Part 2. Atomic Propositional Thought

Chapter 1. The Understanding of Propositions

(4). [cont.]  It follows that, when a subject understands “understanding” is the relating relation, and the terms are and and and similarity and where stands for the form “something and something have some relation”.  Thus a first symbol for the complex will be

This symbol, however, by no means exhausts the analysis of the form of the understanding-complex.  There are many kinds of five-term complexes, and we have to decide what the kind is.

It is obvious, in the first place, that is related to the four other terms in a way different from that in which any of the four other terms are related to each other.

(It is to be observed that we can derive from our five-term complex a complex having any smaller number of terms by replacing any one or more of the terms by “something”.  If is replaced by “something”, the resulting complex is of a different form from that which results from replacing any other term by “something”.  This explains what is meant by saying that enters in a different way from the other constituents.)

It is obvious, in the second place, that enters in a different way from the other three objects, and that “similarity” has a different relation to from that which and have, while and have the same relation to   Also, because we are dealing with a proposition asserting a symmetrical relation between and and have each the same relation to “similarity”, whereas, if we had been dealing with an asymmetrical relation, they would have had different relations to it.  Thus we are led to the following map of our five-term complex.

In this figure, one relation goes from to the four objects;  one relation goes from to similarity, and another to and while one relation goes from similarity to and

This figure, I hope, will help to make clearer the map of our five-term complex.  But to explain in detail the exact abstract meaning of the various items in the figure would demand a lengthy formal logical discussion.  Meanwhile the above attempt must suffice, for the present, as an analysis of what is meant by “understanding a proposition”.  (Russell, TOK, 117–118).