The Metaphysical Foundations of Natural Science/Preface

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If the word Nature be merely taken in its formal signification, there may be as many natural sciences as there are specifically different things (for each must contain the inner principle special to the determinations pertaining to its existence), inasmuch as it [Nature] signifies the primal inner principle of all that belongs to the existence of a thing.[1] But Nature, regarded in its material significance, means not a quality, but the sum-total of all things, in so far as they can be objects of our senses, and therefore of experience; in short, the totality of all phenomena—the sense-world, exclusive of all non-sensuous objects. Now Nature, in this sense of the word, has two main divisions, in accordance with the main distinction of our sensibility, one of which comprises the objects of the outer, the other the object of the inner sense; thus rendering possible a two-fold doctrine of Nature, the doctrine of body and the doctrine of soul, the first dealing with extended, and the second with thinking, Nature.

Every doctrine constituting a system, namely, a whole of cognition, is termed a science; and as its principles may be either axioms of the empirical or rational connection of cognitions in a whole, so natural science, whether it be doctrine of body or doctrine of soul, would have to be divided into historical and rational natural science, were it not that the word nature (as implying the deduction of the manifold pertaining to the existence of things, from its inner principle) necessitates a knowledge through reason of its system, if it is to deserve the name natural science. Hence, doctrine of nature may be better divided into historical doctrine of nature, comprising nothing but systematically-ordered facts respecting natural things (which again would consist of description of nature as a system of classes according to resemblances, and history of nature as a systematic presentation of the same at different times and in different places), and natural science. Natural science, once more, would be either natural science properly or improperly so-called, of which the first would treat its subject wholly according to principles à priori, and the second according to laws derived from experience.

That only can be called science (wissenschaft) proper whose certainty is apodictic: cognition that can merely contain empirical certainty is only improperly called science. A whole of cognition which is systematic is for this reason called science, and, when the connection of cognition in this system is a system of causes and effects, rational science. But when the grounds or principles it contains are in the last resort merely empirical, as, for instance, in chemistry, and the laws from which the reason explains the given facts are merely empirical laws, they then carry no consciousness of their necessity with them (they are not apodictically certain), and thus the whole does not in strictness deserve the name of science; chemistry indeed should be rather termed systematic art than science.

A rational doctrine of nature deserves the name of natural science only when the natural laws at its foundation are cognised à priori, and are not mere laws of experience. A natural cognition of the first kind is called pure, that of the second applied, rational cognition. As the word nature itself carries with it the conception of law, and this again the conception of the necessity of all the determinations of a thing appertaining to its existence, it is easily seen why natural science must deduce the legitimacy of its designation only from a pure part of it, [a part] namely, which contains the principles à priori of all remaining natural explanations, and why only by virtue of this portion it is properly science, in such wise, that, according to the demands of the reason, all natural knowledge must at last turn on natural science and there find its conclusion. This is because the above necessity of law inseparably attaches to the conception of nature, and hence must be thoroughly comprehended. For this reason the most complete explanation of particular phenomena upon chemical principles, invariably leaves an unsatisfactoriness behind it, because from these accidental laws, learnt by mere experience, no grounds à priori can be adduced.

Thus all natural science proper requires a pure portion, upon which the apodictic certainty required of it by the reason can be based; and inasmuch as this is in its principles wholly heterogeneous from those which are merely empirical, it is at once a matter of the utmost importance, indeed in the nature of the case, as regards method of indispensable duty, to expound this part separately and unmixed with the other, and as far as possible in its completeness; in order that we may be able to determine precisely what the reason can accomplish for itself, and where its capacity begins to require the assistance of empirical principles. Pure cognition of the reason from mere conceptions is called pure philosophy or metaphysics, while that which only bases its cognition on the construction of conceptions, by means of the presentation of the object in an à priori intuition, is termed mathematics.

