Medicine isn't an exact science.
The true method of science which he possessed forced him to condemn as useless the entire form which Schelling's and Hegel's expositions had adopted, especially the dialectic method of the latter, whilst his love of art and beauty, and his appreciation of moral purposes, revealed to him the existence of a transphenomenal world of values into which no exact science could penetrate.
So persistently does the human ear rebel against the division of the tetrachord into two greater tones and a leimma or hemitone, as represented by the fractions 9, 9, 26, that, centuries before the possibility of reconciling the demands of the ear with those of exact science was satisfactorily demonstrated, the Aristoxenian school advocated the use of an empirical scale, sounding pleasant to the sense, in preference to an unpleasing tonality founded upon immutable proportions.
In another respect also he aided in establishing an exact science of medicine by the introduction of the numerical or statistical method.
We can still point to much in exact science that is absolutely his; and we can indicate infinitely more which is due to his inspiration.
