APPENDIX Of the Regulative Employment of the Ideas of Pure Reason

The result of all the dialectical attempts of pure reason not only confirms the truth of what we have already proved in our Transcendental Analytic, namely, that all inferences which would lead us beyond the limits of experience are fallacious and groundless, but it at the same time teaches us this important lesson, that human reason has a natural inclination to overstep these limits, and that transcendental ideas are as much the natural property of the reason as categories are of the understanding. There exists this difference, however, that while the categories never mislead us, outward objects being always in perfect harmony therewith, ideas are the parents of irresistible illusions, the severest and most subtle criticism being required to save us from the fallacies which they induce.

Whatever is grounded in the nature of our powers will be found to be in harmony with the final purpose and proper employment of these powers, when once we have discovered their true direction and aim. We are entitled to suppose, therefore, that there exists a mode of employing transcendental ideas which is proper and immanent; although, when we mistake their meaning, and regard them as conceptions of actual things, their mode of application is transcendent and delusive. For it is not the idea itself, but only the employment of the idea in relation to possible experience, that is transcendent or immanent. An idea is employed transcendently, when it is applied to an object falsely believed to be adequate with and to correspond to it; imminently, when it is applied solely to the employment of the understanding in the sphere of experience. Thus all errors of subreptio- of misapplication, are to be ascribed to defects of judgement, and not to understanding or reason.

Reason never has an immediate relation to an object; it relates immediately to the understanding alone. It is only through the understanding that it can be employed in the field of experience. It does not form conceptions of objects, it merely arranges them and gives to them that unity which they are capable of possessing when the sphere of their application has been extended as widely as possible. Reason avails itself of the conception of the understanding for the sole purpose of producing totality in the different series. This totality the understanding does not concern itself with; its only occupation is the connection of experiences, by which series of conditions in accordance with conceptions are established. The object of reason is, therefore, the understanding and its proper destination. As the latter brings unity into the diversity of objects by means of its conceptions, so the former brings unity into the diversity of conceptions by means of ideas; as it sets the final aim of a collective unity to the operations of the understanding, which without this occupies itself with a distributive unity alone.

I accordingly maintain that transcendental ideas can never be employed as constitutive ideas, that they cannot be conceptions of objects, and that, when thus considered, they assume a fallacious and dialectical character. But, on the other hand, they are capable of an admirable and indispensably necessary application to objects- as regulative ideas, directing the understanding to a certain aim, the guiding lines towards which all its laws follow, and in which they all meet in one point. This point- though a mere idea (focus imaginarius), that is, not a point from which the conceptions of the understanding do really proceed, for it lies beyond the sphere of possible experience- serves, notwithstanding, to give to these conceptions the greatest possible unity combined with the greatest possible extension. Hence arises the natural illusion which induces us to believe that these lines proceed from an object which lies out of the sphere of empirical cognition, just as objects reflected in a mirror appear to be behind it. But this illusion- which we may hinder from imposing upon us- is necessary and unavoidable, if we desire to see, not only those objects which lie before us, but those which are at a great distance behind us; that is to say, when, in the present case, we direct the aims of the understanding, beyond every given experience, towards an extension as great as can possibly be attained.

If we review our cognitions in their entire extent, we shall find that the peculiar business of reason is to arrange them into a system, that is to say, to give them connection according to a principle. This unity presupposes an idea- the idea of the form of a whole (of cognition), preceding the determinate cognition of the parts, and containing the conditions which determine a priori to every part its place and relation to the other parts of the whole system. This idea, accordingly, demands complete unity in the cognition of the understanding- not the unity of a contingent aggregate, but that of a system connected according to necessary laws. It cannot be affirmed with propriety that this idea is a conception of an object; it is merely a conception of the complete unity of the conceptions of objects, in so far as this unity is available to the understanding as a rule. Such conceptions of reason are not derived from nature; on the contrary, we employ them for the interrogation and investigation of nature, and regard our cognition as defective so long as it is not adequate to them. We admit that such a thing as pure earth, pure water, or pure air, is not to be discovered. And yet we require these conceptions (which have their origin in the reason, so far as regards their absolute purity and completeness) for the purpose of determining the share which each of these natural causes has in every phenomenon. Thus the different kinds of matter are all ref erred to earths, as mere weight; to salts and inflammable bodies, as pure force; and finally, to water and air, as the vehicula of the former, or the machines employed by them in their operations- for the purpose of explaining the chemical action and reaction of bodies in accordance with the idea of a mechanism. For, although not actually so expressed, the influence of such ideas of reason is very observable in the procedure of natural philosophers.