What may be called natural science proper presupposes metaphysics of nature; for laws, i.e. principles of the necessity of that which belongs to the existence of a thing, are occupied with a conception which does not admit of construction, because its existence cannot be presented in any à priori intuition; natural science proper, therefore, presupposes metaphysics. Now this must indeed always contain exclusively principles of a non-empirical origin (for, for this reason it bears the name of metaphysics); but it may be either without reference to any definite object of experience, and therefore undetermined as regards the nature of this or that thing of the sense-world, and treat of the laws rendering possible the conception of nature in general, in which case it is the transcendental portion of the metaphysics of nature; or it may occupy itself with the particular nature of this or that kind of thing, of which an empirical conception is given, in such wise, that except what lies in this conception, no other empirical principle will be required for its cognition. For instance: it lays the empirical conception of a matter, or of a thinking entity, at its foundation, and searches the range of the cognition of which the reason is à priori capable respecting these objects; and thus, though such a science must always be termed a metaphysic of nature (namely, of corporeal or thinking nature), it is then not a universal but a particular metaphysical natural science (physics and psychology), in which the above transcendental principles are applied to the two species of sense-objects. But I maintain that in every special natural doctrine only so much science proper is to be met with as mathematics; for, in accordance with the foregoing, science proper, especially [science] of nature, requires a pure portion, lying at the foundation of the empirical, and based upon an à priori knowledge of natural things. Now to cognise anything à priori is to cognise it from its mere possibility; but the possibility of determinate natural things cannot be known from mere conceptions; for from these the possibility of the thought (that it does not contradict itself) can indeed be known, but not of the object, as natural thing which can be given (as existent) outside the thought. Hence, to the possibility of a determinate natural thing, and therefore to cognise it à priori, is further requisite that the intuition corresponding à priori to the conception should be given; in other words, that the conception should be constructed. But cognition of the reason through construction of conceptions is mathematical. A pure philosophy of nature in general, namely, one that only investigates what constitutes a nature in general, may thus be possible without mathematics; but a pure doctrine of nature respecting determinate natural things (corporeal doctrine and mental doctrine), is only possible by means of mathematics; and as in every natural doctrine only so much science proper is to be met with therein as there is cognition à priori, a doctrine of nature can only contain so much science proper as there is in it of applied mathematics.

So long, therefore as no conception is discovered for the chemical effects of substances on one another, which admits of being constructed, that is, no law of the approach or retreat of the parts can be stated in accordance with which (as, for instance, in proportion to their densities) their motions, together with the consequences of these, can be intuited and presented à priori (a demand that will scarcely ever be fulfilled), chemistry will be nothing more than a systematic art or experimental doctrine, but never science proper, its principles being merely empirical and not admitting of any presentation à priori; as a consequence, the principles of chemical phenomena cannot make their possibility in the least degree conceivable, being incapable of the application of mathematics.

But still farther even than chemistry must empirical psychology be removed from the rank of what may be termed a natural science proper; firstly, because mathematics is inapplicable to the phenomena of the internal sense and its laws, unless indeed we consider merely the law of permanence in the flow of its internal changes; but this would be an extension of cognition, bearing much the same relation to that procured by the mathematics of corporeal knowledge, as the doctrine of the properties of the straight line does to the whole of geometry; for the pure internal intuition in which psychical phenomena are constructed is time, which has only one dimension. But not even as a systematic art of analysis, or experimental doctrine, can it ever approach chemistry, because in it the manifold of internal observation is only separated in thought, but cannot be kept separate and be connected again at pleasure; still less is another thinking subject amenable to investigations of this kind, and even the observation itself, alters and distorts the state of the object observed. It can never therefore be anything more than an historical, and as such, as far as possible systematic natural doctrine of the internal sense, i.e. a natural description of the soul, but not a science of the soul, nor even a psychological experimental doctrine. This is the reason why, in the title of this work, which, properly speaking, contains the axioms of corporeal doctrine, we have employed, in accordance with the usual custom, the general name of natural science, because this designation in the strict sense is applicable to it alone, and hence occasions no ambiguity.

