Page:Russell - The Problems of Philosophy, 1912.djvu/199

Rh demand three terms, some four, and so on. Take, for instance, the relation "between." So long as only two terms come in, the relation "between" is impossible: three terms are the smallest number that render it possible. York is between London and Edinburgh; but if London and Edinburgh were the only places in the world, there could be nothing which was between one place and another. Similarly jealousy requires three people: there can be no such relation that does not involve three at least. Such a proposition as "A wishes B to promote C's marriage with D" involves a relation of four terms; that is to say, A and B and C and D all come in, and the relation involved cannot be expressed otherwise than in a form involving all four. Instances might be multiplied indefinitely, but enough has been said to show that there are relations which require more than two terms before they can occur.

The relation involved in judging or believing must, if falsehood is to be duly allowed for, be taken to be a relation between several