Dyadic

Up to now, all the expressions we have called predicates have stood for properties which it makes sense to attribute to a single individual. Such predicates are known as monadic, or one-place, predicates. There are, however, many expressions which we cannot meaningfully apply to single objects, but only to groups of two, three or more objects. We cannot e.g. sensibly say 'x is greater than', but only 'x is greater than y'. Nor can we say 'x is between', or even 'x is between y', but only 'x is between y and z'. We shall say that an expression such as 'greater than' or 'between' stands not for a property of an individual, but for a relation between individuals. Since 'greater than' stands for a relation between two individuals, we shall say that the relation in question is a dyadic or a two-place relation. Similarly, 'between' stands for a triadic or three-place relation; and we can also have four-place, five-place, etc., relations. . . . A dyadic relation holds not simply between a pair of objects, but between those objects in a certain order. It is one thing to say that Bill is father of Tom, and another thing to say that Tom is father of Bill. . . . There are, it is true, certain dyadic relations whose direction is unimportant, in the sense that whenever they hold between x and y, they also hold between y and x; 'parallel to' and 'cousin of' are examples.

The dyadic arithmetic proposes to express all numbers by two characters, 1 and 0. The value of 1 is to double at every remove into a preceding column. Thus, 1 is represented by 1, 2 by 10, 4 by 100, and 8 by 1000; 3 is represented by 11, 5 by 101, 6 by 110, 7 by 111, 9 by 1001, and 10 by 1010. Thus far nothing seems to be gained but simplicity and there is a grievous loss of brevity. But in the huge numbers of the mathematicians this inconvenience was to fall away and the complex operations of addition, subtraction, multiplication, and division, were to sink into mere transcription.

Although dyadic bodies may be more common, they are no more or less "normal" than intersex bodies.