If reason is the faculty of deducing the particular from the general, and if the general be certain in se and given, it is only necessary that the judgement should subsume the particular under the general, the particular being thus necessarily determined. I shall term this the demonstrative or apodeictic employment of reason. If, however, the general is admitted as problematical only, and is a mere idea, the particular case is certain, but the universality of the rule which applies to this particular case remains a problem. Several particular cases, the certainty of which is beyond doubt, are then taken and examined, for the purpose of discovering whether the rule is applicable to them; and if it appears that all the particular cases which can be collected follow from the rule, its universality is inferred, and at the same time, all the causes which have not, or cannot be presented to our observation, are concluded to be of the same character with those which we have observed. This I shall term the hypothetical employment of the reason.

The hypothetical exercise of reason by the aid of ideas employed as problematical conceptions is properly not constitutive. That is to say, if we consider the subject strictly, the truth of the rule, which has been employed as an hypothesis, does not follow from the use that is made of it by reason. For how can we know all the possible cases that may arise? some of which may, however, prove exceptions to the universality of the rule. This employment of reason is merely regulative, and its sole aim is the introduction of unity into the aggregate of our particular cognitions, and thereby the approximating of the rule to universality.

The object of the hypothetical employment of reason is therefore the systematic unity of cognitions; and this unity is the criterion of the truth of a rule. On the other hand, this systematic unity- as a mere idea- is in fact merely a unity projected, not to be regarded as given, but only in the light of a problem- a problem which serves, however, as a principle for the various and particular exercise of the understanding in experience, directs it with regard to those cases which are not presented to our observation, and introduces harmony and consistency into all its operations.

All that we can be certain of from the above considerations is that this systematic unity is a logical principle, whose aim is to assist the understanding, where it cannot of itself attain to rules, by means of ideas, to bring all these various rules under one principle, and thus to ensure the most complete consistency and connection that can be attained. But the assertion that objects and the understanding by which they are cognized are so constituted as to be determined to systematic unity, that this may be postulated a priori, without any reference to the interest of reason, and that we are justified in declaring all possible cognitions- empirical and others- to possess systematic unity, and to be subject to general principles from which, notwithstanding their various character, they are all derivable such an assertion can be founded only upon a transcendental principle of reason, which would render this systematic unity not subjectively and logically- in its character of a method, but objectively necessary.

We shall illustrate this by an example. The conceptions of the understanding make us acquainted, among many other kinds of unity, with that of the causality of a substance, which is termed power. The different phenomenal manifestations of the same substance appear at first view to be so very dissimilar that we are inclined to assume the existence of just as many different powers as there are different effects- as, in the case of the human mind, we have feeling, consciousness, imagination, memory, wit, analysis, pleasure, desire and so on. Now we are required by a logical maxim to reduce these differences to as small a number as possible, by comparing them and discovering the hidden identity which exists. We must inquire, for example, whether or not imagination (connected with consciousness), memory, wit, and analysis are not merely different forms of understanding and reason. The idea of a fundamental power, the existence of which no effort of logic can assure us of, is the problem to be solved, for the systematic representation of the existing variety of powers. The logical principle of reason requires us to produce as great a unity as is possible in the system of our cognitions; and the more the phenomena of this and the other power are found to be identical, the more probable does it become, that they are nothing but different manifestations of one and the same power, which may be called, relatively speaking, a fundamental power. And so with other cases.

