Cardinality and identity

Journal of Philosophical Logic 36 (5):539 - 556 (2007)
Abstract
P.T. Geach has maintained (see, e.g., Geach (1967/1968)) that identity (as well as dissimilarity) is always relative to a general term. According to him, the notion of absolute identity has to be abandoned and replaced by a multiplicity of relative identity relations for which Leibniz's Law - which says that if two objects are identical they have the same properties - does not hold. For Geach relative identity is at least as good as Frege's cardinality thesis which he takes to be strictly connected with relative identity - according to which an ascription of cardinality is always relative to a concept which specifies what, in any particular case, counts as a unit. The idea that there is a close connection between relative identity and Frege's cardinality thesis has been issued again quite recently by Alston and Bennett in (1984). In their opinion, Frege's cardinality thesis is not only similar to relative identity - as Geach maintains - but it implies it. Moreover, they agree with Geach in claiming that a commitment to Frege's cardinality thesis forces a parallel commitment to relative identity. Against Geach, Alston and Bennett we will claim that (Tl): "Frege's cardinality thesis is similar to relative identity" is false and that therefore (T2) "Frege's cardinality thesis implies relative identity" is false as well
Keywords ascription of cardinality  Frege’s cardinality thesis  Leibniz’s law  identity
Categories (categorize this paper)
Options
 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: 9,360
External links
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA

    No citations found.

    Similar books and articles
    Analytics

    Monthly downloads

    Added to index

    2009-01-28

    Total downloads

    31 ( #47,432 of 1,089,047 )

    Recent downloads (6 months)

    1 ( #69,722 of 1,089,047 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


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