FORE:We have not here to examine the scientific achievements of Pythagoras and his school; they belong to the history of science, not to that of pure thought, and therefore lie outside the present discussion. Something, however, must be said of Pythagoreanism as a scheme of moral, religious, and social reform. Alone among the pre-Socratic systems, it undertook to furnish a rule of conduct as well as a theory of being. Yet, as Zeller has pointed out,11 it was only an apparent anomaly, for the ethical teaching of the Pythagoreans was not based on their physical theories, except in so far as a deep reverence for law and order was common to both.13 Perhaps, also, the separation of soul and body, with the ascription of a higher dignity to the former, which was a distinctive tenet of the school, may be paralleled with the position given to number as a kind of spiritual power creating and controlling the world of sense. So also political power was to be entrusted to an aristocracy trained in every noble accomplishment, and fitted for exercising authority over others by self-discipline, by mutual fidelity, and by habitual obedience to a rule of right. Nevertheless, we must look, with Zeller, for the true source of Pythagoreanism as a moral movement in that great wave of religious enthusiasm which swept over Hellas during the sixth century before Christ, intimately associated with the importation of Apollo-worship from Lycia, with the concentration of spiritual authority in the oracular shrine of Delphi, and the political predominance of the Dorian race, those Normans of the ancient world. Legend has thrown this connexion into a poetical form by making Pythagoras the son of Apollo; and the Samian sage, although himself an Ionian, chose the Dorian cities of Southern Italy as a favourable field for his new teaching, just as Calvinism found a readier acceptance in the advanced posts of the Teutonic race than among the people whence its founder sprang. Perhaps the nearest parallel, although on a far more extensive scale, for the religious movement of which we are speaking, is the spectacle offered by mediaeval Europe during the twelfth and thirteenth centuries of our era, when a series of great Popes had concentrated all spiritual power in their own hands, and were sending forth army after army of Crusaders to the East; when all Western Europe had awakened to the consciousness of its common Christianity, and each individual was thrilled by a sense of the tremendous alternatives committed to his choice; when the Dominican and Franciscan orders were founded; when Gothic architecture and Florentine painting arose; when the Troubadours and Minnes?ngers were pour14ing out their notes of scornful or tender passion, and the love of the sexes had become a sentiment as lofty and enduring as the devotion of friend to friend had been in Greece of old. The bloom of Greek religious enthusiasm was more exquisite and evanescent than that of feudal Catholicism; inferior in pure spirituality and of more restricted significance as a factor in the evolution of humanity, it at least remained free from the ecclesiastical tyranny, the murderous fanaticism, and the unlovely superstitions of mediaeval faith. But polytheism under any form was fatally incapable of coping with the new spirit of enquiry awakened by philosophy, and the old myths, with their naturalistic crudities, could not long satisfy the reason and conscience of thinkers who had learned in another school to seek everywhere for a central unity of control, and to bow their imaginations before the passionless perfection of eternal law.The principal business of reason is, as we have seen, to376 form abstract ideas or concepts of things. But before the time of Aristotle it had already been discovered that concepts, or rather the terms expressing them, were capable of being united in propositions which might be either true or false, and whose truth might be a matter either of certainty or of simple opinion. Now, in modern psychology, down to the most recent times, it has always been assumed that, just as there is an intellectual faculty or operation called abstraction corresponding to the terms of which a proposition is composed, so also there is a faculty or operation called judgment corresponding to the entire proposition. Sometimes, again, the third operation, which consists in linking propositions together to form syllogisms, is assigned to a distinct faculty called reason; sometimes all three are regarded as ascending steps in a single fundamental process. Neither Plato nor Aristotle, however, had thought out the subject so scientifically. To both the framing, or rather the discovery, of concepts was by far the most important business of a philosopher, judgment and reasoning being merely subsidiary to it. Hence, while in one part of their logic they were realists and conceptualists, in other parts they were nominalists. Abstract names and the definitions unfolding their connotation corresponded to actual entities in Naturethe eternal Ideas of the one and the substantial forms of the otheras well as to mental representations about whose existence they were agreed, while ascribing to them a different origin. But they did not in like manner treat propositions as the expression of natural laws without, or of judgments within, the mind; while reasoning they regarded much more as an art of thinking, a method for the discovery of ideas, than as the Systematisation of a process spontaneously performed by every human being without knowing it; and, even as such, their tendency is to connect it with the theory of definition rather than with the theory of synthetic propositions. Some approach to a realistic view is, indeed, made by both. The377 restless and penetrating thought of Plato had, probably towards the close of his career, led him to enquire into the mutual relations of those Ideas which he had at first been inclined to regard as absolutely distinct. He shows us in the Sophist how the most abstract notions, such as Being, Identity, and so forth, must, to a certain extent, partake of each others nature; and when their relationship does not lie on the surface, he seeks to establish it by the interposition of a third idea obviously connected with both. In the later books of the Republic he also points to a scheme for arranging his Ideas according to a fixed hierarchy resembling the concatenation of mathematical proofs, by ascending and descending whose successive gradations the mind is to become familiarised with absolute truth; and we shall presently see how Aristotle, following in the same track, sought for a counterpart to his syllogistic method in the objective order of things. Nevertheless, with him, as well as with his master, science was not what it is with us, a study of laws, a perpetually growing body of truth, but a process of definition and classification, a systematisation of what had already been perceived and thought.
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