that there is need of anything more than its mechanism, merely as nature, according to which, without any Idea lying at their root, they can be purposive for our judgement. But I understand by _free formations_ of nature _those_ whereby from a _fluid at rest_, through the volatilisation or separation of a portion of its constituents (sometimes merely of caloric), the remainder in becoming solid assumes a definite shape or tissue (figure or texture), which is different according to the specific difference of the material, but in the same material is constant. Here it is always presupposed that we are speaking of a perfect fluid, _i.e._ that the material in it is completely dissolved, and that it is not a mere medley of solid particles in a state of suspension.
Formation, then, takes place by a _shooting together_, _i.e._ by a sudden solidification, not by a gradual transition from the fluid to the solid state, but all at once by a _saltus_; which transition is also called _crystallisation_. The commonest example of this kind of formation is the freezing of water, where first icicles are produced, which combine at angles of 60°, while others attach themselves to each vertex, until it all becomes ice; and so that, while this is going on, the water does not gradually become viscous, but is as perfectly fluid as if its temperature were far higher, although it is absolutely ice-cold. The matter that disengages itself, which is dissipated suddenly at the moment of solidification, is a considerable quantum of caloric, the disappearance of which, as it was only required for preserving fluidity, leaves the new ice not in the least colder than the water which shortly before was fluid.
Many salts, and also rocks, of a crystalline figure, are produced thus from a species of earth dissolved in water, we do not exactly know how. Thus are formed the glandular configurations of many minerals, the cubical sulphide of lead, the ruby silver ore, etc., in all probability in water and by the shooting together of particles, as they become forced by some cause to dispense with this vehicle and to unite in definite external shapes.
But also all kinds of matter, which have been kept in a fluid state by heat, and have become solid by cooling, show internally, when fractured, a definite texture. This makes us judge that if their own weight or the disturbance of the air had not prevented it, they would also have exhibited on the outer surface their specifically peculiar shapes. This has been observed in some metals on their inner surface, which have been hardened externally by fusion but are fluid in the interior, by the drawing off the internal fluid and the consequent undisturbed crystallisation of the remainder. Many of these mineral crystallisations, such as spars, hematite, arragonite, etc., often present beautiful shapes, the like of which art can only conceive; and the halo in the cavern of Antiparos[102] is merely produced by water trickling down strata of gypsum.
The fluid state is, to all appearance, older than the solid state, and plants as well as animal bodies are fashioned out of fluid nutritive matter, so far as this forms itself in a state of rest. This last of course primarily combines and forms itself in freedom according to a certain original disposition directed towards purposes (which, as will be shown in Part II., must not be judged aesthetically but teleologically according to the principle of realism), but also perhaps in conformity with the universal law of the affinity of materials.
Again, the watery fluids dissolved in an atmosphere that is a mixture of different gases, if they separate from the latter on account of cooling, produce snow figures, which in correspondence with the character of the special mixture of gases, often seem very artistic and are extremely beautiful. So, without detracting from the teleological principle by which we judge of organisation, we may well think that the beauty of flowers, of the plumage of birds, or of shell-fish, both in shape and colour, may be ascribed to nature and its faculty of producing forms in an aesthetically purposive way, in its freedom, without particular purposes adapted thereto, according to chemical laws by the arrangement of the material requisite for the organisation in question.
But what shows the principle of the _Ideality_ of the purposiveness in the beauty of nature, as that which we always place at the basis of an aesthetical judgement, and which allows us to employ, as a ground of explanation for our representative faculty, no realism of purpose, is the fact that in judging beauty we invariably seek its gauge in ourselves _a priori_, and that our aesthetical Judgement is itself legislative in respect of the judgement whether anything is beautiful or not. This could not be, on the assumption of the Realism of the purposiveness of nature; because in that case we must have learned from nature what we ought to find beautiful, and the aesthetical judgement would be subjected to empirical principles. For in such an act of judging the important point is not, what nature is, or even, as a purpose, is in relation to us, but how we take it. There would be an objective purposiveness in nature if it had fashioned its forms for our satisfaction; and not a subjective purposiveness which depended upon the play of the Imagination in its freedom, where it is we who receive nature with favour, not nature which shows us favour. The property of nature that gives us occasion to perceive the inner purposiveness in the relation of our mental faculties in judging certain of its products--a purposiveness which is to be explained on supersensible grounds as necessary and universal--cannot be a natural purpose or be judged by us as such; for otherwise the judgement hereby determined would not be free, and would have at its basis heteronomy, and not, as beseems a judgement of taste, autonomy.
