Accordingly we found that one class of speculators fixed their attention solely on the mere phenomena of nature, and endeavored, amid sensible things, to find a _single_ element which, being more subtile, and pliable, and universally diffused, could be regarded as the ground and original of all the rest, and from which, by a vital transformation, or by a mechanical combination and arrangement of parts, all the rest should be evolved. The other class passed beyond the simple phenomena, and considered only the abstract _relations_ of phenomena among themselves, or the relations of phenomena to the necessary and universal ideas of the reason, and supposed that, in these relations, they had found an explanation of the universe. The former was the Ionian or Sensation school; the latter was the Italian or Idealist school. We have traced the method according to which the Ionian school proceeded, and estimated the results attained. We now come to consider the method and results of THE ITALIAN OR IDEALIST SCHOOL. This school we have found to be naturally subdivided into--1st, The _Mathematical_ sect, which attempted the explanation of the universe by the abstract conceptions of number, proportion, order, and harmony; and, 2d, The _Metaphysical_ school, which attempted the interpretation of the universe according to the _à priori_ ideas of unity, of Being _in se_, of the Infinite, and the Absolute. _Pythagoras of Samos_(born B.C. 605) was the founder of the Mathematical school. We are conscious of the difficulties which are to be encountered by the student who seeks to attain a definite comprehension of the real opinions of Pythagoras. The genuineness of many of those writings which were once supposed to represent his views, is now questioned. "Modern criticism has clearly shown that the works ascribed to Timæus and Archytas are spurious; and the treatise of Ocellus Lucanus on 'The Nature of the All' can not have been written by a Pythagorean."[427] The only writers who can be regarded as at all reliable are Plato and Aristotle; and the opinions they represent are not so much those of Pythagoras as "the Pythagoreans." This is at once accounted for by the fact that Pythagoras taught in secret, and did not commit his opinions to writing. His disciples, therefore, represent the _tendency_ rather than the actual tenets of his system; these were no doubt modified by the mental habits and tastes of his successors. [Footnote 427: Lewes's "Biographical History of Philosophy," p. 24.] We may safely assume that the proposition from which Pythagoras started was the fundamental idea of all Greek speculation--_that beneath the fleeting forms and successive changes of the universe there is some permanent principle of unity_[428] The Ionian school sought that principle in some common physical element; Pythagoras sought, not for "elements," but for "relations," and through these relations for ultimate laws indicating primal forces.