These relatively fundamental powers must again be compared with each other, to discover, if possible, the one radical and absolutely fundamental power of which they are but the manifestations. But this unity is purely hypothetical. It is not maintained, that this unity does really exist, but that we must, in the interest of reason, that is, for the establishment of principles for the various rules presented by experience, try to discover and introduce it, so far as is practicable, into the sphere of our cognitions.

But the transcendental employment of the understanding would lead us to believe that this idea of a fundamental power is not problematical, but that it possesses objective reality, and thus the systematic unity of the various powers or forces in a substance is demanded by the understanding and erected into an apodeictic or necessary principle. For, without having attempted to discover the unity of the various powers existing in nature, nay, even after all our attempts have failed, we notwithstanding presuppose that it does exist, and may be, sooner or later, discovered. And this reason does, not only, as in the case above adduced, with regard to the unity of substance, but where many substances, although all to a certain extent homogeneous, are discoverable, as in the case of matter in general. Here also does reason presuppose the existence of the systematic unity of various powers- inasmuch as particular laws of nature are subordinate to general laws; and parsimony in principles is not merely an economical principle of reason, but an essential law of nature.

We cannot understand, in fact, how a logical principle of unity can of right exist, unless we presuppose a transcendental principle, by which such a systematic unit- as a property of objects themselves- is regarded as necessary a priori. For with what right can reason, in its logical exercise, require us to regard the variety of forces which nature displays, as in effect a disguised unity, and to deduce them from one fundamental force or power, when she is free to admit that it is just as possible that all forces should be different in kind, and that a systematic unity is not conformable to the design of nature? In this view of the case, reason would be proceeding in direct opposition to her own destination, by setting as an aim an idea which entirely conflicts with the procedure and arrangement of nature. Neither can we assert that reason has previously inferred this unity from the contingent nature of phenomena. For the law of reason which requires us to seek for this unity is a necessary law, inasmuch as without it we should not possess a faculty of reason, nor without reason a consistent and self-accordant mode of employing the understanding, nor, in the absence of this, any proper and sufficient criterion of empirical truth. In relation to this criterion, therefore, we must suppose the idea of the systematic unity of nature to possess objective validity and necessity.

We find this transcendental presupposition lurking in different forms in the principles of philosophers, although they have neither recognized it nor confessed to themselves its presence. That the diversities of individual things do not exclude identity of species, that the various species must be considered as merely different determinations of a few genera, and these again as divisions of still higher races, and so on- that, accordingly, a certain systematic unity of all possible empirical conceptions, in so far as they can be deduced from higher and more general conceptions, must be sought for, is a scholastic maxim or logical principle, without which reason could not be employed by us. For we can infer the particular from the general, only in so far as general properties of things constitute the foundation upon which the particular rest.

That the same unity exists in nature is presupposed by philosophers in the well-known scholastic maxim, which forbids us unnecessarily to augment the number of entities or principles (entia praeter necessitatem non esse multiplicanda). This maxim asserts that nature herself assists in the establishment of this unity of reason, and that the seemingly infinite diversity of phenomena should not deter us from the expectation of discovering beneath this diversity a unity of fundamental properties, of which the aforesaid variety is but a more or less determined form. This unity, although a mere idea, thinkers have found it necessary rather to moderate the desire than to encourage it. It was considered a great step when chemists were able to reduce all salts to two main genera- acids and alkalis; and they regard this difference as itself a mere variety, or different manifestation of one and the same fundamental material. The different kinds of earths (stones and even metals) chemists have endeavoured to reduce to three, and afterwards to two; but still, not content with this advance, they cannot but think that behind these diversities there lurks but one genus- nay, that even salts and earths have a common principle. It might be conjectured that this is merely an economical plan of reason, for the purpose of sparing itself trouble, and an attempt of a purely hypothetical character, which, when successful, gives an appearance of probability to the principle of explanation employed by the reason. But a selfish purpose of this kind is easily to be distinguished from the idea, according to which every one presupposes that this unity is in accordance with the laws of nature, and that reason does not in this case request, but requires, although we are quite unable to determine the proper limits of this unity.

