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#### Section 15

15. How far is it true that equality and inequality are characteristic of Quantity?

Triangles, it is significant, are said to be similar rather than equal. But we also refer to magnitudes as similar, and the accepted connotation of similarity does not exclude similarity or dissimilarity in Quantity. It may, of course, be the case that the term "similarity" has a different sense here from that understood in reference to Quality.

Furthermore, if we are told that equality and inequality are characteristic of Quantity, that is not to deny that similarity also may be predicated of certain quantities. If, on the contrary, similarity and dissimilarity are to be confined to Quality, the terms as applied to Quantity must, as we have said, bear a different meaning.

But suppose similarity to be identical in both genera; Quantity and Quality must then be expected to reveal other properties held in common.

May the truth be this: that similarity is predicable of Quantity only in so far as Quantity possesses [qualitative] differences? But as a general rule differences are grouped with that of which they are differences, especially when the difference is a difference of that thing alone. If in one case the difference completes the substance and not in another, we inevitably class it with that which it completes, and only consider it as independent when it is not complementary: when we say "completes the substance," we refer not to Subtance as such but to the differentiated substance; the particular object is to be thought of as receiving an accession which is non-substantial.

We must not however fad to observe that we predicate equality of triangles, rectangles, and figures generally, whether plane or solid: this may be given as a ground for regarding equality and inequality as characteristic of Quantity.

It remains to enquire whether similarity and dissimilarity are characteristic of Quality.

We have spoken of Quality as combining with other entities, Matter and Quantity, to form the complete Sensible Substance; this Substance, so called, may be supposed to constitute the manifold world of Sense, which is not so much an essence as a quale. Thus, for the essence of fire we must look to the Reason-Principle; what produces the visible aspect is, properly speaking, a quale.

Man's essence will lie in his Reason-Principle; that which is perfected in the corporeal nature is a mere image of the Reason-Principle a quale rather than an essence.

Consider: the visible Socrates is a man, yet we give the name of Socrates to that likeness of him in a portrait, which consists of mere colours, mere pigments: similarly, it is a Reason-Principle which constitutes Socrates, but we apply the name Socrates to the Socrates we see: in truth, however, the colours and shapes which make up the visible Socrates are but reproductions of those in the Reason-Principle, while this Reason-Principle itself bears a corresponding relation to the truest Reason-Principle of Man. But we need not elaborate this point.

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