David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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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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Christopher S. Gifford (2013). Against the Modal Argument. Erkenntnis 78 (3):627-646.
L. Horsten (2012). Vom Zahlen Zu den Zahlen: On the Relation Between Computation and Arithmetical Structuralism. Philosophia Mathematica 20 (3):275-288.
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