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Isolation and Non-Arbitrary Division: Frege’s Two Criteria for Counting

  • Author(s) / Creator(s)
  • In §54 of the Grundlagen, Frege advances an interesting proposal on how to distinguish among different sorts of concepts, only some of which he thinks can be associated with number. This paper is devoted to an analysis of the two criteria he offers, isolation and non-arbitrary division. Both criteria say something about the way in which a concept divides its extension; but they emphasize different aspects. Isolation ensures that a concept divides its extension into discrete units. I offer two construals of this: isolation as discreteness, i.e. absence of overlap, between the objects to be counted; and isolation as the drawing of conceptual boundaries. Non-arbitrary division concerns the internal structure of the units we count: it makes sure that we cannot go on dividing them arbitrarily and still find more units of the kind. Non-arbitrary division focuses not only on how long something can be divided into parts of the same kind; it also speaks to the way in which these divisions are made, arbitrarily or non-arbitrarily, as well as to the compositional structure of the objects divided.

  • Date created
    1997
  • Subjects / Keywords
  • Type of Item
    Article (Published)
  • DOI
    https://doi.org/10.7939/R3WM1479N
  • License
    © 1997 K. Koslicki et al. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.
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  • Citation for previous publication
    • Koslicki, K. (1997). Isolation and Non-Arbitrary Division: Frege’s Two Criteria for Counting. Synthese, 112(3), 403-430. http://doi.org/10.1023/A:1004903625876
  • Link to related item
    http://doi.org/10.1023/A:1004903625876