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

Abstract
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
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.1093/philmat/4.2.184
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 59,735
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

Situated Counting.Peter Gärdenfors & Paula Quinon - 2020 - Review of Philosophy and Psychology:1-24.
Semantic Nominalism.Gabriel Uzquiano - 2005 - Dialectica 59 (2):265–282.

View all 8 citations / Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
144 ( #70,252 of 2,432,437 )

Recent downloads (6 months)
6 ( #115,032 of 2,432,437 )

How can I increase my downloads?

Downloads

My notes