In beautiful Art the principle of the Idealism of purposiveness is still clearer. As in the case of the beautiful in Nature, an aesthetical Realism of this purposiveness cannot be perceived by sensations (for then the art would be only pleasant, not beautiful).
But that the satisfaction produced by aesthetical Ideas must not depend on the attainment of definite purposes (as in mechanically designed art), and that consequently, in the very rationalism of the principle, the ideality of the purposes and not their reality must be fundamental, appears from the fact that beautiful Art, as such, must not be considered as a product of Understanding and Science, but of Genius, and therefore must get its rule through _aesthetical_ Ideas, which are essentially different from rational Ideas of definite purposes.
Just as the _ideality_ of the objects of sense as phenomena is the only way of explaining the possibility of their forms being susceptible of _a priori_ determination, so the _idealism_ of purposiveness, in judging the beautiful in nature and art, is the only hypothesis under which Criticism can explain the possibility of a judgement of taste which demands _a priori_ validity for every one (without grounding on concepts the purposiveness that is represented in the Object).
§ 59. _Of Beauty as the symbol of Morality_ Intuitions are always required to establish the reality of our concepts. If the concepts are empirical, the intuitions are called _examples_. If they are pure concepts of Understanding, the intuitions are called _schemata_. If we desire to establish the objective reality of rational concepts, _i.e._ of Ideas, on behalf of theoretical cognition, then we are asking for something impossible, because absolutely no intuition can be given which shall be adequate to them.
All _hypotyposis_ (presentation, _subjectio sub adspectum_), or sensible illustration, is twofold. It is either _schematical_, when to a concept comprehended by the Understanding the corresponding intuition is given _a priori_; or it is _symbolical_. In the latter case to a concept only thinkable by the Reason, to which no sensible intuition can be adequate, an intuition is supplied with which accords a procedure of the Judgement analogous to what it observes in schematism: it accords with it, that is, in respect of the rule of this procedure merely, not of the intuition itself; consequently in respect of the form of reflection merely, and not of its content.
There is a use of the word _symbolical_ that has been adopted by modern logicians, which is misleading and incorrect, _i.e._ to speak of the _symbolical_ mode of representation as if it were opposed to the _intuitive_; for the symbolical is only a mode of the intuitive. The latter (the intuitive), that is, may be divided into the _schematical_ and the _symbolical_ modes of representation. Both are hypotyposes, _i.e._ presentations (_exhibitiones_); not mere _characterisations_, or designations of concepts by accompanying sensible signs which contain nothing belonging to the intuition of the Object, and only serve as a means for reproducing the concepts, according to the law of association of the Imagination, and consequently in a subjective point of view.
These are either words, or visible (algebraical, even mimetical) signs, as mere expressions for concepts.[103] All intuitions, which we supply to concepts _a priori_, are therefore either _schemata_ or _symbols_, of which the former contain direct, the latter indirect, presentations of the concept. The former do this demonstratively; the latter by means of an analogy (for which we avail ourselves even of empirical intuitions) in which the Judgement exercises a double function; first applying the concept to the object of a sensible intuition, and then applying the mere rule of the reflection made upon that intuition to a quite different object of which the first is only the symbol. Thus a monarchical state is represented by a living body, if it is governed by national laws, and by a mere machine (like a hand-mill) if governed by an individual absolute will; but in both cases only _symbolically_.
For between a despotic state and a hand-mill there is, to be sure, no similarity; but there is a similarity in the rules according to which we reflect upon these two things and their causality. This matter has not been sufficiently analysed hitherto, for it deserves a deeper investigation; but this is not the place to linger over it.