If the diversity existing in phenomena- a diversity not of form (for in this they may be similar) but of content- were so great that the subtlest human reason could never by comparison discover in them the least similarity (which is not impossible), in this case the logical law of genera would be without foundation, the conception of a genus, nay, all general conceptions would be impossible, and the faculty of the understanding, the exercise of which is restricted to the world of conceptions, could not exist. The logical principle of genera, accordingly, if it is to be applied to nature (by which I mean objects presented to our senses), presupposes a transcendental principle. In accordance with this principle, homogeneity is necessarily presupposed in the variety of phenomena (although we are unable to determine a priori the degree of this homogeneity), because without it no empirical conceptions, and consequently no experience, would be possible.

The logical principle of genera, which demands identity in phenomena, is balanced by another principle- that of species, which requires variety and diversity in things, notwithstanding their accordance in the same genus, and directs the understanding to attend to the one no less than to the other. This principle (of the faculty of distinction) acts as a check upon the reason and reason exhibits in this respect a double and conflicting interest- on the one hand, the interest in the extent (the interest of generality) in relation to genera; on the other, that of the content (the interest of individuality) in relation to the variety of species. In the former case, the understanding cogitates more under its conceptions, in the latter it cogitates more in them. This distinction manifests itself likewise in the habits of thought peculiar to natural philosophers, some of whom- the remarkably speculative heads- may be said to be hostile to heterogeneity in phenomena, and have their eyes always fixed on the unity of genera, while others- with a strong empirical tendency- aim unceasingly at the analysis of phenomena, and almost destroy in us the hope of ever being able to estimate the character of these according to general principles.

The latter mode of thought is evidently based upon a logical principle, the aim of which is the systematic completeness of all cognitions. This principle authorizes me, beginning at the genus, to descend to the various and diverse contained under it; and in this way extension, as in the former case unity, is assured to the system. For if we merely examine the sphere of the conception which indicates a genus, we cannot discover how far it is possible to proceed in the division of that sphere; just as it is impossible, from the consideration of the space occupied by matter, to determine how far we can proceed in the division of it. Hence every genus must contain different species, and these again different subspecies; and as each of the latter must itself contain a sphere (must be of a certain extent, as a conceptus communis), reason demands that no species or sub-species is to be considered as the lowest possible. For a species or sub-species, being always a conception, which contains only what is common to a number of different things, does not completely determine any individual thing, or relate immediately to it, and must consequently contain other conceptions, that is, other sub-species under it. This law of specification may be thus expressed: entium varietates non temere sunt minuendae.

But it is easy to see that this logical law would likewise be without sense or application, were it not based upon a transcendental law of specification, which certainly does not require that the differences existing phenomena should be infinite in number, for the logical principle, which merely maintains the indeterminateness of the logical sphere of a conception, in relation to its possible division, does not authorize this statement; while it does impose upon the understanding the duty of searching for subspecies to every species, and minor differences in every difference. For, were there no lower conceptions, neither could there be any higher. Now the understanding cognizes only by means of conceptions; consequently, how far soever it may proceed in division, never by mere intuition, but always by lower and lower conceptions. The cognition of phenomena in their complete determination (which is possible only by means of the understanding) requires an unceasingly continued specification of conceptions, and a progression to ever smaller differences, of which abstraction bad been made in the conception of the species, and still more in that of the genus.

This law of specification cannot be deduced from experience; it can never present us with a principle of so universal an application. Empirical specification very soon stops in its distinction of diversities, and requires the guidance of the transcendental law, as a principle of the reason- a law which imposes on us the necessity of never ceasing in our search for differences, even although these may not present themselves to the senses. That absorbent earths are of different kinds could only be discovered by obeying the anticipatory law of reason, which imposes upon the understanding the task of discovering the differences existing between these earths, and supposes that nature is richer in substances than our senses would indicate. The faculty of the understanding belongs to us just as much under the presupposition of differences in the objects of nature, as under the condition that these objects are homogeneous, because we could not possess conceptions, nor make any use of our understanding, were not the phenomena included under these conceptions in some respects dissimilar, as well as similar, in their character.

