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We have on transcendental principles good ground to assume a subjective purposiveness in nature, in its particular laws, in reference to its comprehensibility by human Judgement and to the possibility of the connexion of particular experiences in a system. This may be expected as possible in many products of nature, which, as if they were devised quite specially for our Judgement, contain a specific form conformable thereto; which through their manifoldness and unity serve at once to strengthen and to sustain the mental powers (that come into play in the employment of this faculty); and to which therefore we give the name of beautiful forms.
But that the things of nature serve one another as means to purposes, and that their possibility is only completely intelligible through this kind of causality—for this we have absolutely no ground in the universal Idea of nature, as the complex of the objects of sense. In the above-mentioned case, the representation of things, because it is something in ourselves, can be quite well thought a priori as suitable and useful for the internally purposive determination of our cognitive faculties; but that purposes, which neither are our own nor belong to nature (for we do not regard nature as an intelligent260 being), could or should constitute a particular kind of causality, at least a quite special conformity to law,—this we have absolutely no a priori reason for presuming. Yet more, experience itself cannot prove to us the actuality of this; there must then have preceded a rationalising subtlety which only sportively introduces the concept of purpose into the nature of things, but which does not derive it from Objects or from their empirical cognition. To this latter it is of more service to make nature comprehensible according to analogy with the subjective ground of the connexion of our representations, than to cognise it from objective grounds.
Further, objective purposiveness, as a principle of the possibility of things of nature, is so far removed from necessary connexion with the concept of nature, that it is much oftener precisely that upon which one relies to prove the contingency of nature and of its form. When, e.g. we adduce the structure of a bird, the hollowness of its bones, the disposition of its wings for motion and of its tail for steering, etc., we say that all this is contingent in the highest degree according to the mere nexus effectivus of nature, without calling in the aid of a particular kind of causality, namely that of purpose (nexus finalis). In other words, nature, considered as mere mechanism, could have produced its forms in a thousand other ways without stumbling upon the unity which is in accordance with such a principle. It is not in the concept of nature but quite apart from it that we can hope to find the least ground a priori for this.
Nevertheless the teleological act of judgement is rightly brought to bear, at least problematically, upon the investigation of nature; but only in order261 to bring it under principles of observation and inquiry according to the analogy with the causality of purpose, without any pretence to explain it thereby. It belongs therefore to the reflective and not to the determinant judgement. The concept of combinations and forms of nature in accordance with purposes is then at least one principle more for bringing its phenomena under rules where the laws of simply mechanical causality do not suffice. For we bring in a teleological ground, where we attribute causality in respect of an Object to the concept of an Object, as if it were to be found in nature (not in ourselves); or rather when we represent to ourselves the possibility of the Object after the analogy of that causality which we experience in ourselves, and consequently think nature technically as through a special faculty. If we did not ascribe to it such a method of action, its causality would have to be represented as blind mechanism. If, on the contrary, we supply to nature causes acting designedly, and consequently place at its basis teleology, not merely as a regulative principle for the mere judging of phenomena, to which nature can be thought as subject in its particular laws, but as a constitutive principle of the derivation of its products from their causes; then would the concept of a natural purpose no longer belong to the reflective but to the determinant Judgement. Then, in fact, it would not belong specially to the Judgement (like the concept of beauty regarded as formal subjective purposiveness), but as a rational concept it would introduce into natural science a new causality, which we only borrow from ourselves and ascribe to other beings, without meaning to assume them to be of the same kind with ourselves.
All geometrical figures drawn on a principle display a manifold, oft admired, objective purposiveness; i.e. in reference to their usefulness for the solution of several problems by a single principle, or of the same problem in an infinite variety of ways. The purposiveness is here obviously objective and intellectual, not merely subjective and aesthetical. For it expresses the suitability of the figure for the production of many intended figures, and is cognised through Reason. But this purposiveness does not make the concept of the object itself possible, i.e. it is not regarded as possible merely with reference to this use.
In so simple a figure as the circle lies the key to the solution of a multitude of problems, each of which would demand various appliances; whereas the solution results of itself, as it were, as one of the infinite number of elegant properties of this figure. Are we, for example, asked to construct a triangle, being given the base and vertical angle? The problem is indeterminate, i.e. it can be solved in an infinite number of ways. But the circle embraces them altogether as the geometrical locus263 of the vertices of triangles satisfying the given conditions. Again, suppose that two lines are to cut one another so that the rectangle under the segments of the one should be equal to the rectangle under the segments of the other; the solution of the problem from this point of view presents much difficulty. But all chords intersecting inside a circle divide one another in this proportion. Other curved lines suggest other purposive solutions of which nothing was thought in the rule that furnished their construction. All conic sections in themselves and when compared with one another are fruitful in principles for the solution of a number of possible problems, however simple is the definition which determines their concept.—It is a true joy to see the zeal with which the old geometers investigated the properties of lines of this class, without allowing themselves to be led astray by the questions of narrow-minded persons, as to what use this knowledge would be. Thus they worked out the properties of the parabola without knowing the law of gravitation, which would have suggested to them its application to the trajectory of heavy bodies (for the motion of a heavy body can be seen to be parallel to the curve of a parabola). Again, they found out the properties of an ellipse without surmising that any of the heavenly bodies had weight, and without knowing the law of force at different distances from the point of attraction, which causes it to describe this curve in free motion. While they thus unconsciously worked for the science of the future, they delighted themselves with a purposiveness in the [essential] being of things which yet they were able to present completely a priori in its necessity. Plato, himself master of this science, hinted at such an original264 constitution of things in the discovery of which we can dispense with all experience, and at the power of the mind to produce from its supersensible principle the harmony of beings (where the properties of number come in, with which the mind plays in music). This [he touches upon] in the inspiration that raised him above the concepts of experience to Ideas, which seem to him to be explicable only through an intellectual affinity with the origin of all beings. No wonder that he banished from his school the man who was ignorant of geometry, since he thought he could derive from pure intuition, which has its home in the human spirit, that which Anaxagoras drew from empirical objects and their purposive combination. For in the very necessity of that which is purposive, and is constituted just as if it were designedly intended for our use,—but at the same time seems to belong originally to the being of things without any reference to our use—lies the ground of our great admiration of nature, and that not so much external as in our own Reason. It is surely excusable that this admiration should through misunderstanding gradually rise to the height of fanaticism.
