not general. For any time whatever is thought only as a part of one and the same unmeasured time. If you think two years you cannot represent them to yourself but in a mutually determinate position, and if they do not immediately follow one the other, you cannot think of them except as connected by some intermediate time. Which of different times is first and which later can be defined in no way by any marks conceivable by the intellect, unless you are willing to run into a circle, and the mind discerns it by no more than one intuition. Besides, we conceive of all actual things as posited in time, not as contained as common marks under a general notion of time.
3. The idea of time, therefore, is an intuition, and being conceived before all sensation as the condition of the relations occurring in sensible things, it is not a sensual but pure intuition.
4. Time is a continuous quantity and the principle of the laws of continuity in the changes of the universe. For a continuous quantity is one which does not consist of simple parts. But since by time are only thought relations without any mutually related data, there is in time—as a quantity—composition, which being conceived wholly removed leaves nothing over. But a composite of which, composition being removed, nothing is left, does not consist of simple parts. Therefore, etc. Any part of time, then, is time; and the simple things in time, namely, the moments, are not parts of it, but termini between which time intervenes. For two moments being given, time is not given, except as in them actualities succeed each other; hence, beside the given moment it is necessary that time be given in the latter part of which there is another moment.
The metaphysical law of continuity is this: All changes are continuous or flowing, that is, opposite states succeed each other only by an intermediate series of different states. For since two opposite states are in different moments of time, and some time is always intercepted between two moments, in which infinite series of moments the substance is neither in one assignable state nor the other, nor yet in none, it will be in different states, and so on infinitely.
The celebrated Kästner, calling in question this Leibnitzian law, calls on its defenders to demonstrate that the continuous motion of a point around the sides of a triangle is impossible, it being necessary to prove this if the law of continuity be granted. Here is the demonstration required. Let the letters a b c denote the three angular points of a rectilineal triangle. If the point did move continuously over the lines ab, bc, ca, that is, over the perimeter of the figure, it would be necessary for it to move at the point b in the direction ab, and also at the same point b in the direction bc. These motions being diverse, they cannot be simultaneous. Therefore, the moment of presence of the movable point at vertex b, considered as moving in the direction ab, is different from the moment of presence of the movable point at the same vertex b, considered as moving in the same direction bc. But between two moments there is time; therefore, the movable point is present at point b for some time, that is, it rests. Therefore it does not move continuously, which is contrary to the assumption. The same demonstration is valid for motion over any right lines including an assignable angle. Hence a body does not change its direction in continuous motion except by following a line no part of which is straight, that is, a curve, as Leibnitz maintained.
5. Time is not something objective and real, neither a substance, nor an accident, nor a relation. It is the subjective condition necessary by the nature of the human mind for coordinating any sensible objects among themselves by a certain law; time is a pure intuition. Substances as well as accidents we co-ordinate whether according to simultaneity or succession by the concept only of time; hence the notion of time as the principle of form outranks the concepts of the former. Any relations so far as occurring in sense-perception, whether simultaneous or successive, involve nothing but the determination of positions in time, to wit, either in the same point or in different points of the latter.
Those who assert the objective reality of time either conceive of it as a continuous flow in what exists, without, however, any existing thing, as is done especially by the English philosophers, an absurd fiction, or as something real abstracted from the succession of inner states, as it has been put by Leibnitz and his followers. The falsity of the latter opinion, besides obviously exposing it to the vicious circle in the definition of time, and, moreover, plainly neglecting simultaneity, the most important consequence of time, disturbs all sound reason, because it demands instead of the determining of the laws of motion by the measure of time, that time itself, as to its nature, be determined by what is observed in motion or some series of inner changes, whereby plainly all certitude of rules is abolished. That we can estimate the quantity of time only in the concrete, namely, either by motion or by a series of thoughts, arises from the concept of time resting only on an inherent mental law, it not being a connate intuition; whence the act of the mind co-ordinating the impressions is elicited only by the aid of the senses. So far from its being possible to deduce and explain the concept of time from some other source by force of reason, it is presupposed by the very principle of contradiction, it underlies it by way of condition. For a and not-a are not repugnant unless thought of the same thing simultaneously, that is, at the same time; they may belong to the same thing after each other, at different times. Hence the possibility of changes is not thinkable except in time. Time is not thinkable by changes, but reversely.
6. But although time posited in itself and absolutely be an imaginary thing, yet as appertaining to the immutable law of sensible things as such, it is a perfectly true concept, and the patent condition of intuitive representation throughout all the infinite range of possible sense-objects. For since simultaneous things as such cannot be placed before the senses but by the aid of time, and since changes are unthinkable except by time, it is obvious that this concept contains the universal form of phenomena, and that, indeed, all events observable in the world, all motions, all internal changes, agree necessarily with the temporal axioms of cognition which we have partly expounded, since only under these conditions can they become sense-objects and be co-ordinated. It is, therefore, absurd to excite reason against the primary postulates of pure time, as, for example, continuity, etc., since they follow from laws prior and superior to which nothing is found, and since reason herself in the use of the principle of contradiction cannot dispense with the support of this concept, so primitive and original is it.
