Switch to: References

Add citations

You must login to add citations.
  1. (1 other version)28 Reflection in Apophatic Mathematics and Theology.Neil Barton - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. Boston: De Gruyter. pp. 583-612.
    Download  
     
    Export citation  
     
    Bookmark  
  • The negative theology of absolute infinity: Cantor, mathematics, and humility.Rico Gutschmidt & Merlin Carl - 2024 - International Journal for Philosophy of Religion 95 (3):233-256.
    Cantor argued that absolute infinity is beyond mathematical comprehension. His arguments imply that the domain of mathematics cannot be grasped by mathematical means. We argue that this inability constitutes a foundational problem. For Cantor, however, the domain of mathematics does not belong to mathematics, but to theology. We thus discuss the theological significance of Cantor’s treatment of absolute infinity and show that it can be interpreted in terms of negative theology. Proceeding from this interpretation, we refer to the recent debate (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Ontology of Divinity.Mirosław Szatkowski (ed.) - 2024 - Boston: De Gruyter.
    This volume announces a new era in the philosophy of God. Many of its contributions work to create stronger links between the philosophy of God, on the one hand, and mathematics or metamathematics, on the other hand. It is about not only the possibilities of applying mathematics or metamathematics to questions about God, but also the reverse question: Does the philosophy of God have anything to offer mathematics or metamathematics? The remaining contributions tackle stereotypes in the philosophy of religion. The (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)Universism and extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - 2021 - Review of Symbolic Logic 14 (1):112-154.
    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   5 citations  
  • Maddy On The Multiverse.Claudio Ternullo - 2019 - In Stefania Centrone, Deborah Kant & Deniz Sarikaya (eds.), Reflections on the Foundations of Mathematics: Univalent Foundations, Set Theory and General Thoughts. Springer Verlag. pp. 43-78.
    Penelope Maddy has recently addressed the set-theoretic multiverse, and expressed reservations on its status and merits ([Maddy, 2017]). The purpose of the paper is to examine her concerns, by using the interpretative framework of set-theoretic naturalism. I first distinguish three main forms of 'multiversism', and then I proceed to analyse Maddy's concerns. Among other things, I take into account salient aspects of multiverse-related mathematics , in particular, research programmes in set theory for which the use of the multiverse seems to (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Quantification and Paradox.Edward Ferrier - 2018 - Dissertation, University of Massachusetts Amherst
    I argue that absolutism, the view that absolutely unrestricted quantification is possible, is to blame for both the paradoxes that arise in naive set theory and variants of these paradoxes that arise in plural logic and in semantics. The solution is restrictivism, the view that absolutely unrestricted quantification is not possible. -/- It is generally thought that absolutism is true and that restrictivism is not only false, but inexpressible. As a result, the paradoxes are blamed, not on illicit quantification, but (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Maximality Principles in Set Theory.Luca Incurvati - 2017 - Philosophia Mathematica 25 (2):159-193.
    In set theory, a maximality principle is a principle that asserts some maximality property of the universe of sets or some part thereof. Set theorists have formulated a variety of maximality principles in order to settle statements left undecided by current standard set theory. In addition, philosophers of mathematics have explored maximality principles whilst attempting to prove categoricity theorems for set theory or providing criteria for selecting foundational theories. This article reviews recent work concerned with the formulation, investigation and justification (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • Global Reflection Principles.P. D. Welch - 2017 - In I. Niiniluoto, H. Leitgeb, P. Seppälä & E. Sober (eds.), Logic, Methodology and Philosophy of Science - Proceedings of the 15th International Congress, 2015. College Publications.
    Reflection Principles are commonly thought to produce only strong axioms of infinity consistent with V = L. It would be desirable to have some notion of strong reflection to remedy this, and we have proposed Global Reflection Principles based on a somewhat Cantorian view of the universe. Such principles justify the kind of cardinals needed for, inter alia , Woodin’s Ω-Logic.
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • Philosophy of mathematics.Leon Horsten - 2008 - Stanford Encyclopedia of Philosophy.
    If mathematics is regarded as a science, then the philosophy of mathematics can be regarded as a branch of the philosophy of science, next to disciplines such as the philosophy of physics and the philosophy of biology. However, because of its subject matter, the philosophy of mathematics occupies a special place in the philosophy of science. Whereas the natural sciences investigate entities that are located in space and time, it is not at all obvious that this is also the case (...)
    Download  
     
    Export citation  
     
    Bookmark   25 citations  
  • 32 Naming God’s Essence: Ineffability, Analogy and Set Theory.Claudio Ternullo - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. Boston: De Gruyter. pp. 697-718.
    Download  
     
    Export citation  
     
    Bookmark  
  • (1 other version)Universism and Extensions of V.Carolin Antos, Neil Barton & Sy-David Friedman - 2021 - Review of Symbolic Logic 14 (1):112-154.
    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 favor 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  
  • A Theory of Particular Sets.Paul Blain Levy - manuscript
    ZFC has sentences that quantify over all sets or all ordinals, without restriction. Some have argued that sentences of this kind lack a determinate meaning. We propose a set theory called TOPS, using Natural Deduction, that avoids this problem by speaking only about particular sets.
    Download  
     
    Export citation  
     
    Bookmark  
  • Introduction: An Incomplete Guide to Ontology of Divinity.Mirosław Szatkowski - 2024 - In Ontology of Divinity. Boston: De Gruyter. pp. 1-36.
    Download  
     
    Export citation  
     
    Bookmark  
  • The Limits of Computation.Andrew Powell - 2022 - Axiomathes 32 (6):991-1011.
    This article provides a survey of key papers that characterise computable functions, but also provides some novel insights as follows. It is argued that the power of algorithms is at least as strong as functions that can be proved to be totally computable in type-theoretic translations of subsystems of second-order Zermelo Fraenkel set theory. Moreover, it is claimed that typed systems of the lambda calculus give rise naturally to a functional interpretation of rich systems of types and to a hierarchy (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • 25 Quantity Has a Quality All Its Own.Leon Horsten - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. Boston: De Gruyter. pp. 511-530.
    Download  
     
    Export citation  
     
    Bookmark