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E. B. DAVIES, Empiricism in Arithmetic and Analysis, Philosophia Mathematica, Volume 11, Issue 1, February 2003, Pages 53–66, https://doi.org/10.1093/philmat/11.1.53
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Abstract
We discuss the philosophical status of the statement that (9n – 1) is divisible by 8 for various sizes of the number n. We argue that even this simple problem reveals deep tensions between truth and verification. Using Gillies's empiricist classification of theories into levels, we propose that statements in arithmetic should be classified into three different levels depending on the sizes of the numbers involved. We conclude by discussing the relationship between the real number system and the physical continuum.
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©2003 PHILOSOPHIA MATHEMATICA
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