7. Time, then, is the absolutely first formal principle of the sensible world. For all sensible things of whatsoever description are unthinkable except as posited either simultaneously or one after another, and, indeed, as if involved and mutually related by determinate position in the tract of unique time, so that by this primary concept of everything sensuous originates necessarily that formal whole which is not a part of another, that is, the phenomenal World.
A. The concept of space is not abstracted from external sensations. For I am unable to conceive of anything posited without me unless by representing it as in a place different from that in which I am, and of things as mutually outside of each other unless by locating them in different places in space. Therefore the possibility of external perceptions, as such, presupposes and does not create the concept of space, so that, although what is in space affects the senses, space cannot itself be derived from the senses.
B. The concept of space is a singular representation comprehending all things in itself, not an abstract and common notion containing them under itself. What are called several spaces are only parts of the same immense space mutually related by certain positions, nor can you conceive of a cubic foot except as being bounded in all directions by surrounding space.
C. The concept of space, therefore, is a pure intuition, being a singular concept, not made up by sensations, but itself the fundamental form of all external sensation. This pure intuition is in fact easily perceived in geometrical axioms, and any mental construction of postulates or even problems. That in space there are no more than three dimensions, that between two points there is but one straight line, that in a plane surface from a given point with a given right line a circle is describable, are not conclusions from some universal notion of space, but only discernible in space as in the concrete. Which things in a given space lie toward one side and which are turned toward the other can by no acuteness of reasoning be described discursively or reduced to intellectual marks. There being in perfectly similar and equal but incongruous solids, such as the right and the left hand, conceived of solely as to extent, or spherical triangles in opposite hemispheres, a difference rendering impossible the coincidence of their limits of extension, although for all that can be stated in marks intelligible to the mind by speech they are interchangeable, it is patent that only by pure intuition can the difference, namely, incongruity, be noticed. Geometry, therefore, uses principles not only undoubted and discursive but falling under the mental view, and the obviousness of its demonstrations—which means the clearness of certain cognition in as far as assimilated to sensual knowledge—is not only greatest, but the only one which is given in the pure sciences, and the exemplar and medium of all obviousness in the others. For, since geometry considers the relations of space, the concept of which contains the very form of all sensual intuition, nothing that is perceived by the external sense can be clear and perspicuous unless by means of that intuition which it is the business of geometry to contemplate. Besides, this science does not demonstrate its universal propositions by thinking the object through the universal concept, as is done in intellectual disquisition, but by submitting it to the eyes in a single intuition, as is done in matters of sense.
D. Space is not something objective and real, neither substance, nor accident, nor relation; but subjective and ideal, arising by fixed law from the nature of the mind like an outline for the mutual co-ordination of all external sensations whatsoever. Those who defend the reality of space either conceive of it as an absolute and immense receptacle of possible things, an opinion which, besides the English, pleases most geometricians, or they contend for its being the relation of existing things itself, which clearly vanishes in the removal of things and is thinkable only in actual things, as besides Leibnitz, is maintained by most of our countrymen. The first inane fiction of the reason, imagining true infinite relation without any mutually related things, pertains to the world of fable. But the adherents of the second opinion fall into a much worse error. Whilst the former only cast an obstacle in the way of some rational or noumenal concepts, otherwise most recondite, such as questions concerning the spiritual world, omnipresence, etc., the latter place themselves in fiat opposition to the very phenomena, and to the most faithful interpreter of all phenomena, to geometry. For, not to enlarge upon the obvious circle in which they become involved in defining space, they cast forth geometry, thrown down from the pinnacle of certitude, into the number of those sciences whose principles are empirical. If we have obtained all the properties of space by experience from external relations only, geometrical axioms have only comparative universality, such as is acquired by induction. They have universality evident as far as observed, but neither necessity, except as far as the laws of nature may be established, nor precision, except what is arbitrarily made. There is hope, as in empirical sciences, that a space may some time be discovered endowed with other primary properties, perchance even a rectilinear figure of two lines.
E. Though the concept of space as an objective and real thing or quality is imaginary, it is nevertheless in respect to all sensible things not only perfectly true, it is the foundation of truth in external sensibility. Things cannot appear to the senses under any form but by means of a power of the soul co-ordinating all sensations in accordance with a fixed law implanted in its nature. Since, therefore, nothing at all can be given the senses except conformably to the primary axioms of space and their consequences which are taught by geometry, though their principle be but subjective, yet the soul will necessarily agree with them, since to this extent it agrees with itself; and the laws of sensuality will be the laws of nature so far as it can be perceived by our senses. Nature, therefore, is subject with absolute precision to all the precepts of geometry as to all the properties of space there demonstrated, this being the subjective condition, not hypothetically but intuitively given, of every phenomenon in which nature can ever be revealed to the senses. Surely, unless the concept of space were originally given by the nature of the mind, so as to cause him to toil in vain who should labor to fashion mentally any relations other than those prescribed by it, since in the fiction he would be compelled to employ the aid of this very same concept, geometry could not be used very safely in natural philosophy, For it might be doubted whether this same notion drawn from experience would agree sufficiently with nature, the determinations from which it was abstracted being, perchance, denied, a suspicion of which has entered some minds already. Space, then, is the absolutely first formal principle of the sensible world, not only because by its concept the objects of the universe can be phenomena, but especially for the reason that it is. essentially but one, comprising all externally sensible things whatsoever; and hence constitutes the principle of the universe, that is, of that whole which cannot be the part of another.
