The Notion of Number and the Notion of Class

Excerpt from The Notion of Number and the Notion of ClassWe shall first be concerned with the notion of number as it appeared to Mill and the Kantians and shall attempt to Show that the various historical positions are liable to one or both of the following objections (a) subjective mental states have been introduced, (b) violence has been done to the facts. Frege's distinction here between a posteriori and a priori methods is important. He holds that a priori is deductive, a posteriori, inductive; synthetic means that which uses conceptions belong ing to a special science while an analytic proposition is derived from pure logic alone. Frege held that the concepts and laws of arithmetic are analytic a priori, that they are derived from the fundamental definitions and axioms of logic. We shall find Bertrand Russell espousing the same cause although inde pendently and from slightly different motives.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.