Philosophia Mathematica 4 (2):184-189 (1996)

What Numbers Could Not Be’) that an adequate account of the numbers and our arithmetic practice must satisfy not only the conditions usually recognized to be necessary: (a) identify some w-sequence as the numbers, and (b) correctly characterize the cardinality relation that relates a set to a member of that sequence as its cardinal number—it must also satisfy a third condition: the ‘<’ of the sequence must be recursive. This paper argues that adding this further condition was a mistake—any w-sequence would do, no matter how undecidable its ‘<’ relation
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DOI 10.1093/philmat/4.2.184
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Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology:1-24.
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