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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 [Footnote: From the Greek, eurhioko.] 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.

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 itselfโ€”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 diversityโ€”in accordance with the principle of specification; another, the interest of unityโ€”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 circumstancesโ€”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 Bonnetโ€”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 orderโ€”it being still undetermined how far it extendsโ€”as really existing in nature, is beyond doubt a legitimate and excellent principle of reasonโ€”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.

Of the Ultimate End of the Natural Dialectic of Human Reason.

The ideas of pure reason cannot be, of themselves and in their own nature, dialectical; it is from their misemployment alone that fallacies and illusions arise. For they originate in the nature of reason itself, and it is impossible that this supreme tribunal for all the rights and claims of speculation should be itself undeserving of confidence and promotive of error. It is to be expected, therefore, that these ideas have a genuine and legitimate aim. It is true, the mob of sophists raise against reason the cry of inconsistency and contradiction, and affect to despise the government of that faculty, because they cannot understand its constitution, while it is to its beneficial influences alone that they owe the position and the intelligence which enable them to criticize and to blame its procedure.

We cannot employ an a priori conception with certainty, until we have made a transcendental deduction therefore. The ideas of pure reason do not admit of the same kind of deduction as the categories.

But if they are to possess the least objective validity, and to represent anything but mere creations of thought (entia rationis ratiocinantis), a deduction of them must be possible. This deduction will complete the critical task imposed upon pure reason; and it is to this part Of our labours that we now proceed.

There is a great difference between a thingโ€™s being presented to the mind as an object in an absolute sense, or merely as an ideal object. In the former case I employ my conceptions to determine the object; in the latter case nothing is present to the mind but a mere schema, which does not relate directly to an object, not even in a hypothetical sense, but which is useful only for the purpose of representing other objects to the mind, in a mediate and indirect manner, by means of their relation to the idea in the intellect.

Thus I say the conception of a supreme intelligence is a mere idea; that is to say, its objective reality does not consist in the fact that it has an immediate relation to an object (for in this sense we have no means of establishing its objective validity), it is merely a schema constructed according to the necessary conditions of the unity of reasonโ€”the schema of a thing in general, which is useful towards the production of the highest degree of systematic unity in the empirical exercise of reason, in which we deduce this or that object of experience from the imaginary object of this idea, as the ground or cause of the said object of experience. In this way, the idea is properly a heuristic, and not an ostensive, conception; it does not give us any information respecting the constitution of an object, it merely indicates how, under the guidance of the idea, we ought to investigate the constitution and the relations of objects in the world of experience. Now, if it can be shown that the three kinds of transcendental ideas (psychological, cosmological, and theological), although not relating directly to any object nor determining it, do nevertheless, on the supposition of the existence of an ideal object, produce systematic unity in the laws of the empirical employment of the reason, and extend our empirical cognition, without ever being inconsistent or in opposition with it-it must be a necessary maxim of reason to regulate its procedure according to these ideas. And this forms the transcendental deduction of all speculative ideas, not as constitutive principles of the extension of our cognition beyond the limits of our experience, but as regulative principles of the systematic unity of empirical cognition, which is by the aid of these ideas arranged and emended within its own proper limits, to an extent unattainable by the operation of the principles of the understanding alone.

I shall make this plainer. Guided by the principles involved in these ideas, we must, in the first place, so connect all the phenomena, actions, and feelings of the mind, as if it were a simple substance, which, endowed with personal identity, possesses a permanent existence (in this life at least), while its states, among which those of the body are to be included as external conditions,

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