Ever since the age of Parmenides and Heracleitus, Greek thought had been haunted by a pervading dualism which each system had in turn attempted to reconcile, with no better result than its reproduction under altered names. And speculation had latterly become still further perplexed by the question whether the antithetical couples supposed to divide all Nature between them could or could not be reduced to so many aspects of a single opposition. In the last chapter but one we showed that there were four such competing pairs—Being and Not-Being, the One and the Many, the Same and the Other, Rest and Motion. Plato employed his very subtlest dialectic in tracing out their connexions, readjusting their relationships, and diminishing the total number of terms which they involved. In what was probably his last great speculative effort, the _Timaeus_, he seems to have selected Sameness and Difference as the couple best adapted to bear the heaviest strain of thought. There is some reason for believing that in his spoken lectures he followed the Pythagorean system more closely, giving the preference to the One and the Many; or he may have employed the two expressions indifferently. The former would sooner commend itself to a dialectician, the latter to a mathematician. Aristotle was both, but he was before all things a naturalist. As such, the antithesis of Being and Not-Being, to which Plato attached little or no value, suited him best. Accordingly, he proceeds to work it out with a clearness before unknown in Greek philosophy. The first and surest of all principles, he declares, is, that a thing cannot both be and not be, in the same sense of the words, and furthermore that it must either be or not be. Subsequent logicians prefixed to these axioms another, declaring that whatever is is. The three together are known as the laws of Identity, Contradiction, and Excluded Middle. By all, except Hegelians, they are recognised as the highest laws of thought; and even Hegel was indebted to them, through Fichte, for the ground-plan of his entire system.[235] The whole meaning and value of such excessively abstract propositions must lie in their application to the problems which they are employed to solve. Aristotle made at once too much and too little of his. Too much—for he employed them to refute doctrines not really involving any logical inconsistency—the theory of Heracleitus, that everything is in motion; the theory of Anaxagoras, that everything was originally confused together; the theory of Protagoras, that man is the measure of all things. Too little—for he admitted a sphere of possibilities where logical definition did not apply, and where subjects simultaneously possessed the capacity of taking on one or other of two contradictory attributes.