II.
Although astronomy is an “eminently mathematical” science, the method of working by observation is used in it. The astronomer observes before calculating, and he observes again after having calculated. The art of observation for which there is no use in mathematics appears here then, and, with it, the inductive method.
Indeed there is no “absolute separation” between observing and reasoning.[121] The mind does not first observe facts in a receptive or “passive” manner, in order to work out combinations of these facts afterwards. In reality every observation is a combination, and this is particularly true in astronomical observation. The facts which we observe are really constructed. We can only see simultaneous or successive directions, according to which the mind must construct the form or the movement which the eye could not take in. The necessary and constant association “between prevision and inspection” is more intimate and more evident here than in any other science.
In the same way, hypothesis (which is inseparable from observation) can be studied in astronomy in its most simple form. Here it is presented in its clearest aspect, and, if one may say so, in the one which most reveals its essential nature. Now, hypothesis in astronomy “serves to fill up the necessary gaps in observation.” It provisionally supplements the knowledge—not indeed of causes, for positive science seeks nothing of this kind—but of facts and laws which we ignore. For instance, the simple geometrical sketch of a diurnal motion would remain impossible without an abstract hypothesis which being compared with the concrete spectacle presented by the movement itself enables us to connect together the various celestial positions. Modern astronomy, which has destroyed primitive assumptions regarded as real laws of the world, has maintained their permanent value for conveniently representing phenomena provisionally. And, as we are not deceived as to the reality of such assumptions we can use without scruple any one which seems to us most advantageous.[122]
The use of hypothesis, as it is employed in astronomy, must be carried into the other sciences. This mode of procedure everywhere remains like to itself, although we do not always conceive it so clearly. “Its normal domain coincides with that of observation.” An hypothesis completes by anticipation what we know of facts and of their laws. Consequently, it is subject to be modified, corrected, or contradicted by a wider or deeper knowledge of facts. Hypotheses then are only valid during the time when they are advantageous, that is to say, as long as they serve to unite and co-ordinate our observations. As has been said, they labour to render themselves useless. But they are indispensable, and science, without them, could neither advance nor even begin. Far from giving too small a share to hypothesis, like Bacon, Comte would rather incur the reproof of having given it too large a one. He made too much use of it himself at the end of his life. But the theory which he gave of it in the Cours de philosophie positive and of which certain features appeal again in Claude Bernard’s Introduction a l’étude de la médecine experiméntale, was a careful study of its nature and function.