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The solution of the difficulties which formerly surrounded the mathematical infinite is probably the greatest achievement of which our own age has to boast. Since the beginnings of Greek thought these difficulties have been known; in every age the finest intellects have vainly endeavoured to answer the apparently unanswerable questions that had been asked by Zeno the Eleatic.
To sum up: the Parmenides of Plato is a critique, first, of the Platonic Ideas, and secondly, of the Eleatic doctrine of Being. Neither are absolutely denied. But certain difficulties and consequences are shown in the assumption of either, which prove that the Platonic as well as the Eleatic doctrine must be remodelled.
Of the three other great Italic leaders of thought of the early period, Xenophanes came rather late in life to Elea and founded the famous Eleatic School, of which Parmenides became the most distinguished ornament. These two were Ionians, and they lived in the sixth century before our era. Empedocles, the Sicilian, was of Doric origin.
II. The Parmenides is not only a criticism of the Eleatic notion of Being, but also of the methods of reasoning then in existence, and in this point of view, as well as in the other, may be regarded as an introduction to the Sophist.
Those who wish to know the nature of these things need only read the works of such men as Peano or Georg Cantor; they will there find exact and indubitable expositions of all these quondam mysteries. In this capricious world, nothing is more capricious than posthumous fame. One of the most notable examples of posterity's lack of judgment is the Eleatic Zeno.
Even Anaximander, and his immediate followers in the Ionic school, while writing in prose, appear, from a few fragments left to us, to have had much recourse to poetical expression, and often convey a dogma by an image; while, in the Eleatic school, Xenophanes and Parmenides adopted the form itself of verse, as the medium for communicating their theories; and Zeno, perhaps from the new example of the drama, first introduced into philosophical dispute that fashion of dialogue which afterward gave to the sternest and loftiest thought the animation and life of dramatic pictures.
THE ELEATIC SCHOOL. The Eleatic School conceived of the world as one in substance, and held that the natural phenomena which we behold, in all their variety and change, are unreal. Zeno sought to vindicate this theory logically by disproving the possibility of motion.
In them Plato brings his philosophic conceptions into striking relation with earlier or rival theories such as the Eleatic, the Megarian, the Cyrenaic, and the Cynic, and touches in these connections on many problems of deep and permanent import.
The Eleatic school followed from the two former, although its development was contemporary with the more perfect stage of these, and its influence upon them was to some extent reactionary. Thales taught that everything was derived from one unique principle, namely water.
To men who maintained that science was impossible, philosophy is not much indebted, although they were disciples of Socrates. Euclid not the mathematician, who was about a century later merely gave a new edition of the Eleatic doctrines, and Phaedo speculated on the oneness of "the good." It was not till Plato arose that a more complete system of philosophy was founded.
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