57. Suppose we take an uneducated person and point out to him a number of learned men, telling him that one of them knows more than all the rest. The uneducated person has no idea of what the man knows who knows the most, nor the man who knows the least; he has no idea of the degrees of science, nor of what science itself is; but he possesses the general ideas of degree, of more and less, and also of knowledge, and this enables him to speak, without contradiction or confusion, of the greater science of the one and the less science of the others, and even to solve with certainty the questions concerning the science of those individuals, in so far as these questions are contained in the general idea that the science of one is greater than that of all the others. A servant in an establishment where the most beautiful products of art are collected, may speak of them all without contradiction or confusion, although he may be incapable of knowing their merit, and entirely ignorant of the circumstances which constitute the beauty of the objects. It is sufficient for him to have the idea of perfection or beauty in general, and to arrange by certain arbitrary signs the degrees of perfection or beauty of the objects, in order to be able to point them out to visitors, and talk of the greater skill of one artist, the poorer success of another; the greater effect and value of the works of the former, and the inferiority of those of the second, and to make other remarks of a similar nature, which at first might make us suppose him a consummate artist, or, at the least, an amateur of a great intellect and exquisite taste. 58. It would be easy to show by other examples, how fruitful some general ideas are, and how they may undergo innumerable combinations, without presenting any thing determinate to the intellect. This is precisely what happens with the idea of the infinite: in vain we ask what there is within us which corresponds to it: the conception of being in general and of the negation of limit present nothing fixed, except certain abstract conditions to which we continually reduce the objects which come under our intuition, or are presented to us with certain characteristic properties which permit us to form a less vague idea of the negation of limit. CHAPTER VIII. THE DEFINITION OF INFINITY CONFIRMED BY APPLICATION TO EXTENSION. 59. We have explained the idea of infinity in general, by the indeterminate conceptions of being and the negation of limit. In order to assure ourselves that the explanation is well grounded, and that we have pointed out the essential marks of the conception, let us examine whether their application to determinate objects corresponds to what we have established in general. If the idea of infinity is what we have defined it to be, we may apply it to all objects of sensible intuition or of the pure understanding, and we shall obtain the results which we ought to obtain, including the anomalies already referred to.[38]