Reason thus prepares the sphere of the understanding for the operations of this faculty: 1. By the principle of the homogeneity of the diverse in higher genera; 2. By the principle of the variety of the homogeneous in lower species; and, to complete the systematic unity, it adds, 3. A law of the affinity of all conceptions which prescribes a continuous transition from one species to every other by the gradual increase of diversity. We may term these the principles of the homogeneity, the specification, and the continuity of forms. The latter results from the union of the two former, inasmuch as we regard the systematic connection as complete in thought, in the ascent to higher genera, as well as in the descent to lower species. For all diversities must be related to each other, as they all spring from one highest genus, descending through the different gradations of a more and more extended determination.

We may illustrate the systematic unity produced by the three logical principles in the following manner. Every conception may be regarded as a point, which, as the standpoint of a spectator, has a certain horizon, which may be said to enclose a number of things that may be viewed, so to speak, from that centre. Within this horizon there must be an infinite number of other points, each of which has its own horizon, smaller and more circumscribed; in other words, every species contains sub-species, according to the principle of specification, and the logical horizon consists of smaller horizons (subspecies), but not of points (individuals), which possess no extent. But different horizons or genera, which include under them so many conceptions, may have one common horizon, from which, as from a mid-point, they may be surveyed; and we may proceed thus, till we arrive at the highest genus, or universal and true horizon, which is determined by the highest conception, and which contains under itself all differences and varieties, as genera, species, and subspecies.

To this highest standpoint I am conducted by the law of homogeneity, as to all lower and more variously-determined conceptions by the law of specification. Now as in this way there exists no void in the whole extent of all possible conceptions, and as out of the sphere of these the mind can discover nothing, there arises from the presupposition of the universal horizon above mentioned, and its complete division, the principle: Non datur vacuum formarum. This principle asserts that there are not different primitive and highest genera, which stand isolated, so to speak, from each other, but all the various genera are mere divisions and limitations of one highest and universal genus; and hence follows immediately the principle: Datur continuum formarum. This principle indicates that all differences of species limit each other, and do not admit of transition from one to another by a saltus, but only through smaller degrees of the difference between the one species and the other. In one word, there are no species or sub-species which (in the view of reason) are the nearest possible to each other; intermediate species or sub-species being always possible, the difference of which from each of the former is always smaller than the difference existing between these.

The first law, therefore, directs us to avoid the notion that there exist different primal genera, and enounces the fact of perfect homogeneity; the second imposes a check upon this tendency to unity and prescribes the distinction of sub-species, before proceeding to apply our general conceptions to individuals. The third unites both the former, by enouncing the fact of homogeneity as existing even in the most various diversity, by means of the gradual transition from one species to another. Thus it indicates a relationship between the different branches or species, in so far as they all spring from the same stem.

But this logical law of the continuum specierum (formarum logicarum) presupposes a transcendental principle (lex continui in natura), without which the understanding might be led into error, by following the guidance of the former, and thus perhaps pursuing a path contrary to that prescribed by nature. This law must, consequently, be based upon pure transcendental, and not upon empirical, considerations. For, in the latter case, it would come later than the system; whereas it is really itself the parent of all that is systematic in our cognition of nature. These principles are not mere hypotheses employed for the purpose of experimenting upon nature; although when any such connection is discovered, it forms a solid ground for regarding the hypothetical unity as valid in the sphere of nature- and thus they are in this respect not without their use. But we go farther, and maintain that it is manifest that these principles of parsimony in fundamental causes, variety in effects, and affinity in phenomena, are in accordance both with reason and nature, and that they are not mere methods or plans devised for the purpose of assisting us in our observation of the external world.

