5 found
Order:
  1.  79
    Universism and Extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - forthcoming - Review of Symbolic Logic:1-50.
    A central area of current philosophical debate in the foundations of mathematics concerns whether or not there is a single, maximal, universe of set theory. Universists maintain that there is such a universe, while Multiversists argue that there are many universes, no one of which is ontologically privileged. Often model-theoretic constructions that add sets to models are cited as evidence in favour of the latter. This paper informs this debate by developing a way for a Universist to interpret talk that (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  2.  54
    Maximality and Ontology: How Axiom Content Varies Across Philosophical Frameworks.Sy-David Friedman & Neil Barton - 2017 - Synthese 197 (2):623-649.
    Discussion of new axioms for set theory has often focused on conceptions of maximality, and how these might relate to the iterative conception of set. This paper provides critical appraisal of how certain maximality axioms behave on different conceptions of ontology concerning the iterative conception. In particular, we argue that forms of multiversism and actualism face complementary problems. The latter view is unable to use maximality axioms that make use of extensions, where the former has to contend with the existence (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  3. The Search for New Axioms in the Hyperuniverse Programme.Claudio Ternullo & Sy-David Friedman - 2016 - In Andrea Sereni & Francesca Boccuni (eds.), Objectivity, Realism, and Proof. FilMat Studies in the Philosophy of Mathematics. Berlin: Springer. pp. 165-188.
    The Hyperuniverse Programme, introduced in Arrigoni and Friedman (2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the `maximal iterative concept', and the programme identi fies higher-order statements motivated by the maximal iterative concept. The satisfaction of these statements (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  41
    Introduction to Special Issue on the Foundations of Mathematics.Carolin Antos, Neil Barton, Sy-David Friedman, Claudio Ternullo & John Wigglesworth - 2020 - Synthese 197.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  5.  23
    Set Theory and Structures.Neil Barton & Sy-David Friedman - 2019 - In Deniz Sarikaya, Deborah Kant & Stefania Centrone (eds.), Reflections on the Foundations of Mathematics. Springer Verlag.
    Set-theoretic and category-theoretic foundations represent different perspectives on mathematical subject matter. In particular, category-theoretic language focusses on properties that can be determined up to isomorphism within a category, whereas set theory admits of properties determined by the internal structure of the membership relation. Various objections have been raised against this aspect of set theory in the category-theoretic literature. In this article, we advocate a methodological pluralism concerning the two foundational languages, and provide a theory that fruitfully interrelates a `structural' perspective (...)
    Download  
     
    Export citation  
     
    Bookmark