Here, then, are two principles of sensuous cognition, not, as in intellectual knowledge, general concepts, but single and nevertheless pure intuition, in which the parts, and especially the simple parts, do not, as the laws of reason prescribe, contain the possibility of the composite, but, according to the pattern of sensuous intuition, the infinite contains the reason of the part, and finally of its thinkable simple part or rather limit. For unless infinite space as well as infinite time be given, no definite space and time is assignable by limitation, and a point as well as a moment is unthinkable by itself and only conceived in a space and time already given as the limits. All primitive properties of these concepts are then beyond the purview of reason, and hence cannot intellectually be explained in any way. Nevertheless, they are what underlies the intellect when from intuitive primary data it derives consequences according to logical laws with the greatest possible certainty. One of these concepts properly concerns the intuition of the object; the other the state, especially the representative state. Hence space is employed as the type even of the concept of time itself, representing it by a line, and its limits—moments—by points. Time, on the other hand, approaches more to a universal and rational concept, comprising under its relations all things whatsoever, to wit, space itself, and besides, those accidents which are not comprehended in the relations of space, such as the thoughts of the soul. Again, time, besides this, though it certainly does not dictate the laws of reason, yet constitutes the principal conditions under favor of which the mind compares its notions according to the laws of reason. Thus, I cannot judge what is impossible except by predicating a and not-a of the same subject at the same time. And especially, considering experience, though the reference of cause to effect in external objects were to lack the relations of space, still in all things, external or internal, the mind could by the auxiliary relation of time alone be informed which is the first and which latter or caused. And even the quantity of space itself cannot be rendered intelligible unless, referring it to measure as to a unity, we set it forth in number, which itself is but multiplicity distinctly cognized by numeration, that is, by the successive addition of one to one in a given time.
Lastly, the question will arise in any one as if spontaneously, whether either concept be connate or acquired. The latter by what has been shown seems refuted already, but the former, smoothing the way for lazy philosophy, declaring vain by the citing of a first cause any further quest, is not to be admitted thus rashly. But beyond doubt either concept is acquired, not, it is true, abstracted from the sense of objects, for sensation gives the matter not the form of human cognition, but from the very action of the mind co-ordinating its sense-percepts in accordance with perpetual laws, as though an immutable type, and hence to be known intuitively. For sensations excite this act of the mind but do not influence intuition, neither is there anything connate here except the law of the soul in accordance with which it conjoins in a certain way its sensations derived from the presence of an object.
ON THE PRINCIPLE OF THE FORM OF THE INTELLIGIBLE WORLD
Those who deem space and time to be something real and the absolute bond, so to speak, of all possible substances in space, hold nothing else to be required in order to conceive how an original relation can belong to several existing things as the primitive condition of possible influence and the principle of the essential form of the universe. For since whatever exists is, according to their opinion, necessarily somewhere, it seems to them quite superfluous to inquire why things are present to one another in a certain manner, since this is of itself determined by the universality of all-comprehending space. But this concept, besides relating as has been shown rather to the sensuous laws of the subject than to the conditions of the objects themselves, even granting it the greatest reality, still denotes nothing but the intuitively given possibility of universal co-ordination, leaving undealt with the question solvable only by the intellect: In what principle does this very relation of all substances rest, which intuitively regarded is called space? The question of the principle of the form of the intelligible world turns, therefore, upon making apparent in what manner it is possible for several substances to be in mutual commerce, and for this reason to pertain to the same whole, which is called world. We do not here consider the world, let it be understood, as to matter, that is, as to the nature of the substances of which it consists, whether they be material or immaterial, but as to form, that is to say, how among several things taken separately a connection, and among them all, totality can have place.
Several substances being given, the principle of their possible intercommunication is not apparent from their existence solely, but something else is required besides from which their mutual relations may be understood. For on account of mere existence they are not necessarily related to anything, unless it be to their cause; but the relation of an effect to the cause is not intercommunication, but dependence. Therefore, if any commerce intervenes among them, there is need of an exactly determining specific reason.
The sham cause in physical influence consists in rashly assuming that the commerce of substance and transitive forces is sufficiently knowable from their mere existence. Hence it is not so much a system as rather the neglect of all philosophical system as a superfluity in the argument. Freeing the concept from this defect, we shall have a species of commerce alone deserving to be called real, and from which the whole constituting the world merits being called real, and not ideal or imaginary.