But it is plain that this continuity of forms is a mere idea, to which no adequate object can be discovered in experience. And this for two reasons. First, because the species in nature are really divided, and hence form quanta discreta; and, if the gradual progression through their affinity were continuous, the intermediate members lying between two given species must be infinite in number, which is impossible. Secondly, because we cannot make any determinate empirical use of this law, inasmuch as it does not present us with any criterion of affinity which could aid us in determining how far we ought to pursue the graduation of differences: it merely contains a general indication that it is our duty to seek for and, if possible, to discover them.

When we arrange these principles of systematic unity in the order conformable to their employment in experience, they will stand thus: Variety, Affinity, Unity, each of them, as ideas, being taken in the highest degree of their completeness. Reason presupposes the existence of cognitions of the understanding, which have a direct relation to experience, and aims at the ideal unity of these cognitions- a unity which far transcends all experience or empirical notions. The affinity of the diverse, notwithstanding the differences existing between its parts, has a relation to things, but a still closer one to the mere properties and powers of things. For example, imperfect experience may represent the orbits of the planets as circular. But we discover variations from this course, and we proceed to suppose that the planets revolve in a path which, if not a circle, is of a character very similar to it. That is to say, the movements of those planets which do not form a circle will approximate more or less to the properties of a circle, and probably form an ellipse. The paths of comets exhibit still greater variations, for, so far as our observation extends, they do not return upon their own course in a circle or ellipse. But we proceed to the conjecture that comets describe a parabola, a figure which is closely allied to the ellipse. In fact, a parabola is merely an ellipse, with its longer axis produced to an indefinite extent. Thus these principles conduct us to a unity in the genera of the forms of these orbits, and, proceeding farther, to a unity as regards the cause of the motions of the heavenly bodies- that is, gravitation. But we go on extending our conquests over nature, and endeavour to explain all seeming deviations from these rules, and even make additions to our system which no experience can ever substantiate- for example, the theory, in affinity with that of ellipses, of hyperbolic paths of comets, pursuing which, these bodies leave our solar system and, passing from sun to sun, unite the most distant parts of the infinite universe, which is held together by the same moving power.

The most remarkable circumstance connected with these principles is that they seem to be transcendental, and, although only containing ideas for the guidance of the empirical exercise of reason, and although this empirical employment stands to these ideas in an asymptotic relation alone (to use a mathematical term), that is, continually approximate, without ever being able to attain to them, they possess, notwithstanding, as a priori synthetical propositions, objective though undetermined validity, and are available as rules for possible experience. In the elaboration of our experience, they may also be employed with great advantage, as heuristic* principles. A transcendental deduction of them cannot be made; such a deduction being always impossible in the case of ideas, as has been already shown.

*From the Greek, eurhioko.

We distinguished, in the Transcendental Analytic, the dynamical principles of the understanding, which are regulative principles of intuition, from the mathematical, which are constitutive principles of intuition. These dynamical laws are, however, constitutive in relation to experience, inasmuch as they render the conceptions without which experience could not exist possible a priori. But the principles of pure reason cannot be constitutive even in regard to empirical conceptions, because no sensuous schema corresponding to them can be discovered, and they cannot therefore have an object in concreto. Now, if I grant that they cannot be employed in the sphere of experience, as constitutive principles, how shall I secure for them employment and objective validity as regulative principles, and in what way can they be so employed?

