Edition: Forgotten Books|
Date of issue: 27 Sep 2015
Format files: EPUB, TXT, PDF, DOCX
The author of the book: Richard an Arms
The size of the: 6.37 MB
Description of the book "The Notion of Number and the Notion of Class (Classic Reprint)":
Excerpt from The Notion of Number and the Notion of Class
Discussions about the nature of number may be readily divided into various types. It is one of the striking characteristics of the true mathematician that anything in the way of a vague statement causes him acute discomfort. He desires a change from the suggestive impressionistic expression of the subjectively self-evident to an objective explicit derivation. A striking example of this is Frege's rebellion against psychological theories of number. "States of mind have no place in mathematics," says the mathematician, and, so far from differing with him, we may PDF well inquire whether, as such, they have any place in philosophy.
To the post-Kantian metaphysician no such ideal ever presented itself. For him the boasted Copemican revolution had indeed taken place, and like our pragmatists, he could think of no problem except in connection with some mind. Number depends upon the way we think of it and the logically simple is what we can think of most readily. The method used is introspection. Opposed to these is the empiricist who demands that all be reduced to physical terms. Crudities such as this represent J. S. Mill ePub's rash intrusion into the philosophy of arithmetic.
Corresponding to these three classes of thinkers we find widely different conceptions of number and three variants of Aristotelian logic. The empiricist defines number as a physical property of external objects and emphasizes induction; the Kantian talks about thought-content, introducing all manner of the psychology of reasoning into his so-called logic. It remains for the formalistic mathematician to regard number as definable in terms of class and that bewildering maze of symbolic ramifications which has gained the title of logistic as the pinnacle of mathematical method.
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Richard an Arms
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