...fundamental principles of generalization have been well formulated by EH Moore in the statement: " The existence of analogies between central features...theories implies the existence of a general theory ichich underlies the particular theories and unifies them with respect to those central features."...

...specific cases may be theories. Accordingly the principle of generalization by abstraction becomes: A*) The existence of analogies between central features...various theories implies the existence of a general abstract theory which underlies the particular theories and unifies them with respect to those central...

...integral to an algebraic sum. We lay down a fundamental principle of generalization by abstraction: The existence of analogies between central features...unifies them with respect to those central features. This formulation was the dominant note of my series of lectures: On the Theory of Bilinear Functional...

...integral to an algebraic sum. We lay down a fundamental principle of generalization by abstraction : The existence of analogies between central features...various theories implies the existence of a general tfleory which underlies the particular theories and unifies them with respect to those central features....

...1'ress (1910). The groat breadth of view of the author in this work is well shown by his own statement: the existence of analogies between central features...theory which underlies the particular theories and unities them with respect to those central features. The great generality and abstractness of the problem...

...which I have formulated äs follows: The existence of analogies between central features of rariovs theories implies the existence of a general theory...unifies them with respect to those central features. For the case of the real-valued Symmetrie kernel, and in fact for the more general case of the complex-valued...

...then illustrated and discussed. (1) The principle of comparison is, in the words of EH Moore, that "the existence of analogies between central features...unifies them with respect to those central features." (2) The principle of continuation is that the existence of a class of particular elements (or operanda)...

...phenomena of Mathematics may be theories (doctrines), we may enunciate the following heuristic principle : The existence of analogies between central features of various theories implies the existence of a more fundamental general theory embracing the special theories as particular instances and unifying...

...analogies in theories that relate to diverse subjects, proceeding according to Professor Moore's dictum, " The existence of analogies between central features...unifies them with respect to those central features," or we may merely make an abstraction of the formal nature of a single given development, and define...

...analogies in theories that relate to diverse subjects, proceeding according to Professor Moore's dictum, " The existence of analogies between central features...unifies them with respect to those central features," or we may merely make an abstraction of the formal nature of a single given development, and define...