ON RELATIONS |
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assumed that everything could be expressed in a subject-predicate form. As we shall see, this is not true. Restriction to the subject-predicate form leaves out some of the most important structural means we have for representing this world and ourselves and has resulted in a general state of un-sanity. The explicit introduction of 'relations' is rather a recent innovation. A few words may be said about them, although the term 'relation' is one of the terms that we may accept as undefined, or that we may define in terms of multi-dimensional order.
Some relations, when they hold between A and B, hold also between B and A. Such relations are called
symmetrical. For instance, the relation 'spouse'. If it holds between A and B, it holds also between B and A. If A is the spouse of B, B is the spouse of A. Terms like 'similarity' and 'dissimilarity' also designate relations of this kind. If A is similar or dissimilar to B, so is B similar or dissimilar to A. In general, a symmetrical relation is such that, if it holds between A and B, it also holds between B and A. In other words, the order in which we consider the relation of our entities is immaterial.It is easy to see that not all relations are of such a character. For instance, in the relation 'A is the brother of B', B is not necessarily a brother of A, because B might be the sister of A. In general, relations which hold between A and B, but not necessarily between B and A, are called
non-symmetrical. In these relations order becomes important. It is not a matter of indifference in what order we consider our entities.If a relation is such that, if it holds between A and B, it
never holds between B and A, it is called asymmetrical. Let us take, for instance, me relations 'father', 'mother', 'husband',. We readily see that if A is a father, or mother, or husband of B, B is never a father, or mother, or husband of A. The reversal of order is impossible in asymmetrical relations, and so any asymmetrical relation establishes a definite order.Relations such as
before, after, greater, more, less, above, to the right, to the left, part, and whole, and a great many others of the most important terms we have, are asymmetrical. The reader may easily verify this for himself. For instance, if A is more than B, B is never more than A,. We see at once that the troublesome little words, which are necessary to express order as 'before' and 'after'; terms of evaluation, such as 'more' and 'less'; and terms on which elementalism or non-elementalism depends, such as 'part' and 'whole', are in the list of asymmetrical relations.Relations can be classified in another way, when three or more terms are considered. Some relations, called transitive, are such that, whenever they hold between A and B and also between B and C, they |
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