=The Later Pythagoreans.= Had the Pythagorean band remained what Pythagoras had designed it, had it not had its political aspirations crushed at the battle of Crotona and the members scattered far and wide, it would probably have for the historian of to-day only the importance of a local band of political and religious reformers. The adversity at Crotona was, however, a blessing in disguise for the Pythagoreans and for Greece, for it turned the Pythagoreans from religious politics to science and metaphysics. _In the first place_, they became the authors of an important metaphysical theory. This was the theory of numbers, which influenced Plato, became the foundation of a vigorous school in Alexandria in the Hellenic-Roman Period, flourished during the Middle Ages, and united with the doctrines of the Jews in what is called the Cabala. To-day the magic numbers persist in our superstitions. _In the second place_, the Pythagoreans turned to science,――especially to mathematics and astronomy,――and in these two branches became very celebrated in ancient times. Their astronomical theory had a most extraordinary history. With modifications it was preserved by Plato and Aristotle, and later became the basis of the Ptolemaic system of astronomy. This system was the scientifically accepted system for fifteen hundred years, when it was supplanted by the Newtonian theory. It is a most singular fact that the cosmological background of the Epics of Dante and Milton is the astronomical system of the Pythagoreans as expressed in the Ptolemaic system. The Pythagoreans, be it remarked, were “Reconcilers,” but they were more. The original ethical motive of Pythagoras influenced them as scientists. They did not attempt to formulate a science of ethics, but the ethical motive was always back of their mathematics and astronomy. =1. The Pythagorean Conception of Being.= The Pythagorean conception of reality is the most advanced of any cosmological theory in this period. The Pythagoreans were hylozoists, but they come the nearest to transcending the hylozoism of their time. The influence of the later Pythagoreans, whom Plato met in Italy, upon Plato shows that Pythagorean philosophy forms a link between the cosmology of the colonies and the following comprehensive systems of thought. The important position in the evolution of Greek thought occupied by the Pythagoreans depends upon their conception of that Being that abides amid all change. Pythagoreanism is usually spoken of as “the number theory.” This is, however, only a suggestion of its import. For numbers are not to the Pythagoreans what the different kinds of cosmic matter were to the early monists, or what the several elements were to the pluralists,――Empedocles, Anaxagoras, and the atomists. Neither are they abstractions merely, such as we use in scientific reckoning. The Pythagoreans were pluralists and hylozoists whose plural numbers look beyond hylozoism.