242 W. L. DAVIDSON :

Sciences, therefore, according to dignity QIC worth, ; and, placing Ethics at the top, they descended from it, through Physics, to Logic. It is difficult to say whether the principle adopted or the limited number of the sciences recognised is the more naive feature here ; neither, does much credit to the remark- able sect that gained its philosophical reputation in the fields of Ethics and Logic, and neither had any general influence in the history of philosophy. The first notable attempt at a classification is in connexion with the Seven Liberal Arts. This, probably, dates far back ; but it comes into pro- minence for us with the Latins of the fifth and sixth centuries of our era, more especially with the Roman philosopher and patrician Boethius. Boethius not only exhausts the circle of the sciences (in so far as recognised in his day), but consciously classes them upon the principle, Begin with the primary and fundamental, and go on from that to the dependent and derived. We have not indeed from him a detailed handling of the whole of the sciences, trivium 1 and quadrivium both ; but, in sketching the latter, he does so in the determinate order Arithmetic, Geometry, Music and Astronomy, and supplies us with his reasons. Some of his reasons are curious enough, and smack of Plato and Pytha- goras ; but others of them are far more than mere historical curiosities. Thus, he says that, of the four mathematical sciences, Arithmetic comes first, because the destruction of what is prior in nature means the destruction of what is posterior, whereas the posterior may perish without the prior being affected. " Take away numbers, and whence do you get the triangle and the square and the other figures of geometry seeing they are all denominative of numbers ? But take away the triangle and the square, and indeed the whole of geometry, and three and four and the names of the other numbers will not disappear. ... In like manner, musical modulation is denoted by names of numbers." So too with Astronomy : geometry, music and arithmetic are all presupposed here. Moreover, " Motion is subsequent to rest, and rest is the prior in nature. But astronomy is the science of the movable and geometry of the immovable, and the very motion of the stars obeys the laws of harmony." Now, vast as has been the extension of the circle of the sciences in modern times, and great though the difficulty be in establishing the precise character and place of each, it is something noteworthy that the main principle on which the 1 This word is not Boethius's, but appears to be a barbarous coinage of the seventh century.