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THREE:What remains of the visible world after deducting its ideal elements is pure space. This, which to some seems the clearest of all conceptions, was to Plato one of the obscurest. He can only describe it as the formless substance out of which the four elements, fire, air, water, and earth, are differentiated. It closes the scale of existence and even lies half outside it, just as the Idea of Good in the Republic transcends the same scale at the other end. We may conjecture that the two principles are opposed as absolute self-identity and absolute self-separation; the whole intermediate series of forms serving to bridge over the interval between them. It will then be easy to understand how, as Aristotle tells us, Plato finally came to adopt the Pythagorean nomenclature and designated his two generating principles as the monad and the indefinite dyad. Number was formed by their combination, and all other things were made out of number. Aristotle267 complains that the Platonists had turned philosophy into mathematics; and perhaps in the interests of science it was fortunate that the transformation occurred. To suppose that matter could be built up out of geometrical triangles, as Plato teaches in the Timaeus, was, no doubt, a highly reprehensible confusion; but that the systematic study of science should be based on mathematics was an equally new and important aper?u. The impulse given to knowledge followed unforeseen directions; and at a later period Plato’s true spirit was better represented by Archimedes and Hipparchus than by Arcesilaus and Carneades.

THREE:Now, it is a remarkable fact, and one as yet not sufficiently attended to, that a metaphysical issue first raised between the Platonists and Aristotle, and regarded, at least by the latter, as of supreme importance for philosophy, should have been totally neglected at a time when abundant documents on both sides were open to consultation, and taken up with passionate eagerness at a time when not more than one or two dialogues of Plato and two or three tracts of Aristotle continued to be read in the western world. Various explanations of this singular anomaly may be offered. It may be said, for instance, that after every moral and religious question on which the schools of Athens were divided had been closed by the authoritative ruling of Catholicism, nothing remained to quarrel over but points too remote or too obscure for the Church to interfere in their decision; and that these were accordingly seized upon as the only field where human intelligence could exercise itself with any approach to freedom. The truth, however, seems to be that to take any interest in the controversy between Realism and Nominalism, it was first necessary that European thought as a whole should rise to a level with the common standpoint of their first supporters. This revolution was effected by the general adoption of a monotheistic faith.

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