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An Introduction To Non-aristotelian Systems And General Semantics.

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ON STRUCTURE
57
and not to an 'isolated' object. Such characteristics as arise from the fact that the object belongs to a collection are called 'relations'.
In such collections, we have the possibility of ordering the objects, and so, for instance, we may discover a relation that one object is 'before' or 'after' the other, or that A is the father of B. There are many ways in which we can order a collection, and many relations which we can find. It is important to notice that 'order' and 'relations' are, for the most part, empirically present and that, therefore, this language is fit to represent the facts as we know them. The structure of the actual world is such that it is impossible entirely to isolate an object. An A subject-predicate language, with its tendency to treat objects as in isolation and to have no place for relations (impossible in complete 'isolation'), obviously has a structure not similar to the structure of the world, in which we deal only with collections, of which the members are related.
Obviously, under such empirical conditions, only a language originating in the analysis of collections, and, therefore, a language of 'relations', 'order'., would have a similar structure to the world around us. From the use of a subject-predicate form of language alone, many of our fallacious anti-social and 'individualistic' metaphysics and s.r follow, which we will not analyse here, except to mention that their structural implications follow the structure of the language they use.
If we carry the analysis a step further, we can find relations between relations, as, for instance, the similarity of relations. We follow the definition of Russell. Two relations are said to be similar if there is a one-one correspondence between the terms of their fields, which is such that, whenever two terms have the relation P, their correlates have the relation Q, and vice versa. For example, two series are similar when their terms can be correlated without change of order, an accurate map is similar to the territory it represents, a book spelt phonetically is similar to the sounds when read, .*
When two relations are similar, we say that they have a similar structure, which is defined as the class of all relations similar to the given relation.
We see that the terms 'collection', 'aggregate', 'class', 'order', 'relations', 'structure' are interconnected, each implying the others. If we decide to face empirical 'reality' boldly, we must accept the Einstein-Minkowski four-dimensional language, for 'space' and 'time' cannot be separated empirically, and so we must have a language of similar structure and consider the facts of the world as series of interrelated ordered events, to which, as above explained, we must ascribe 'structure'. Ein-