A whole from necessary substances is impossible. For, since the existence of each stands for itself without dependence on any other, a dependence which in necessary substances clearly cannot befall, it is plain that not only does the intercommunication of substances (that is, the reciprocal dependence of their states) not follow from their existence, but as necessary substances cannot belong to them at all.
The whole, therefore, of substances is a whole of contingent things, and the world consists essentially of only contingent things. Besides, no necessary substance is in connection with the world except as a cause with the effect, and, therefore, not as a part with its complements making up a whole, since the bond connecting parts is mutual dependence, which in a necessary being cannot occur. The cause, therefore, of the world is an extramundane being, and so is not the soul of the world, nor is its presence in the world local, but virtual.
The mundane substances are beings from, another being; not from several, but all from one. For, suppose them to be caused by several necessary beings. In intercommunication there are not effects from causes alien to all mutual relation. Hence, the unity in the conjunction of the substances of the universe is the consequence of the dependence of all on one. Therefore, the form of the universe witnesses the cause of matter, and only the sole cause of all things is the cause of the universe, nor is there an architect of the world not at the same time its creator.
If there were several primary and necessary causes together with their effects, their works would be worlds, not a world, since they would in no wise be connected into one whole. And vice versa, if there be several actual worlds without one another, several primary and necessary causes are given, so, however, as to give intercommunication neither to one world with another, nor to the cause of one with the world caused by another.
Several actual worlds without one another are not, therefore, impossible by the very concept, as Wolf hastily concluded from the notion of a complex or multiplicity which he deemed sufficient to a whole, as such, but only on condition that there exist but one necessary cause of all things. If several are admitted, several worlds without one another will be possible in the strictest metaphysical sense.
If, as we validly conclude from a given world to a single cause of all its parts, we may similarly argue reversely from the given cause common to all to their interconnection, and hence to the form of the world—though I confess this conclusion does not seem as plain to me—then the primary connection of substances will not be contingent but by the sustentation of all by the common principle, necessary, and hence the harmony proceeding from their very subsistence founded in a common cause would proceed according to the usual rules. Such a harmony I term established generally; as that which does not take place except as far as any individual states of a substance are adapted to the condition of another is harmony established particularly; the communion by the former being real and physical, by the latter ideal and sympathetic. All communion, then, of the substance of the universe is eternally established by the common cause of all, and either established generally by physical influence—as amended; see paragraph 17—or adapted particularly to their states; and the latter either rests originally in the primary constitution of every substance or is impressed on the occasion of any change whatever; the first being called pre-established harmony, the latter occasionalism. If, then, on account of the sustentation of all substances by one, the conjunction of all constituting them a unit be necessary, the universal commerce of substances will be by physical influence, and the world a real whole; if not, the commerce will be sympathetic, that is a harmony without true commerce, and the world only an ideal whole. To me the former, though not demonstrated, appears abundantly proved by other reasons.
If it were right to overstep a little the limits of apodictic certainty befitting metaphysics, it would seem worth while to trace out some things pertaining not merely to the laws but even to the causes of sensuous intuition, which are only intellectually knowable. Of course the human mind is not affected by external things, and the world does not lie open to its insight infinitely, except as far as itself together with all other things is sustained by the same infinite power of one. Hence it does not perceive external things but by the presence of the same common sustaining cause; and hence space, which is the universal and necessary condition of the joint presence of everything known sensuously, may be called the phenomenal omnipresence, for the cause of the universe is not present to all things and everything, as being in their places, but their places, that is the relations of the substances, are possible, because it is intimately present to all. Furthermore, since the possibility of the changes and successions of all things whose principle as far as sensuously known resides in the concept of time, supposes the continuous existence of the subject whose opposite states succeed; that whose states are in flux, lasting not, however, unless sustained by another; the concept of time as one infinite and immutable in which all things are and last, is the phenomenal eternity of the general cause. But it seems more cautious to hug the shore of the cognitions granted to us by the mediocrity of our intellect than to be carried out upon the high seas of such mystic investigations, like Malebranche, whose opinion that we see all things in God is pretty nearly what has here been expounded.
