Abstract
In developing modern logic, Frege aims to substantiate the logicist view of arithmetic. In this view, arithmetic is reducible to logic: one can define all arithmetical notions using only logical notions, and prove all arithmetic truths using only logical truths together with definitions of arithmetical notions. A key component of his attempt to show this is his analysis of numbers as extensions of ‘concepts’ or properties (Frege, 1884: 80).1 Russell, who shares Frege’s logicism, accepts the same analysis of number. In his early analysis of mathematics, he writes:
... a number is nothing but a class of similar classes: this definition allows the deduction of all the usual properties of numbers ... and is the only one (so far as I know) which is possible in terms of the fundamental concepts of general logic. (POM: 116)2
Like Frege, Russell identifies classes as extensions and considers the notion of extension a logical notion because it pertains to the logic or semantics of predicates.
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© 2013 Byeong-uk Yi
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Yi, Bu. (2013). The Logic of Classes of the No-Class Theory. In: Griffin, N., Linsky, B. (eds) The Palgrave Centenary Companion to Principia Mathematica. History of Analytic Philosophy. Palgrave Macmillan, London. https://doi.org/10.1057/9781137344632_6
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DOI: https://doi.org/10.1057/9781137344632_6
Publisher Name: Palgrave Macmillan, London
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