Part 2. Atomic Propositional Thought

Chapter 1. The Understanding of Propositions

(4).  We come now to the last problem which has to be treated in this chapter, namely:  What is the logical structure of the fact which consists in a given subject understanding a given proposition?  The structure of an understanding varies according to the proposition understood.  At present, we are only concerned with the understanding of atomic propositions;  the understanding of molecular propositions will be dealt with in Part 3.

Let us again take the proposition “A and B are similar”.

It is plain, to begin with, that the complex “A and B being similar”, even if it exists, does not enter in, for if it did, we could not understand false propositions, because in their case there is no such complex.

It is plain, also, from what has been said, that we cannot understand the proposition unless we are acquainted with A and B and similarity and the form “something and something have some relation”.  Apart from these four objects, there does not appear, so far as we can see, to be any object with which we need be acquainted in order to understand the proposition.

It seems to follow that these four objects, and these only, must be united with the subject in one complex when the subject understands the proposition.  It cannot be any complex composed of them that enters in, since they need not form any complex, and if they do, we need not be acquainted with it.  But they themselves must all enter in, since if they did not, it would be at least theoretically possible to understand the proposition without being acquainted with them.

In this argument, I appeal to the principle that, when we understand, those objects with which we must be acquainted when we understand, and those only, are object-constituents (i.e. constituents other than understanding itself and the subject) of the understanding-complex.  (Russell, TOK, 116–117).