ON THE METHOD RESPECTING THE SENSUOUS AND THE INTELLECTUAL IN METAPHYSICS
In all sciences whose principles are given intuitively, whether by sensual intuition, that is, experience, or by an intuition sensuous, to be sure, but pure—the concepts of space, time, and number—that is to say, in the natural and in the mathematical sciences, use gives method, and by trying and finding after the science has been carried to some degree of copiousness and consonancy it appears by what method and in what direction we must proceed in order to finish and to purify it by removing the defects of error as well as of confused thoughts; exactly as grammar after the more copious use of speech, and style after the appearance of choice examples in poetry and oratory, furnished vantage-ground to rules and to discipline. But the use of the intellect in the sciences whose primitive concepts as well as axioms are given by sensuous intuition is only logical, that is, by it we only subordinate cognitions to one another according to their relative universality conformably to the principle of contradiction, phenomena to more general phenomena, and consequences of pure intuition to intuitive axioms. But in pure philosophy, such as metaphysics, in which the use of the intellect in respect to principles is real, that is to say, where the primary concept of things and relations and the very axioms are given originally by the pure intellect itself, and not being intuitions do not enjoy immunity from error, the method precedes the whole science, and whatever is attempted before its precepts are thoroughly discussed and firmly established is looked upon as rashly conceived and to be rejected among vain instances of mental playfulness. For, since here the right use of the reason constitutes the very principles and the objects as well, what axioms are to be thought of concerning them become primarily known solely by its own nature, the exposition of the laws of pure reason is the very origin of the science, and their distinction from spurious laws the criterion of truth. The method of the science not being practiced much nowadays, except what logic prescribes to all sciences generally, that fitted for the peculiar nature of metaphysics being simply ignored, it is no wonder that those who everlastingly turn the Sisyphean stone of this inquiry do not seem so far to have made much progress. Though here I neither can nor will expatiate upon so important and extensive a subject, I shall briefly shadow forth what constitutes no despicable part of this method, namely, the infection between sensuous and intellectual cognition, not only as creeping in on those incautious in the application of principles, but even producing spurious principles under the appearance of axioms.
In substance the whole method of metaphysics as to the sensuous and the intellectual amounts to this precept; to take care not to allow the principles at home in sensuous cognition to outstray their limits and affect the intellectual concepts. For, since the predicate in any judgment enounced intellectually is a condition in the absence of which the subject is asserted to be unthinkable, the predicate hence being the principle of cognition, it will, if a sensuous concept, be only the condition of a possible sensuous cognition—and hence will square well enough with the subject of a judgment whose concept is also sensuous. But if it be applied to an intellectual concept, the judgment will be valid only according to subjective laws, and hence must not be affirmed objectively and predicated of the intellectual notion itself, but only as a condition in the absence of which the sensuous cognition of the given concept does not take place.
Now, since the tricks of the intellect by the subordination of sensuous concepts as though intellectual marks may be called, analogously to the accepted meaning, a fallacy of subreption, the exchanging of intellectual and sensual concepts will be a metaphysical fallacy of subreption, the intellectualized phenomenon, if the barbarous expression be permissible, and hence I call such a hybrid axiom as palms off the sensuous as necessarily adhering to the intellectual concept, a surreptitious axiom. From these spurious axioms have gone forth, and are rife throughout metaphysics, principles deceiving the intellect. In order that we may have, however, a readily and clearly knowable criterion of those judgments, a touchstone, so to speak, by which to distinguish them from genuine judgments, and at the same time if, perhaps, they seem to cling tenaciously to the intellect, an assaying art by which we can justly estimate how much belongs to the sensuous and how much to the intellectual sphere, I think it necessary to go into the question more deeply.
Here, then, is the principle of reduction for any spurious axiom: If concerning any intellectual concept something pertaining to time and space relations be predicated generally, it is not to be enounced objectively, but denotes only the condition without which the given concept is not knowable sensuously. That such an axiom is spurious, and, if not false, at least a rash and question-begging assertion, appears thus: the subject of the judgment being intellectually conceived pertains to the object, whilst the predicate, since it contains the determinations of space and time, pertains only to the conditions of human sensuous cognition, which, not adhering of necessity to any cognition whatsoever of the object, cannot be enounced concerning the given intellectual concept universally. The intellect’s being so readily subject to this fallacy of subreption comes of its being deceived under the plea of another and perfectly true rule. For we rightly suppose that that which can be cognized by no intuition whatever is utterly unthinkable and hence impossible. But since we cannot attain by any mental striving, even fictitiously, to any other intuition but that according to the form of space and time, it happens that we deem all intuition whatever impossible which is not bound by these laws, passing by the pure intellectual intuition exempt from the laws of the senses, such as the divine, by Plato called the Idea, and hence subject all possible given things to the sensual axioms of space and time.
All sleights of substitution of sensuous cognition under guise of intellectual concepts, from which spurious axioms originate, can be reduced to three species, whose general formulae are the following:
1. The sensual condition under which alone the intuition of an object is possible, is the condition of its possibility.
2. The sensual condition under which alone data can be compared in order to form the intellectual concept of the object, is the condition of the very possibility of the object.
3. The sensual condition under which alone the subsumption of an object under a given intellectual concept is possible, is the condition of the possibility of the object.
