15 found
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  1. (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 (...)
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  2. (1 other version)Multiverse Conceptions in Set Theory.Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo - 2015 - Synthese 192 (8):2463-2488.
    We review different conceptions of the set-theoretic multiverse and evaluate their features and strengths. In Sect. 1, we set the stage by briefly discussing the opposition between the ‘universe view’ and the ‘multiverse view’. Furthermore, we propose to classify multiverse conceptions in terms of their adherence to some form of mathematical realism. In Sect. 2, we use this classification to review four major conceptions. Finally, in Sect. 3, we focus on the distinction between actualism and potentialism with regard to the (...)
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  3.  52
    Models as Fundamental Entities in Set Theory: A Naturalistic and Practice-based Approach.Carolin Antos - 2022 - Erkenntnis 89 (4):1683-1710.
    This article addresses the question of fundamental entities in set theory. It takes up J. Hamkins’ claim that models of set theory are such fundamental entities and investigates it using the methodology of P. Maddy’s naturalism, Second Philosophy. In accordance with this methodology, I investigate the historical case study of the use of models in the introduction of forcing, compare this case to contemporary practice and give a systematic account of how set-theoretic practice can be said to introduce models as (...)
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  4. Explanation in Descriptive Set Theory.Carolin Antos & Mark Colyvan - 2024 - In Katie Robertson & Alastair Wilson, Levels of Explanation. Oxford University Press.
  5.  32
    (1 other version)Hyperclass forcing in Morse-Kelley class theory.Carolin Antos & Sy-David Friedman - 2017 - Journal of Symbolic Logic 82 (2):549-575.
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  6. Defectiveness of formal concepts.Carolin Antos - manuscript
    It is often assumed that concepts from the formal sciences, such as mathematics and logic, have to be treated differently from concepts from non-formal sciences. This is especially relevant in cases of concept defectiveness, as in the empirical sciences defectiveness is an essential component of lager disruptive or transformative processes such as concept change or concept fragmentation. However, it is still unclear what role defectiveness plays for concepts in the formal sciences. On the one hand, a common view sees formal (...)
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  7.  16
    Class Forcing in Class Theory.Carolin Antos - 2018 - In Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo, The Hyperuniverse Project and Maximality. Basel, Switzerland: Birkhäuser. pp. 1-16.
    In this article we show that Morse-Kelley class theory provides us with an adequate framework for class forcing. We give a rigorous definition of class forcing in a model \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$$$ \end{document} of MK, the main result being that the Definability Lemma can be proven without restricting the notion of forcing. Furthermore we show under which conditions the axioms are preserved. We conclude by proving that Laver’s Theorem does not hold for (...)
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  8. Modern Class Forcing.Carolin Antos & Victoria Gitman - forthcoming - In D. Gabbay M. Fitting, Research Trends in Contemporary Logic. College Publications.
    We survey recent developments in the theory of class forcing for- malized in the second-order set-theoretic setting.
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  9.  35
    The Hyperuniverse Project and Maximality.Carolin Antos, Sy-David Friedman, Radek Honzik & Claudio Ternullo (eds.) - 2018 - Basel, Switzerland: Birkhäuser.
    This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John (...)
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  10. Expanding the notion of inconsistency in mathematics: the theoretical foundations of mutual inconsistency.Carolin Antos - forthcoming - From Contradiction to Defectiveness to Pluralism in Science: Philosophical and Formal Analyses.
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  11. A general framework for a Second Philosophy analysis of set-theoretic methodology.Carolin Antos & Deborah Kant - manuscript
    Penelope Maddy’s Second Philosophy is one of the most well-known ap- proaches in recent philosophy of mathematics. She applies her second-philosophical method to analyze mathematical methodology by reconstructing historical cases in a setting of means-ends relations. However, outside of Maddy’s own work, this kind of methodological analysis has not yet been extensively used and analyzed. In the present work, we will make a first step in this direction. We develop a general framework that allows us to clarify the procedure and (...)
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  12. (1 other version)Conceptions of infinity and set in Lorenzen’s operationist system.Carolin Antos - 2004 - In S. Rahman, Logic, Epistemology, and the Unity of Science. Dordrecht: Kluwer Academic Publishers.
    In the late 1940s and early 1950s Lorenzen developed his operative logic and mathematics, a form of constructive mathematics. Nowadays this is mostly seen as the precursor to the more well-known dialogical logic and one could assumed that the same philosophical motivations were present in both works. However we want to show that this is not always the case. In particular, we claim, that Lorenzen’s well-known rejection of the actual infinite as stated in Lorenzen (1957) was not a major motivation (...)
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  13. Introduction.Carolin Antos, Neil Barton, Sy-David Friedman, Claudio Ternullo & John Wigglesworth - 2020 - Synthese 197 (2):469-475.
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  14.  46
    Foundations of Higher-Order Forcing.Carolin Antos - 2018 - Bulletin of Symbolic Logic 24 (4):457-457.
  15.  20
    The Palgrave Companion to the Philosophy of Set Theory.Carolin Antos, Neil Barton & Giorgio Venturi (eds.) - 2025 - Palgrave.
    This volume showcases some of the up-and-coming voices of an emerging field - the philosophy of set theory - which in recent years has gained prominence in the philosophy of mathematics. The chapters in this volume both present new topics and propose solutions to old problems. It contains a broad picture of the philosophy of set theory, examining questions from epistemology and ontology, whilst touching on the use of formal theories in the study of mathematical infinity. Key features of this (...)
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