STRUCTURAL FACTORS IN NON-ARISTOTELIAN
Without objects conceived as unique individuals, we can have no Classes. Without classes we can, as we have seen, define no Relations, without relations we can have no Order. But to be reasonable is to conceive of order-systems, real or ideal. Therefore, we have an absolute logical need to conceive of individual objects as the elements of our ideal order systems. This postulate is the condition of denning clearly any theoretical conception whatever. The further metaphysical aspects of the concept of an individual we may here ignore. To conceive of individual objects is a necessary presupposition of all orderly activity. (449) josiah royce
The connections shown by these particular examples hold in general: given a transformation, you have a function and a relation; given a function, you have a relation and a transformation; given a relation, you have a transformation and a function: one thing - three aspects; and the fact is exceedingly interesting and weighty. (264) cassius j. keyser
It can, you see, be said, with the same approximation to truth, that the whole of science, including mathematics, consists in the study of transformations or in the study of relations. (264) cassius j. keyser
Science is never merely knowledge; it is orderly knowledge. (449)
Philosophers have, as a rule, failed to notice more than two types of sentence, exemplified by the two statements "this is yellow" and "buttercups are yellow." They mistakenly suppose that these two were one and the same type, and also that all propositions were of this type. The former error was exposed by Frege and Peano; the latter was found to make the explanation of order impossible. Consequently the traditional view that all propositions ascribe a predicate to a subject collapsed, and with it the metaphysical systems which were based upon it, consciously or unconsciously. (457) BERTRAND RUSSELL
Interesting analyses by Van Woerkom have shown a general incapacity in aphasics for grasping relations, realizing ordered syntheses, etc.; all of them are operations which are based, in the normal individual, on the use of verbal symbolization. When confronted by groups of figures or of geometrical forms, the aphasic, even though he may perceive them correctly, is unable to analyse or to order the elements, to grasp their succession . . .
(411) HENRI PIERON