A spurious axiom of the first class is: Whatever is, is somewhere and sometime. Now by this spurious principle all beings, even though they be intellectually cognized, are restricted in existence by the conditions of space and time. Hence people discuss all sorts of inane questions, such as concerning the places of immaterial substances—of which, for that very reason, there is no sensuous intuition, nor, under that form, any representation—in the corporeal universe, or the seat of the soul; and as they improperly mix sensual things with intellectual concepts, like square figures with round, it oftens happens that of the disputants one appears as milking a he-goat, and the other as holding the sieve under. The presence of immaterial substances in the corporeal world is virtual, not local, though thus improperly talked about. Space does not contain the conditions of possible mutual activities, except those of matter. What may constitute the external relations of forces in immaterial substances, as well among themselves as toward bodies, altogether escapes the human intellect, as was acutely noted, for instance, in a letter to a German prince by the clear-sighted Euler, otherwise a great investigator and judge of phenomena. But when people have arrived at the concept of a highest and extra-mundane being, they are fooled by these shadows flitting before the intellect to a degree beyond the force of language to express. The presence of God they figure to themselves as a local one, involving God in the world as if also comprised in infinite space, compensating Him for this limitation by a locality, so to speak, eminently conceived, that is, infinite. But it is absolutely impossible to be at the same time in several places, since different places are mutually without each other, and hence what is in several places is outside of itself, which implies being present to itself externally. But as to time, having not only exempted it from the laws of sensual knowledge, but transferred it beyond the limits of the world to the extra-mundane Being Himself as a condition of His existence, they involve themselves in an inextricable labyrinth. Hence they cudgel their brains with absurd questions, such as, for instance, why God did not make the world many centuries earlier. They persuade themselves that it is easy to conceive, to be sure, how God may discern what is present, that is, what is actual in the time in which he is, but how He may foresee what is future, that is, what is actual in the time in which He is not yet, they deem an intellectual difficulty; as if the existence of the Necessary Being descended through all the moments of an imaginary time, and, having already exhausted a part of His duration, saw before Him the eternity He was yet to live simultaneously with the present events of the world. All these difficulties upon proper insight into the notion of time vanish like smoke.
The prejudices of the second species, since they impose upon the intellect by the sensual conditions restricting the mind if it wishes in certain cases to attain to what is intellectual, lurk more deeply. One of them is that which affects knowledge of quantity, the other that affecting knowledge of qualities generally. The former is: every actual multiplicity can be given numerically, and hence, every infinite quantity; the latter, whatever is impossible contradicts itself. In either of them the concept of time, it is true, does not enter into the very notion of the predicate, nor is it attributed as a qualification to the subject. But yet it serves as a means for forming an idea of the predicate, and thus, being a condition, affects the intellectual concept of the subject to the extent that the latter is only attained by its aid.
As to the first, as every quantity and any series whatever are distinctly known only by successive co-ordination, the intellectual concept of amount and multiplicity arises only by the aid of this concept of time, and never attains to completeness unless the synthesis can be gone through with in finite time. It is hence that the infinite series of co-ordinate things cannot be comprehended distinctly according to the limits of our intellect; it hence by the fallacy of subreption seems impossible. According to the laws of pure intellect any series of effects has its principle, that is, there is not given in a series of effects a regress without a limit; whilst according to sensual laws any series of co-ordinate things has its assignable beginning. These propositions, the latter of which involves the mensurability of the series, the former the dependence of the whole, are taken hastily for identical. In the same way, to the argument of the intellect, proving that a substantial composite being given so are the elements of composition, that is, the simple things, there is adjoined a supposititious one suborned from sensual knowledge, namely, that in such a composite there is not given an infinite regress in the composition of the parts, that is to say, that in any composite there is given a definite number of parts, a sense certainly not germane to the former, and hence substituted rashly for it. For that the quantity of the world is limited, not the maximum, that it owns a principle, that bodies consist of simple parts, can certainly be cognized rationally. But that the universe as to its mass is mathematically finite, that its age as elapsed can be given by measure, that the number of simple parts constituting any body whatever is a definite number, are propositions openly proclaiming their origin from the nature of sensual knowledge; however true they may be held to be, they bear the undoubted stigma of their origin.
As for the latter spurious axiom, it originates from a rash conversion of the principle of contradiction. For to this primitive judgment the concept of time adheres to the extent that contradictorily opposed data being given at the same time in the same thing, the impossibility is plain, which is enounced thus: whatever simultaneously is and is not, is impossible. Here, as the intellect predicates something in a case given according to sensual laws, the judgment is perfectly true and obvious. On the contrary, converting this axiom, saying: whatever is impossible is and is not at the same time, or involves a contradiction, we predicate through sensual knowledge something concerning the object of reason generally, thus subjecting the intellectual conception of the possible and the impossible to the conditions of sensual knowledge, namely, to the relations of time; which certainly is true enough of the laws restricting and limiting the human intellect, but cannot be conceded objectively and generally by any means. Of course, our intellect perceives no impossibility except where it can note the simultaneous enunciation of opposites concerning the same thing, that is, only where contradiction occurs. Wherever, therefore, this contradiction does not occur, there is no room for the judgment of impossibility by the human intellect. But that on this account it should be open to no intellect whatever, and hence that what does not involve contradiction is therefore possible, is concluded rashly by taking the subjective conditions of judgment for objective ones. It is for this reason that a host of fictitious forces, gotten up ad libitum, bursts, in the absence of self-contradiction, from any constructive, or, if you prefer, from every chimerical mind. For as a force is nothing but a relation of a substance a to something else b, an accident, as of a reason to the consequence, the possibility of any force does not rest in the identity of the cause and the effect, or the substance and the accident, and hence even the impossibility of forces made up falsely does not depend solely on contradiction. Therefore it is not permissible to assume as possible any original force unless the force be given by experience. Neither can the possibility be conceived a priori by any perspicacity of the intellect.
