The character of generality which, with that of abstraction, is made use of to institute the hierarchy of phenomena is thus reduced to the idea of dependence. It is the consideration of this dependence which assigns to astronomy its place between mathematics and physics in the encyclopædic ladder of the sciences. Considered singly in themselves, the phenomena studied by astronomy are purely geometrical and mechanical. They would not, therefore, constitute the object of a science distinct from mathematics. But positive philosophy considers everything from the point of view of humanity. Now, for humanity, this “special case” is of unequalled importance. All the other phenomena given to us by experience (except the mathematical phenomena) depend, in a more or less direct manner, upon astronomical phenomena. The knowledge of astronomical laws is therefore the necessary condition for the knowledge of all the others. Thus, the infringement of the principle of the hierarchy of fundamental sciences is only apparent. An analogous case is found in chemistry. The analysis of air and water is incorporated in abstract chemistry, because air and water constitutes the general _milieu_, “in which all ulterior phenomena occur.”[118] The place given to astronomy is therefore justified. This science, moreover, remains abstract. For it to be a concrete science, all aspects of the existence of celestial bodies would have to be studied and considered in their relations, to each other in it. But, on the contrary, astronomy only studies the geometrical and mechanical phenomena in the celestial bodies, all physical and chemical considerations, etc., being eliminated. Comte concludes that in passing on to the celestial case mathematics does not lose its abstract nature. It only becomes more developed in the case of a special example, whose extreme importance demands such a specialisation. The abstract character of astronomy belongs to it almost _a priori_. The facts upon which it rests are only revealed to us by one of our senses, the most intellectual of them indeed, but by which we are only informed of the mathematical properties of bodies. Our eyes alone touch the stars. There is no astronomy for a blind race. Dark stars, if such there be, are for ever hidden from us. All that is given to us, therefore, is the shape, the position and the motion of visible celestial bodies. We can never by any means know how to study their chemical composition, nor their mineral structure, nor _a fortiori_ the nature of the organic bodies which may live upon them. Comte might have formulated in less categorical terms affirmations which were soon to be contradicted by spectral analysis and by photography. But he was confirmed in the entirely abstract and mathematical conception which he had of astronomy by his persuasion that no discoveries of so far-reaching a nature were possible.