In the passage quoted in the previous post Bertrand Russell addresses the question, “What is the logical structure of the fact which consists in a given subject understanding a given proposition?” and he selects a proposition of the form to demonstrate his way of analyzing the fact. Russell wraps up his discussion of the example in the passage quoted below.
Excerpt from Bertrand Russell • “Theory of Knowledge” (1913)
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).
- Bertrand Russell, Theory of Knowledge : The 1913 Manuscript, edited by Elizabeth Ramsden Eames in collaboration with Kenneth Blackwell, Routledge, London, UK, 1992. First published, George Allen and Unwin, 1984.