The spurious axioms of the third kind from conditions proper to the subject whence they are transferred rashly to the object are plentiful, not, as in those of the Second Class, because the only way to the intellectual concept lies through the sensuous data, but because only by aid of the latter can the concept be applied to that which is given by experience, that is, can we know whether something is contained under a certain intellectual concept or not. To this class belongs the threadbare one of the schools: whatever exists contingently does at some time not exist. This spurious principle springs from the poverty of the intellect, having insight frequently into the nominal, rarely into the real, marks of contingency or necessity. Hence, whether the opposite of any substance be possible, an insight hardly obtained from a priori marks, is not otherwise known than by its being evident that at some time that substance was not; and changes rather witness contingency than contingency mutability, so that were nothing fleeting and transitory to occur in the world, a notion of contingence would hardly be possible in us. Therefore, though the direct proposition is perfectly true: whatever at some time was not is contingent, its converse indicates nothing but the conditions under which we can alone distinguish whether something exists necessarily or contingently. Hence if enunciated as a subjective law, which indeed it is, it should be enounced thus: Sufficient marks of contingency of that of which it is not evident that at some time it was not, are not, by common intelligence, given. This, however, tacitly deviates into an objective condition, as though in its absence there were no room for contingence; which being done, a counterfeit and erroneous axiom arises. For this world though existing contingently is sempiternal, that is, simultaneous with all time. It is a rash assertion that there was a time when it did not exist.
To these spurious principles must be added some others of great affinity with them, not imparting to the given intellectual concept any blemish of sensuous cognition, but deceiving the intellect so as to take them for arguments drawn from the object, though they are commended to us only by the peculiar nature. of the intellect for the convenience of its free and ample use. Therefore, these as well as those enumerated above, rest in subjective reasons, although not in the laws of sensuous, but in those of intellectual cognition itself, namely, in the conditions under which it appears easy and quick to the mind to make use of its insight. I shall beg leave to throw in here, by way of conclusion, some mention of these principles, not as yet, as far as I know, set forth distinctly. I call, then, principles of convenience rules of judging to which we freely submit, and to which we adhere as if they were axioms, for the only reason that, were we to depart from them, scarcely any judgment concerning a given object would be permissible to our intellect. In this list belong the following: First, that by which we assume that everything in the universe is done according to the order of nature, which principle by Epicurus was proclaimed without any restriction, and by all other philosophers unanimously with extremely rare exceptions, not to be admitted but from supreme necessity. Still we thus affirm, not on account of possessing so ample a knowledge of the events of the world according to the common laws of nature, or because the impossibility or smaller hypothetical possibility of supernatural things is plain to us, but because departing from the order of nature there would be no use for the intellect, the rash citation of the supernatural being the couch of lazy understandings. For the same reason we take care to shut out from the exposition of phenomena comparative miracles, namely, the influence of spirits, since, as we do not know their nature, the intellect, to its great detriment, would be turned aside from the light of experience, by which alone it is able to provide for itself laws of judging, into the night of species and causes unknown to us. The second is the partiality for unity proper to the philosophical mind, whence this wide-spread canon has flown forth: principles are not to be multiplied beyond supreme necessity, to which we give in our adhesion, not because we have insight into causal unity in the world either by reason or experience, but as seeking it by an impulse of the intellect which seems to itself to have by thus much advanced in the explication of phenomena, by as much as it is granted to it to descend from the same principle to a greater number of consequences, The third of this kind of principles is: matter neither originates nor perishes; all the changes in the world concern form only; a postulate which on the recommendation of common sense has spread through all philosophical schools, not because it is to be taken as having been found so, or as having been demonstrated by arguments a priori, but because if we were to admit that matter itself is fleeting and transitory, nothing at all that is stable and lasting would be left any longer to serve for the explication of phenomena according to universal and perpetual laws, and hence nothing at all would be left for the exercise of the intellect.
This method, especially in respect to the distinction between sensual and intellectual knowledge, which, when reduced by more careful investigation to exactness, will occupy the position of a propaedeutical science, will certainly be of unlimited benefit to all intending to penetrate into the very recesses of metaphysics.
