ABSTRACT
This chapter shows that all order depends upon transitive asymmetrical relations. It is concerned with asymmetrical relations. Relations may be divided into several classes, according as they do or do not possess either of two attributes, transitiveness and symmetry. Relations which are both symmetrical and transitive are formally of the nature of equality. Any term of the field of such a relation has the relation in question to itself, though it may not have the relation to any other term. Quantitative equality is only reflexive as applied to quantities; of other terms, it is absurd to assert that they have quantitative equality with themselves. Logical equality is only reflexive for classes, or propositions, or relations. An adjective involving a reference is merely a cumbrous way of describing a relation. The chapter examines the application of the monadistic theory to quantitative relations.
