The followers of Plato generally adhered strictly to his psychological theories. Several, however, like Xenocrates, ventured into bolder speculations. Speusippus, the nephew and successor of the great philosopher, was the author of the _Numerical Analysis_, a treatise on the Pythagorean numbers. Some of his speculations are not found in the written _Dialogues_; but as he was a listener to the unwritten lectures of Plato, the judgment of Enfield is doubtless correct, that he did not differ from his master. He was evidently, though not named, the antagonist whom Aristotle criticised, when professing to cite the argument of Plato against the doctrine of Pythagoras, that all things were in themselves numbers, or rather, inseparable from the idea of numbers. He especially endeavored to show that the Platonic doctrine of ideas differed essentially from the Pythagorean, in that it presupposed numbers and magnitudes to exist apart from things. He also asserted that Plato taught that there could be no _real_ knowledge, if the object of that knowledge was not carried beyond or above the sensible. But Aristotle was no trustworthy witness. He misrepresented Plato, and he almost caricatured the doctrines of Pythagoras. There is a canon of interpretation, which should guide us in our examinations of every philosophical opinion: “The human mind has, under the necessary operation of its own laws, been compelled to entertain the same fundamental ideas, and the human heart to cherish the same feelings in all ages.” It is certain that Pythagoras awakened the deepest intellectual sympathy of his age, and that his doctrines exerted a powerful influence upon the mind of Plato. His cardinal idea was that there existed a permanent principle of unity beneath the forms, changes, and other phenomena of the universe. Aristotle asserted that he taught that “numbers are the first principles of all entities.” Ritter has expressed the opinion that the formula of Pythagoras should be taken symbolically, which is doubtless correct. Aristotle goes on to associate these _numbers_ with the “forms” and “ideas” of Plato. He even declares that Plato said: “forms are numbers,” and that “ideas {xvi} are substantial existences—real beings.” Yet Plato did not so teach. He declared that the final cause was the Supreme Goodness—το ἀγαθόν. “Ideas are objects of pure conception for the human reason, and they are attributes of the Divine Reason.”[11] Nor did he ever say that “forms are numbers.” What he did say may be found in the _Timæus_: “God formed things as they first arose according to forms and numbers.”