But to render possible the application of mathematics to the doctrine of body, by which alone it can become natural science, principles of the construction of conceptions belonging to the possibility of matter in general must precede. Hence a complete analysis of the conception of a matter in general must be laid at its foundation; this is the business of pure philosophy, which for the purpose makes use of no special experiences, but only of those which it meets with in separate (although in themselves empirical) conceptions, with reference to pure intuitions in space and time (according to laws, essentially depending on the conception of nature in general), thus constituting it a real metaphysic of corporeal nature.

All natural philosophers, who wished to proceed mathematically in their work, have hence invariably (although unknown to themselves) made use of metaphysical principles, and must make use of such, it matters not how energetically they may otherwise repudiate any claim of metaphysics on their science. Without doubt by the latter they understood the illusion of manufacturing possibilities at pleasure, and playing with conceptions, perhaps quite incapable of being presented in intuition, and possessing no other guarantee of their objective reality than that they do not stand in contradiction with themselves. But all true metaphysics is taken from the essential nature of the thinking faculty itself, and therefore in nowise invented, since it is not borrowed from experience, but contains the pure operations of thought, that is, conceptions and principles à priori, which the manifold of empirical presentations first of all brings into legitimate connection, by which it can become empirical knowledge, i.e. experience. These mathematical physicists were thus quite unable to dispense with such metaphysical principles, and amongst them, not even with that which makes the conception of their own special subject, namely, matter, available à priori, in its application to external experience (as the conception of motion, of the filling of space, of inertia, etc.). But to allow merely empirical principles to obtain in such a question, they rightly held as quite unsuited to the apodictic certainty they desired to give to their natural laws, and hence they preferred to postulate such, without investigating their sources à priori.

But it is of the utmost importance in the progress of the sciences, to sever heterogeneous principles from one another, to bring each into a special system, so that it may constitute a science of its own kind, and thereby to avoid the uncertainty springing from their confusion, owing to our not being able to distinguish to which of the two, on the one hand the limitations, and on the other the mistakes occurring in their use, are to be attributed. For this reason I have regarded it as necessary to present in one system the first principles of the pure portion of natural science (physica generalis) where mathematical constructions traverse one another, and at the same time the principles of the construction of these conceptions; in short, the possibility of a mathematical doctrine of nature itself. This separation, besides the uses already mentioned, has the special charm, which the unity of knowledge brings with it, if we take care that the boundaries of the sciences do not run into one another, but occupy properly their subdivided fields.

It may serve as a second ground for gauging this procedure, that in all that is called metaphysics the absolute completeness of the sciences may be hoped for, in such a manner as can be promised by no other species of knowledge, and therefore, just as in the metaphysics of nature generally, so here also, the completeness of corporeal nature may be confidently expected; the reason being, that in metaphysics the object is considered merely according to the universal laws of thought, but in other sciences as it must be presented according to data of intuition (empirical as well as pure). Hence the former, because the object must be invariably compared with all the necessary laws of thought, must furnish a definite number of cognitions, which can be fully exhausted; but the latter, because it offers an endless multiplicity of intuitions (pure or empirical), and therefore of objects of thought, can never attain to absolute completeness, but can be extended to infinity, as in pure mathematics and empirical natural knowledge. This metaphysical corporeal doctrine I believe myself to have, as far as it reaches, completely exhausted, but do not affect thereby to have achieved any great work.

The scheme for the completeness of a metaphysical system, whether of nature in general, or of corporeal nature in particular, is the table of the categories.[2] For there are not any more pure conceptions of the Understanding, which concern the nature of things. Under the four classes of Quantity, Quality, Relation, and finally Modality, all the determinations of the universal conception of a matter in general, and, therefore, of all that can be thought à priori respecting it, that can be presented in mathematical construction, or given in experience as its definite object, must be capable of being brought. There is no more to do in the way of discovery or addition, although certainly, should there be anything lacking in clearness or thoroughness, it may be made better.

