# Introduction to Mathematical Philosophy

By Bertrand Russell | Go to book overview

CHAPTER V
KINDS OF RELATIONS

A GREAT part of the philosophy of mathematics is concerned with relations, and many different kinds of relations have different kinds of uses. It often happens that a property which belongs to all relations is only important as regards relations of certain sorts; in these cases the reader will not see the bearing of the proposition asserting such a property unless he has in mind the sorts of relations for which it is useful. For reasons of this description, as well as from the intrinsic interest of the subject, it is well to have in our minds a rough list of the more mathematically serviceable varieties of relations.

We dealt in the preceding chapter with a supremely important class, namely, serial relations. Each of the three properties which we combined in defining series--namely, asymmetry, transitiveness, and connexity--has its own importance. We will begin by saying something on each of these three.

Asymmetry, i.e. the property of being incompatible with the converse, is a characteristic of the very greatest interest and importance. In order to develop its functions, we will consider various examples. The relation husband is asymmetrical, and so is the relation wife; i.e. if a is husband of b, b cannot be husband of a, and similarly in the case of wife. On the other hand, the relation "spouse" is symmetrical: if a is spouse of b, then b is spouse of a. Suppose now we are given the relation spouse, and we wish to derive the relation husband. Husband is the same as male spouse or spouse of a female; thus the relation husband can

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