Review - Foundations of Arithmetic (Frege)

Review - Foundations of Arithmetic (Frege) - concept F is...

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This subtitle, “A Logico-mathematical Enquiry into the Concept of Number,” indicates very well the nature of the work. The first three quarters of the book are devoted to a critical analysis of the idea of previous writers (Kant, Leibnitz, Grassmann, Mill, Lipschitz, Hankel, Jevons, Cantor, Schröder, Hobbers, Hume, and others) on the subject of number, and Frege does not find the ideas of any of these philosophers and mathematicians entirely satisfactory. His conclusions is “that a statement of a number contains an assertion about a concept,” and his definition of number is: The number which belongs to the
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Unformatted text preview: concept F is the extension of the concept equal to the concept F. Frege regards the number zero as belonging to to the natural or counting numbers, whereas we subscribe to the view that zero is not a counting number at all (the first of the counting numbers being 1) and is only properly used when we regard a number as a relative-magnitude, zero being the relative-magnitude of two equal counting numbers. This work of Freges has considerable historical interest as a forerunner of the work of Whitehead and Russell. The translation is excellent and the printing leaves nothing to be desired....
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