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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 to265 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 a266 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;267 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,268 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.
Experience leads our Judgement to the concept of an objective and material purposiveness, i.e. to the concept of a purpose of nature, only when105 we have to judge of a relation of cause to effect which we find ourselves able to apprehend as legitimate only by presupposing the Idea of the effect of the causality of the cause as the fundamental condition, in the cause, of the possibility of the effect. This can take place in two ways. We may regard the effect directly as an art product, or only as material for the art of other possible natural beings; in other words, either as a purpose or as a means towards the purposive employment of other causes. This latter purposiveness is called utility (for man) or mere advantage (for other creatures), and is merely relative; while the former is an inner purposiveness of the natural being.
For example, rivers bring down with them all kinds of earth serviceable for the growth of plants269 which sometimes is deposited inland, often also at their mouths. The tide brings this mud to many coasts over the land or deposits it on the shore; and so, more especially if men give their aid so that the ebb shall not carry it back again, the fruit-bearing land increases in area, and the vegetable kingdom gains the place which formerly was the habitation of fish and shells. In this way has nature itself brought about most of the extensions of the land, and still continues to do so, although very slowly.—Now the question is whether this is to be judged a purpose of nature, because it contains utility for men. We cannot put it down to the account of the vegetable kingdom, because just as much is subtracted from sea-life as is added to land-life.
