The classical continuum without points

Review of Symbolic Logic 6 (3):488-512 (2013)
Abstract
We develop a point-free construction of the classical one-dimensional continuum, with an interval structure based on mereology and either a weak set theory or a logic of plural quantification. In some respects, this realizes ideas going back to Aristotle, although, unlike Aristotle, we make free use of contemporary . Also, in contrast to intuitionistic analysis, smooth infinitesimal analysis, and Eret Bishopgunky lineindecomposabilityCantor structure of ℝ as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own
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: 9,357
External links
  •   Try with proxy.
  •   Try with proxy.
  •   Try with proxy.
  • Through your library Configure
    References found in this work BETA
    Hellman Geoffrey (1996). Structuralism Without Structures. Philosophia Mathematica 4 (2):100-123.
    Peter Roeper (2006). The Aristotelian Continuum. A Formal Characterization. Notre Dame Journal of Formal Logic 47 (2):211-232.
    Peter Roeper (1997). Region-Based Topology. Journal of Philosophical Logic 26 (3):251-309.
    Citations of this work BETA

    No citations found.

    Similar books and articles
    Michael J. White (1988). On Continuity: Aristotle Versus Topology? History and Philosophy of Logic 9 (1):1-12.
    Geoffrey Hellman (1994). Real Analysis Without Classes. Philosophia Mathematica 2 (3):228-250.
    Richard Jozsa (1986). An Approach to the Modelling of the Physical Continuum. British Journal for the Philosophy of Science 37 (4):395-404.
    Daniel Dzierzgowski (1995). Models of Intuitionistic TT and N. Journal of Symbolic Logic 60 (2):640-653.
    Analytics

    Monthly downloads

    Added to index

    2012-11-07

    Total downloads

    30 ( #49,032 of 1,088,601 )

    Recent downloads (6 months)

    6 ( #17,280 of 1,088,601 )

    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.