Our language [_i.e._ German] is full of indirect presentations of this sort, in which the expression does not contain the proper schema for the concept, but merely a symbol for reflection. Thus the words _ground_ (support, basis), _to depend_ (to be held up from above), to _flow_ from something (instead of, to follow), _substance_ (as _Locke_ expresses it, the support of accidents), and countless others, are not schematical but symbolical hypotyposes and expressions for concepts, not by means of a direct intuition, but only by analogy with it, _i.e._ by the transference of reflection upon an object of intuition to a quite different concept to which perhaps an intuition can never directly correspond. If we are to give the name of cognition to a mere mode of representation (which is quite permissible if the latter is not a principle of the theoretical determination of what an object is in itself, but of the practical determination of what the Idea of it should be for us and for its purposive use), then all our knowledge of God is merely symbolical; and he who regards it as schematical, along with the properties of Understanding, Will, etc., which only establish their objective reality in beings of this world, falls into Anthropomorphism, just as he who gives up every intuitive element falls into Deism, by which nothing at all is cognised, not even in a practical point of view.
Now I say the Beautiful is the symbol of the morally Good, and that it is only in this respect (a reference which is natural to every man and which every man postulates in others as a duty) that it gives pleasure with a claim for the agreement of every one else. By this the mind is made conscious of a certain ennoblement and elevation above the mere sensibility to pleasure received through sense, and the worth of others is estimated in accordance with a like maxim of their Judgement.
That is the _intelligible_, to which, as pointed out in the preceding paragraph, Taste looks; with which our higher cognitive faculties are in accord; and without which a downright contradiction would arise between their nature and the claims made by taste. In this faculty the Judgement does not see itself, as in empirical judging, subjected to a heteronomy of empirical laws; it gives the law to itself in respect of the objects of so pure a satisfaction, just as the Reason does in respect of the faculty of desire. Hence, both on account of this inner possibility in the subject and of the external possibility of a nature that agrees with it, it finds itself to be referred to something within the subject as well as without him, something which is neither nature nor freedom, but which yet is connected with the supersensible ground of the latter. In this supersensible ground, therefore, the theoretical faculty is bound together in unity with the practical, in a way which though common is yet unknown. We shall indicate some points of this analogy, while at the same time we shall note the differences.
(1) The beautiful pleases _immediately_ (but only in reflective intuition, not, like morality, in its concept). (2) It pleases _apart from any interest_ (the morally good is indeed necessarily bound up with an interest, though not with one which precedes the judgement upon the satisfaction, but with one which is first of all produced by it).
(3) The _freedom_ of the Imagination (and therefore of the sensibility of our faculty) is represented in judging the beautiful as harmonious with the conformity to law of the Understanding (in the moral judgement the freedom of the will is thought as the harmony of the latter with itself according to universal laws of Reason). (4) The subjective principle in judging the beautiful is represented as _universal_, _i.e._ as valid for every man, though not cognisable through any universal concept. (The objective principle of morality is also expounded as universal, _i.e._ for every subject and for every action of the same subject, and thus as cognisable by means of a universal concept). Hence the moral judgement is not only susceptible of definite constitutive principles, but is possible _only_ by grounding its maxims on these in their universality.
A reference to this analogy is usual even with the common Understanding [of men], and we often describe beautiful objects of nature or art by names that seem to put a moral appreciation at their basis. We call buildings or trees majestic and magnificent, landscapes laughing and gay; even colours are called innocent, modest, tender, because they excite sensations which have something analogous to the consciousness of the state of mind brought about by moral judgements. Taste makes possible the transition, without any violent leap, from the charm of Sense to habitual moral interest; for it represents the Imagination in its freedom as capable of purposive determination for the Understanding, and so teaches us to find even in objects of sense a free satisfaction apart from any charm of sense.
