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An Introduction To Non-aristotelian Systems And General Semantics.

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B, and we merely state that they are unequal or of different magnitudes, we imply the possibility that B is greater than A, which is false to facts. To give an adequate account, and to prevent false implications, there is no other way than to say which one is greater than the other. We see that it is impossible to give an A adequate account when asymmetrical relations are present. The possession of the 'same' 'property', or of different 'properties', are both symmetrical relations and seem covered by the subject-predicate form. But it is impossible to account adequately for asymmetrical relations in terms of 'properties'. In other words, we see that a language and 'logic' based upon subject-predicate structure may perhaps express symmetrical relations, but fail to express adequately asymmetrical relations, because both 'sameness' and difference of predicates are symmetrical.1 Asymmetrical relations introduce a language of new structure, involving new s.r. Yet asymmetrical relations include many of the most important ones. They are involved in all order, all series, all function, in 'space', in 'time', in 'greater' and 'less', 'more' and 'less', 'whole' and 'part', 'infinity', 'space-time',. If we are restricted to the use of forms of representation unfitted for the expression of asymmetrical relations, ordinal, serial, functional, and structural problems could not be dealt with adequately. We should also have many insoluble semantic puzzles in connection with 'space', 'time', 'cause and effect', and many other relations in the world around us, and ourselves.
A very interesting structural and semantic fact should be noticed. that in symmetrical relations order is immaterial, in non-symmetrical relations it is important, and in asymmetrical relations order plays an all-important role and cannot be reversed. Order itself is expressed in terms of asymmetrical relations; as, for instance, 'before' or 'after', which apply to 'space', to 'time', 'space-time', 'structure'., and also to all processes and activities, the activities of the nervous system included. The asymmetrical relations 'greater', 'father'., imply ordering, while the 'unequal' (having different 'properties') or a 'relative'., do npi imply ordering. If we consider subject-predicate forms as expressing a relation between the 'observer' and the 'observed', excluding humans, this last relation is also asymmetrical. Applying correct symbolism: if a leaf appears green to me, I certainly do not 'appear green' to the leaf! The last remark suggests that any A revision of the A -system is structurally impossible. To attempt a revision, we must begin with the formulation of a-system of different structure.
The above simple considerations have very far-reaching consequences, as without relations, and particularly without asymmetrical relations, we cannot have order, and without order, in the analysis of