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Logic and Arithmetic. Natural Numbers

Mind 85 (337):129-131 (1976)

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  1. Reference to numbers in natural language.Friederike Moltmann - 2013 - Philosophical Studies 162 (3):499 - 536.
    A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...)
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  • What are numbers?Joongol Kim - 2013 - Synthese 190 (6):1099-1112.
    This paper argues that (cardinal) numbers are originally given to us in the context ‘Fs exist n-wise’, and accordingly, numbers are certain manners or modes of existence, by addressing two objections both of which are due to Frege. First, the so-called Caesar objection will be answered by explaining exactly what kind of manner or mode numbers are. And then what we shall call the Functionality of Cardinality objection will be answered by establishing the fact that for any numbers m and (...)
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  • (1 other version)Recent Publications in Logic.Susan Haack - 1974 - Philosophy 51 (195):62-79.
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