APPENDIX The division of a Critique into Elementology and Methodology, as preparatory to science, is not applicable to the Critique of taste, because there neither is nor can be a science of the Beautiful, and the judgement of taste is not determinable by means of principles. As for the scientific element in every art, which regards _truth_ in the presentation of its Object, this is indeed the indispensable condition (_conditio sine qua non_) of beautiful art, but not beautiful art itself. There is therefore for beautiful art only a _manner_ (_modus_), not a _method of teaching_ (_methodus_). The master must show what the pupil is to do and how he is to do it; and the universal rules, under which at last he brings his procedure, serve rather for bringing the main points back to his remembrance when occasion requires, than for prescribing them to him. Nevertheless regard must be had here to a certain ideal, which art must have before its eyes, although it cannot be completely attained in practice. It is only through exciting the Imagination of the pupil to accordance with a given concept, by making him note the inadequacy of the expression for the Idea, to which the concept itself does not attain because it is an aesthetical Idea, and by severe criticism, that he can be prevented from taking the examples set before him as types and models for imitation, to be subjected to no higher standard or independent judgement. It is thus that genius, and with it the freedom of the Imagination, is stifled by its very conformity to law; and without these no beautiful art, and not even an accurately judging individual taste, is possible.
The propaedeutic to all beautiful art, regarded in the highest degree of its perfection, seems to lie, not in precepts, but in the culture of the mental powers by means of those elements of knowledge called _humaniora_, probably because _humanity_ on the one side indicates the universal _feeling of sympathy_, and on the other the faculty of being able to _communicate_ universally our inmost [feelings].
For these properties taken together constitute the characteristic social spirit[104] of humanity by which it is distinguished from the limitations of animal life. The age and peoples, in which the impulse towards a _law-abiding_ social life, by which a people becomes a permanent community, contended with the great difficulties presented by the difficult problem of uniting freedom (and therefore equality also) with compulsion (rather of respect and submission from a sense of duty than of fear)--such an age and such a people naturally first found out the art of reciprocal communication of Ideas between the cultivated and uncultivated classes and thus discovered how to harmonise the large-mindedness and refinement of the former with the natural simplicity and originality of the latter. In this way they first found that mean between the higher culture and simple nature which furnishes that true standard for taste as a sense common to all men which no universal rules can supply.
With difficulty will a later age dispense with those models, because it will be always farther from nature; and in fine, without having permanent examples before it, a concept will hardly be possible, in one and the same people, of the happy union of the law-abiding constraint of the highest culture with the force and truth of free nature which feels its own proper worth.
Now taste is at bottom a faculty for judging of the sensible illustration of moral Ideas (by means of a certain analogy involved in our reflection upon both these); and it is from this faculty also and from the greater susceptibility grounded thereon for the feeling arising from the latter (called moral feeling), that the pleasure is derived which taste regards as valid for mankind in general and not merely for the private feeling of each. Hence it appears plain that the true propaedeutic for the foundation of taste is the development of moral Ideas and the culture of the moral feeling; because it is only when sensibility is brought into agreement with this that genuine taste can assume a definite invariable form.
THE CRITIQUE OF JUDGEMENT PART II CRITIQUE OF THE TELEOLOGICAL JUDGEMENT § 61. _Of the objective purposiveness of Nature_ 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 intelligent 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 order 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.
FIRST DIVISION ANALYTIC OF THE TELEOLOGICAL JUDGEMENT § 62. _Of the objective purposiveness which is merely formal as distinguished from that which is material_ 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 locus 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 original 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.
But this intellectual purposiveness, although no doubt objective (not subjective like aesthetical purposiveness), is in reference to its possibility merely formal (not real). It can only be conceived as purposiveness in general without any [definite] purpose being assumed as its basis, and consequently without teleology being needed for it.
The figure of a circle is an intuition which is determined by means of the Understanding according to a principle. The unity of this principle which I arbitrarily assume and use as fundamental concept, applied to a form of intuition (space) which is met with in myself as a representation and yet _a priori_, renders intelligible the unity of many rules resulting from the construction of that concept, which are purposive for many possible designs. But this purposiveness does not imply a _purpose_ or any other ground whatever. It is quite different if I meet with order and regularity in complexes of _things_, external to myself, enclosed within certain boundaries; as, _e.g._ in a garden, the order and regularity of the trees, flower-beds, and walks. These I cannot expect to derive _a priori_ from my bounding of space made after a rule of my own; for this order and regularity are existing things which must be given empirically in order to be known, and not a mere representation in myself determined _a priori_ according to a principle. So then the latter (empirical) purposiveness, as _real_, is dependent on the concept of a purpose.