The understanding is the object of reason, as sensibility is the object of the understanding. The production of systematic unity in all the empirical operations of the understanding is the proper occupation of reason; just as it is the business of the understanding to connect the various content of phenomena by means of conceptions, and subject them to empirical laws. But the operations of the understanding are, without the schemata of sensibility, undetermined; and, in the same manner, the unity of reason is perfectly undetermined as regards the conditions under which, and the extent to which, the understanding ought to carry the systematic connection of its conceptions. But, although it is impossible to discover in intuition a schema for the complete systematic unity of all the conceptions of the understanding, there must be some analogon of this schema. This analogon is the idea of the maximum of the division and the connection of our cognition in one principle. For we may have a determinate notion of a maximum and an absolutely perfect, all the restrictive conditions which are connected with an indeterminate and various content having been abstracted. Thus the idea of reason is analogous with a sensuous schema, with this difference, that the application of the categories to the schema of reason does not present a cognition of any object (as is the case with the application of the categories to sensuous schemata), but merely provides us with a rule or principle for the systematic unity of the exercise of the understanding. Now, as every principle which imposes upon the exercise of the understanding a priori compliance with the rule of systematic unity also relates, although only in an indirect manner, to an object of experience, the principles of pure reason will also possess objective reality and validity in relation to experience. But they will not aim at determining our knowledge in regard to any empirical object; they will merely indicate the procedure, following which the empirical and determinate exercise of the understanding may be in complete harmony and connection with itself- a result which is produced by its being brought into harmony with the principle of systematic unity, so far as that is possible, and deduced from it.

I term all subjective principles, which are not derived from observation of the constitution of an object, but from the interest which Reason has in producing a certain completeness in her cognition of that object, maxims of reason. Thus there are maxims of speculative reason, which are based solely upon its speculative interest, although they appear to be objective principles.

When principles which are really regulative are regarded as constitutive, and employed as objective principles, contradictions must arise; but if they are considered as mere maxims, there is no room for contradictions of any kind, as they then merely indicate the different interests of reason, which occasion differences in the mode of thought. In effect, Reason has only one single interest, and the seeming contradiction existing between her maxims merely indicates a difference in, and a reciprocal limitation of, the methods by which this interest is satisfied.

This reasoner has at heart the interest of diversity- in accordance with the principle of specification; another, the interest of unity- in accordance with the principle of aggregation. Each believes that his judgement rests upon a thorough insight into the subject he is examining, and yet it has been influenced solely by a greater or less degree of adherence to some one of the two principles, neither of which are objective, but originate solely from the interest of reason, and on this account to be termed maxims rather than principles. When I observe intelligent men disputing about the distinctive characteristics of men, animals, or plants, and even of minerals, those on the one side assuming the existence of certain national characteristics, certain well-defined and hereditary distinctions of family, race, and so on, while the other side maintain that nature has endowed all races of men with the same faculties and dispositions, and that all differences are but the result of external and accidental circumstances- I have only to consider for a moment the real nature of the subject of discussion, to arrive at the conclusion that it is a subject far too deep for us to judge of, and that there is little probability of either party being able to speak from a perfect insight into and understanding of the nature of the subject itself. Both have, in reality, been struggling for the twofold interest of reason; the one maintaining the one interest, the other the other. But this difference between the maxims of diversity and unity may easily be reconciled and adjusted; although, so long as they are regarded as objective principles, they must occasion not only contradictions and polemic, but place hinderances in the way of the advancement of truth, until some means is discovered of reconciling these conflicting interests, and bringing reason into union and harmony with itself.

The same is the case with the so-called law discovered by Leibnitz, and supported with remarkable ability by Bonnet- the law of the continuous gradation of created beings, which is nothing more than an inference from the principle of affinity; for observation and study of the order of nature could never present it to the mind as an objective truth. The steps of this ladder, as they appear in experience, are too far apart from each other, and the so-called petty differences between different kinds of animals are in nature commonly so wide separations that no confidence can be placed in such views (particularly when we reflect on the great variety of things, and the ease with which we can discover resemblances), and no faith in the laws which are said to express the aims and purposes of nature. On the other hand, the method of investigating the order of nature in the light of this principle, and the maxim which requires us to regard this order- it being still undetermined how far it extends- as really existing in nature, is beyond doubt a legitimate and excellent principle of reason- a principle which extends farther than any experience or observation of ours and which, without giving us any positive knowledge of anything in the region of experience, guides us to the goal of systematic unity.

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