Note.—As in this last section the tracing out of the method occupies all the space at disposal, and the rules prescribing the true form of arguing concerning sensuous things shine by their own light and do not borrow it from the illustrative examples, I have thrown in but a cursory mention of the latter. For this reason it is not strange if some things should seem to have been asserted with more audacity than truth, they certainly calling, when a broader treatment shall be possible, for greater force of arguments. Thus, what is alleged in paragraph 27 on the locality of immaterial substances lacks an explication which, if the reader please, may be found in Euler in the place cited, Vol. II, pp. 49, 52. For the soul is not in communion with the body as being detained in a certain place in the latter, but a determined place in the universe is attributed to it, for the reason that it is in mutual commerce with some body, which commerce being dissolved all its position in space is removed. Its locality, therefore, is derivative and contingently applied to it, not primitive and a necessary condition of its existence, because whatever things cannot by themselves be objects of external senses such as man’s, that is, immaterial substances, are exempt altogether from the universal condition of externally sensible things, namely, space. Hence absolute and immediate locality may be denied to the soul, while yet hypothetical and mediate locality may be attributed to it.
- To the words analysis and synthesis a two-fold meaning is commonly given; for the synthesis is either qualitative, a progress in a series of subordinates from the reason to the consequence, or quantitative, a progress in a series of coordinates from the given part through its complements to the whole. Similarly, analysis, taken in the first sense, is a regress from the consequence to the reason, but in the latter meaning a regress from a whole to its possible or mediate parts, that is, to the parts of parts; hence it is not a division but a subdivision of the given composite. Synthesis as well as analysis are here taken only in the latter sense.
- Those who reject the actual mathematical infinite do not take much trouble. They frame a definition of the infinite from which they can shape out some contradiction. The infinite is said by them to be a quantity than which none greater is possible, and the mathematical infinite the multiplicity—of an assignable unit—than which none greater is possible. Having substituted greatest for infinite they easily conclude against an infinite of their own making, as a greatest multiplicity is impossible; or, they call an infinite multiplicity an infinite number, and show this to be absurd; which is plain enough, but a battle with their own fancy only. But if they would conceive of a mathematical infinite as a quantity which being referred to measure as unity is a multiplicity greater than all number; if, furthermore, they would take note that mensurability here denotes only the relation to the smallness of the human intellect, to which it is given to attain to a definite concept of multiplicity only by the successive addition of unit to unit, and to the sum total called number only by going through with this progress within a finite time, they would gain the clear insight that what does not fall in with a certain law of some subject does not on that account exceed all intellection; since an intellect may exist, though not a human one, perceiving a multiplicity distinctly by a single insight, without the successive application of measurement.
- Something is considered theoretically when we attend only to what belongs to the thing; practically, when we view what by liberty should be in it.
- Höhere Mechanik, p. 354.
- Simultaneous facts are not such for the reason that they do not succeed each other. Removing succession, to be sure, a conjunction is withdrawn which existed by the time-series. Yet thence does not originate another true relation, the conjunction of all things in the same moment. For simultaneous things are joined in the same moment of time exactly as successive things are joined in different moments. Hence, though time is of but one dimension, still the ubiquity of time, to speak with Newton, by which all things sensuously thinkable are some time, adds to the quantity of actual things another dimension, inasmuch as they hang, so to speak, on the same point of time. For designating time by a straight line produced infinitely, and the simultaneous things at any point of time whatever by lines applied in succession, the surface thus generated will represent the phenomenal world, both as to substance and accidents.
- As the necessity of conceiving space as a continuous quantity is easy to demonstrate, I pass it by. It is a consequence from this that the simple in space is not a part, but a limit. A limit generally, is that in a continuous quantity which contains the limited portion. Space not the limit of another is a solid. The limit of a solid is a surface, of a surface the line, of a line the point; hence there are three kinds of limits in space, as there are three dimensions. Two of these limits, the surface and the line, are themselves spaces. The concept of limit enters into no quantity besides time and space.
- The moments of time do not appear to follow one another, since if they did another time would have to be premised for the succession of moments; but by sensuous intuition the actual things appear to descend, as it were, through a continuous series of moments.
- The use of this criterion is fruitful and easy in distinguishing principles which enunciate laws of sensuous cognition only from those prescribing besides something concerning the objects themselves. If the predicate be an intellectual concept, its reference to the subject of the judgment, though this subject be thought of as an object of sense, always denotes a mark belonging to the object itself. If the predicate be a sensuous concept, then, since the laws of sensuous cognition are not conditions of the possibility of things themselves, it is not valid as to the subject of the judgment conceived intellectually, and hence it cannot be enounced objectively. Thus in the common axiom whatever exists is somewhere, as the predicate contains conditions of sensuous knowledge it cannot be enounced as to the subject of the judgment, namely, anything existing, generally; hence this formula as an objective rule is false. But converting the proposition, so as to make the predicate an intellectual concept, it becomes perfectly true; thus: whatever is somewhere, exists.
- Space and time are conceived as comprehending in them all things in any way offered to the senses. Hence, according to the laws of the human mind, the intuition of nothing is given except as contained in space and time. To this prejudice another may be compared which is not properly a spurious axiom but a play of the fancy, and which may be set forth in the general formula: In whatever exists are space and time, that is to say, every substance is extended and continuously changed. But though people of dense conception are bound firmly by this law of imagination, even they see readily that it pertains only to the efforts of fancy, shadowing forth to itself the appearance of things, not to the conditions of existence.