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A STUDY OF PLATONIC TERMINOLOGY. 481 always equal to themselves (&xrauTa><? del e^ovra Kara ravrd del Kara ravra ovra, ibid.); as pure (icaOapd, d/jLiKrd) in con- trast to sensations which are confused, mixed, or unstable, transient (peovresi), imperfect (evSeea-repoi), incapable of perfectly resembling the eiSr) corresponding to them (ot- Bwdrai roiovrov elvai oiov exeivo TrpoBvpelrai irdvra ravra elvat oiov eKeivo, Phado, 74). One of the most suggestive examples used by Plato to illustrate the contrast mentioned above is that which consists in contrasting the equal in itself (TO la-ov) with equal things (ra i<ra) which are always imperfectly so and always apt to cease to be so. It is difficult to find another that could serve better than this to illustrate the assertion, expressed by Aristotle (Metaphys., xii., 4) that the first motive of the intro- duction of the ei8r) was the need of finding a defence or a point of support against the destructive tendencies of those philosophical theories, which, by insisting on the continual mutability and corruptibility of material things, seemed to remove every basis for any formal doctrine and to distrust any distinction whatever between vulgar opinions (S6at) and scientific knowledge (eTna-rrj^rf) represented at that time es- pecially by the mathematical sciences. On this point it may be said that the theory of Ideas fulfilled to a certain extent the same office for these latter sciences as is now fulfilled for the physical and mechanical sciences by the so-called law of causality, inasmuch as this law also consists precisely in anticipating and imagining as existing among phenomena regularities and uniformities greater than, and surpassing, those which superficial ob- servation could have made to appear possible. The characteristics of invariableness, purity, and precision which, as we have seen, were attributed by Plato to the el&rj, do not, in fact, differ from those which are attributed by modern logicians to natural laws as contrasted with merely empirical generalisations. There are passages in which Plato speaks of the analysis of, and search for the etBrj, in terms which might be adopted, without any change, to describe the tracing of the single causes or laws which co- operate or combine in the production of a complex effect. When the Platonic theory is divested of the ethical and aesthetic implications which, to a certain extent, constitute an accessory characteristic of it, it manifests itself as an energetic assertion of the right of the scientist or the philo- sopher to form or construct a more regular, simpler, more perfect world, than the one whose existence the data furnished by the senses and the inductions based on these data, would, by themselves, lead one to admit.