But the ground of admiration for a perceived purposiveness, although it be in the being of things (so far as their concepts can be constructed), may very well be seen, and seen to be legitimate.
The manifold rules whose unity (derived from a principle) excites admiration, are all synthetical and do not follow from the _concept_ of the Object, _e.g._ of a circle; but require this Object to be given in intuition. Hence this unity gets the appearance of having empirically an external basis of rules distinct from our representative faculty; as if therefore the correspondence of the Object to that need of rules which is proper to the Understanding were contingent in itself, and therefore only possible by means of a purpose expressly directed thereto. Now because this harmony, notwithstanding all this purposiveness, is not cognised empirically but _a priori_, it should bring us of itself to this point--that space, through whose determination (by means of the Imagination, in accordance with a concept) the Object is alone possible, is not a characteristic of things external to me, but a mere mode of representation in myself.
Hence, in the figure which I draw _in conformity with a concept_, _i.e._ in my own mode of representing that which is given to me externally, whatever it may be in itself, _it is I that introduce the purposiveness_; I get no empirical instruction from the Object about the purposiveness, and so I require in it no particular purpose external to myself. But because this consideration already calls for a critical employment of Reason, and consequently cannot be involved in the judging of the Object according to its properties; so this latter [judging] suggests to me immediately nothing but the unification of heterogeneous rules (even according to their very diversity) in a principle. This principle, without requiring any particular _a priori_ basis external to my concept, or indeed, generally speaking, to my representation, is yet cognised _a priori_ by me as true. Now _wonder_ is a shock of the mind arising from the incompatibility of a representation, and the rule given by its means, with the principles already lying at its basis; which provokes a doubt as to whether we have rightly seen or rightly judged. _Admiration_, however, is wonder which ever recurs, despite the disappearance of this doubt.
Consequently the latter is a quite natural effect of that observed purposiveness in the being of things (as phenomena). It cannot indeed be censured, whilst the unification of the form of sensible intuition (space)--with the faculty of concepts (the Understanding)--is inexplicable to us; and that not only on account of the union being just of the kind that it is, but because it is enlarging for the mind to surmise [the existence of] something lying outside our sensible representations in which, although unknown to us, the ultimate ground of that agreement may be met with. We are, it is true, not necessitated to cognise this if we have only to do _a priori_ with the formal purposiveness of our representations; but the fact that we are compelled to look out beyond it inspires at the same time an admiration for the object that impels us thereto.
We are accustomed to speak of the above-mentioned properties of geometrical figures or of numbers as _beautiful_, on account of a certain _a priori_ purposiveness they have for all kinds of cognitive uses, this purposiveness being quite unexpected on account of the simplicity of the construction. We speak, _e.g._ of this or that _beautiful_ property of the circle, which was discovered in this or that way. But there is no aesthetical act of judgement through which we find it purposive, no act of judgement without a concept which renders noticeable a mere _subjective_ purposiveness in the free play of our cognitive faculties; but an intellectual act according to concepts which enables us clearly to cognise an objective purposiveness, _i.e._ availableness for all kinds of (infinitely manifold) purposes.
We must rather call this _relative perfection_ than a beauty of the mathematical figure. To speak thus of an _intellectual beauty_ cannot in general be permissible; for otherwise the word beauty would lose all determinate significance, or the intellectual satisfaction all superiority over the sensible. We should rather call a _demonstration_ of such properties beautiful, because through it the Understanding as the faculty of concepts, and the Imagination as the faculty of presenting them, feel themselves strengthened _a priori_. (This, when viewed in connexion with the precision introduced by Reason, is spoken of as elegant.) Here, however, the satisfaction, although it is based on concepts, is subjective; while perfection brings with itself an objective satisfaction.
§ 63. _Of the relative, as distinguished from the inner, purposiveness of nature_ Experience leads our Judgement to the concept of an objective and material purposiveness, _i.e._ to the concept of a purpose of nature, only when[105] we have to judge of a relation of cause to effect which we find ourselves able to apprehend as legitimate only by presupposing