The conceptual basis of numerical abilities: One-to-one correspondence versus the successor relation

Philosophical Psychology 21 (4):459 – 473 (2008)
In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one correspondence relation for numerical abilities is assessed and additional empirical tests are proposed. In the final part, it is argued that the fact that the successor relation and the one-to-one correspondence relation can play independent roles in number concept acquisition may be a complication for testing the Whorfian hypothesis.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,351
External links
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA
    Gottlob Frege (1964). The Basic Laws of Arithmetic. Berkeley, University of California Press.

    View all 8 references

    Citations of this work BETA
    Similar books and articles

    Monthly downloads

    Added to index


    Total downloads

    14 ( #95,211 of 1,088,384 )

    Recent downloads (6 months)

    1 ( #69,601 of 1,088,384 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature

    Start a new thread
    There  are no threads in this forum
    Nothing in this forum yet.