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Principia mathematica, vol. 1 (of 3)

*24. THE UNIVERSAL CLASS, THE NULL-CLASS, AND THE EXISTENCE OF CLASSES.

Project Gutenberg EPUB3 edition Whitehead, Alfred North and Russell, Bertrand
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In this proposition, the conditions of significance require that should be a class of classes. The condition "" is one required as hypothesis in many propositions. In virtue of the above proposition, this hypothesis may be replaced by "."
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This proposition is frequently used in later parts of the work. We often have to deal with classes of existent classes, and the most convenient form in which to state that all the members of a class of classes exist is "."

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Principia mathematica, vol. 1 (of 3), Project Gutenberg eBook #78050

*23. CALCULUS OF RELATIONS. *25. THE UNIVERSAL RELATION, THE NULL RELATION, AND THE EXISTENCE OF RELATIONS.