On categorical theory-building: Beyond the formal

Abstract
Formal Axiomatic method as exemplified in Hilbert’s Grundlagen der Geometrie is based on a structuralist vision of mathematics and science according to which theories and objects of these theories are to be construed “up to isomorphism”. This structuralist approach is tightly linked with the idea of making Set theory into foundations of mathematics. Category theory suggests a generalisation of Formal Axiomatic method, which amounts to construing objects and theories “up to general morphism” rather than up to isomorphism. It is shown that this category-theoretic method of theorybuilding better fits mathematical and scientific practice. Moreover so since the requirement of being determined up to isomorphism (i.e. categoricity in the usual model-theoretic sense) turns to be unrealistic in many important cases. The category-theoretic approach advocated in this paper suggests an essential revision of the structuralist philosophy of mathematics and science. It is argued that a category should be viewed as a far-reaching generalisation of the notion of structure rather than a particular kind of structure. Finally, I compare formalisation and categorification as two alternative epistemic strategies.
Keywords No keywords specified (fix it)
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 Only published papers are available at libraries
    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

    27 ( #54,509 of 1,088,854 )

    Recent downloads (6 months)

    1 ( #69,666 of 1,088,854 )

    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.