ONT Re: Russell's Theory Of Knowledge
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RTOK. Note 3
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| It follows that, when a subject S understands "A and B are similar",
| "understanding" is the relating relation, and the terms are S and
| A and B and similarity and R(x, y), where R(x, y) stands for the
| form "something and something have some relation". Thus a first
| symbol for the complex will be:
|
| U{S, A, B, similarity, R(x, y)}.
|
| 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 S 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 S 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 S enters in
| a different way from the other constituents.)
|
| It is obvious, in the second place, that R(x, y) enters in a different
| way from the other three objects, and that "similarity" has a different
| relation to R(x, y) from that which A and B have, while A and B have the
| same relation to R(x, y). Also, because we are dealing with a proposition
| asserting a symmetrical relation between A and B, A and B 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:
|
| A o
| \ <
| ^\ *
| \ *
| % \ *
| \ *
| % \ R(x, y) *
| o------o------> o---------<---------o Similarity
| % / ^ * ^
| / | * /
| /% | * /
| / |* /
| / % * | /
| / < | /
| B o % | /
| ^ | /
| \ % | /
| \ | /
| \ % | /
| \ | /
| \ % | /
| \ | /
| \ % | /
| \ | /
| \ % | /
| \ | /
| \%| /
| \| /
| o
| S
|
| In this figure, one relation goes from S to the four objects;
| one relation goes from R(x, y) to similarity, and another to
| A and B, while one relation goes from similarity to A and B.
|
| 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, pp. 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 & Unwin, 1984.
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