Categories for the working mathematician: Making the impossible possible

Synthese 162 (1):1 - 13 (2008)
Abstract
This paper discusses the notion of necessity in the light of results from contemporary mathematical practice. Two descriptions of necessity are considered. According to the first, necessarily true statements are true because they describe ‘unchangeable properties of unchangeable objects’. The result that I present is argued to provide a counterexample to this description, as it concerns a case where objects are moved from one category to another in order to change the properties of these objects. The second description concerns necessary ‘structural properties’. Although I grant that mathematical statements could be considered as necessarily true in this sense, I question whether this justifies the claim that mathematics as a whole is necessary.
Keywords Philosophy of mathematical practice  Necessity
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
  • Through your library Configure
    References found in this work BETA

    View all 13 references

    Citations of this work BETA

    No citations found.

    Similar books and articles
    Analytics

    Monthly downloads

    Added to index

    2009-01-28

    Total downloads

    22 ( #65,967 of 1,088,905 )

    Recent downloads (6 months)

    1 ( #69,735 of 1,088,905 )

    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.