instance, the not-Being of solidity is essential to the Being of fluidity. On the other hand, Zeno proves that what changes, cannot be; and his fulcrum is that not-Being excludes Being. To repeat his position: in the world of change there is no Being. The proof is this: if the world of change included Being, it would include the permanent, because Being and the permanent are identical; but the permanent is excluded from the changeable by the very terms of the conception, therefore Being is excluded from the world of change; in other words, in the world of change there is no Being. Such is the negative supplement by means of which Zeno reinforced the positive argument of Parmenides. In the sphere of Being, or the one, the universal, says Parmenides, there can be no not-Being (and consequently no change), because to introduce not-Being here would be to assign opposite determinations to the same subject. And in the sphere of not-Being, the many, the particular, says Zeno, there can be no Being (and consequently nothing but change), because to introduce Being here would, in like manner, be to assign opposite determinations to the same subject. The reasonings of the Eleatics are impregnable if their principle, namely, that contrary determinations cannot belong to the same subject, be conceded.