Hence the conception of matter had to be carried out through all the four functions of the conceptions of the understanding (in four divisions), in each of which a new determination of the same was added. The fundamental determination of a something that is to be an object of the external sense, must be motion, for thereby only can this sense be affected. The understanding leads all other predicates pertaining to the nature of matter back to this, and thus natural science is throughout either a pure or an applied doctrine of motion. The metaphysical foundations of natural science may thus be brought under four main divisions, of which the firstmotion considered as pure quantum, according to its composition, without any quality of the movable, may be termed Phoronomy; the second, which regards it as belonging to the quality of the matter, under the name of an original moving force, may be called Dynamics; and the third, where matter with this quality is conceived as by its own reciprocal motion in relation, appears under the name of Mechanics; and the fourth, where its motion or rest [is conceived], merely in reference to the mode of presentation or modality, in other words as determined as phenomenon of the external sense, is called Phenomenology.

But besides the above internal necessity, whereby the metaphysical foundations of the doctrine of body are not only to be distinguished from physics, which employs empirical principles, but even from the rational premises of the latter, in which the employment of mathematics is to be met with, there is an external, and, though only accidental, at the same time an important reason, for separating its thorough working-out from the general system of metaphysics, and for presenting it systematically as a special whole. For if it be permissible to indicate the boundaries of a science, not merely according to the construction of its object, and its specific kind of cognition, but also according to the aim that is kept in view as a further use of the science itself, and it is found that metaphysics has engaged so many heads, and will continue to engage them, not in order to extend natural knowledge (which could be done much more easily and certainly by observation, experiment, and the application of mathematics to external phenomena), but in order to attain to a knowledge of that which lies wholly beyond all the boundaries of experience, of God, Freedom, and Immortality; [in this case] one gains in the promotion of this object, if one liberates it from a shoot springing indeed from its own stem, but only detrimental to its regular growth, and plants this [shoot] apart, without thereby mistaking its origination, or ignoring its entire growth from the system of general metaphysics. This does not affect the completeness of the latter, but it facilitates the uniform progress of this science towards its goal, if in all cases where the universal doctrine of body is required, one can call to aid the separate system of such a science, without encumbering it with the larger system [viz. of metaphysics in general]. It is indeed very remarkable (though it cannot here be thoroughly entered into), that universal metaphysics, in all cases where it requires instances (intuitions) to procure significance for its pure conceptions of the understanding, must always take them from the universal doctrine of body; in other words, from the form and principle of external intuition; and if these are not found to hand in their entirety, it gropes uncertainly and tremblingly amid mere empty conceptions. Hence the well-known disputes, or at least the obscurity in questions, as to the possibility of an opposition of realities, of intensive quantity, &c., by which the understanding is only taught, through instances from corporeal nature, what the conditions are under which the above conceptions can alone have objective reality, that is, significance and truth. And thus a separate metaphysics of corporeal nature does excellent and indispensable service to the universal [metaphysics], in that it procures instances (cases in concreto) in which to realise the conceptions and doctrines of the latter (properly the transcendental philosophy), that is, to give to a mere form of thought sense and meaning.

I have in this treatise followed the mathematical method, if not with all strictness (for which more time would have been necessary than I had to devote to it), at least imitatively, not in order, by a display of profundity, to procure a better reception for it, but because I believe such a system to be quite capable of it, and that perfection may in time be obtained by a cleverer hand, if stimulated by this sketch, mathematical investigators of nature should find it not unimportant to treat the metaphysical portion, which anyway cannot be got rid of, as a special fundamental department of general physics, and to bring it into unison with the mathematical doctrine of motion.

Newton, in the preface to his mathematical principles of natural science (after having remarked that geometry only requires two of the mechanical actions which it postulates, namely, to describe a straight line and a circle) says: geometry is proud of being able to achieve so much while taking so little from extraneous sources.[3] One might say of metaphysics, on the other hand: it stands astonished, that with so much offered it by pure mathematics it can effect so little. In the meantime, this little is something which mathematics indispensably requires in its application to natural science, which, inasmuch as it must here necessarily borrow from metaphysics, need not be ashamed to allow itself to be seen in company with the latter.


  1. 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).
  2. I find doubts expressed in the criticism of Professor Ulrich’s Institutiones Logicae et Metaphysicae, 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.
  3. Gloria geometria, quod tam paucis principiis aliunde petitis tam multa praestet.—Newton, Princ. Phil. Nat. Math. Praefat.