Results for 'Jenifer Barton'

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  1. Is (un)countabilism restrictive?Neil Barton - manuscript
    Let's suppose you think that there are no uncountable sets. Have you adopted a restrictive position? It is certainly tempting to say yes---you've prohibited the existence of certain kinds of large set. This paper argues that this intuition can be challenged. Instead, I argue that there are some considerations based on a formal notion of restrictiveness which suggest that it is restrictive to hold that there are uncountable sets.
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  2. On Representations of Intended Structures in Foundational Theories.Neil Barton, Moritz Müller & Mihai Prunescu - 2022 - Journal of Philosophical Logic 51 (2):283-296.
    Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power (...)
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  3. Forcing and the Universe of Sets: Must We Lose Insight?Neil Barton - 2020 - Journal of Philosophical Logic 49 (4):575-612.
    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 forcing constructions that add subsets to models are cited as evidence in favour of the latter. This paper informs this debate by analysing ways the Universist might interpret this discourse that seems (...)
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  4. Varieties of Class-Theoretic Potentialism.Neil Barton & Kameryn J. Williams - 2024 - Review of Symbolic Logic 17 (1):272-304.
    We explain and explore class-theoretic potentialism—the view that one can always individuate more classes over a set-theoretic universe. We examine some motivations for class-theoretic potentialism, before proving some results concerning the relevant potentialist systems (in particular exhibiting failures of the $\mathsf {.2}$ and $\mathsf {.3}$ axioms). We then discuss the significance of these results for the different kinds of class-theoretic potentialists.
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  5. On Forms of Justification in Set Theory.Neil Barton, Claudio Ternullo & Giorgio Venturi - 2020 - Australasian Journal of Logic 17 (4):158-200.
    In the contemporary philosophy of set theory, discussion of new axioms that purport to resolve independence necessitates an explanation of how they come to be justified. Ordinarily, justification is divided into two broad kinds: intrinsic justification relates to how `intuitively plausible' an axiom is, whereas extrinsic justification supports an axiom by identifying certain `desirable' consequences. This paper puts pressure on how this distinction is formulated and construed. In particular, we argue that the distinction as often presented is neither well-demarcated nor (...)
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  6. Absence perception and the philosophy of zero.Neil Barton - 2020 - Synthese 197 (9):3823-3850.
    Zero provides a challenge for philosophers of mathematics with realist inclinations. On the one hand it is a bona fide cardinal number, yet on the other it is linked to ideas of nothingness and non-being. This paper provides an analysis of the epistemology and metaphysics of zero. We develop several constraints and then argue that a satisfactory account of zero can be obtained by integrating an account of numbers as properties of collections, work on the philosophy of absences, and recent (...)
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  7. Inner-Model Reflection Principles.Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, Joel David Hamkins, Jonas Reitz & Ralf Schindler - 2020 - Studia Logica 108 (3):573-595.
    We introduce and consider the inner-model reflection principle, which asserts that whenever a statement \varphi(a) in the first-order language of set theory is true in the set-theoretic universe V, then it is also true in a proper inner model W \subset A. A stronger principle, the ground-model reflection principle, asserts that any such \varphi(a) true in V is also true in some non-trivial ground model of the universe with respect to set forcing. These principles each express a form of width (...)
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  8. Make It So: Imperatival Foundations for Mathematics.Neil Barton, Ethan Russo & Chris Scambler - manuscript
    This article articulates and assesses an imperatival approach to the foundations of mathematics. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. We apply this idea to provide a novel formalisation of arithmetic and set theory in terms of such procedures, and discuss the significance of this perspective for the philosophy of mathematics.
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  9. Countabilism and Maximality Principles.Neil Barton & Sy-David Friedman - manuscript
    It is standard in set theory to assume that Cantor's Theorem establishes that the continuum is an uncountable set. A challenge for this position comes from the observation that through forcing one can collapse any cardinal to the countable and that the continuum can be made arbitrarily large. In this paper, we present a different take on the relationship between Cantor's Theorem and extensions of universes, arguing that they can be seen as showing that every set is countable and that (...)
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  10. Indeterminateness and `The' Universe of Sets: Multiversism, Potentialism, and Pluralism.Neil Barton - 2021 - In Melvin Fitting (ed.), Research Trends in Contemporary Logic (Series: Landscapes in Logic). College Publications. pp. 105-182.
    In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.
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  11. What makes a `good' modal theory of sets?Neil Barton - manuscript
    I provide an examination and comparison of modal theories for underwriting different non-modal theories of sets. I argue that there is a respect in which the `standard' modal theory for set construction---on which sets are formed via the successive individuation of powersets---raises a significant challenge for some recently proposed `countabilist' modal theories (i.e. ones that imply that every set is countable). I examine how the countabilist can respond to this issue via the use of regularity axioms and raise some questions (...)
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  12. Language, Models, and Reality: Weak existence and a threefold correspondence.Neil Barton & Giorgio Venturi - manuscript
    How does our language relate to reality? This is a question that is especially pertinent in set theory, where we seem to talk of large infinite entities. Based on an analogy with the use of models in the natural sciences, we argue for a threefold correspondence between our language, models, and reality. We argue that so conceived, the existence of models can be underwritten by a weak notion of existence, where weak existence is to be understood as existing in virtue (...)
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  13. Independence and Ignorance: How agnotology informs set-theoretic pluralism.Neil Barton - 2017 - Journal of the Indian Council of Philosophical Research 34 (2):399-413.
    Much of the discussion of set-theoretic independence, and whether or not we could legitimately expand our foundational theory, concerns how we could possibly come to know the truth value of independent sentences. This paper pursues a slightly different tack, examining how we are ignorant of issues surrounding their truth. We argue that a study of how we are ignorant reveals a need for an understanding of set-theoretic explanation and motivates a pluralism concerning the adoption of foundational theory.
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  14. Mathematical Gettier Cases and Their Implications.Neil Barton - manuscript
    Let mathematical justification be the kind of justification obtained when a mathematician provides a proof of a theorem. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I argue that Gettier cases are possible (and indeed actual) in mathematical (...)
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  15. Structural Relativity and Informal Rigour.Neil Barton - 2022 - In Gianluigi Oliveri, Claudio Ternullo & Stefano Boscolo (eds.), Objects, Structures, and Logics, FilMat Studies in the Philosophy of Mathematics. Springer. pp. 133-174.
    Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing considerations of (...)
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  16. Analytic Metaphysics versus Naturalized Metaphysics: The Relevance of Applied Ontology.Baptiste Le Bihan & Adrien Barton - 2021 - Erkenntnis 86 (1):21-37.
    The relevance of analytic metaphysics has come under criticism: Ladyman & Ross, for instance, have suggested do discontinue the field. French & McKenzie have argued in defense of analytic metaphysics that it develops tools that could turn out to be useful for philosophy of physics. In this article, we show first that this heuristic defense of metaphysics can be extended to the scientific field of applied ontology, which uses constructs from analytic metaphysics. Second, we elaborate on a parallel by French (...)
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  17. Richness and Reflection.Neil Barton - 2016 - Philosophia Mathematica 24 (3):330-359.
    A pervasive thought in contemporary philosophy of mathematics is that in order to justify reflection principles, one must hold universism: the view that there is a single universe of pure sets. I challenge this kind of reasoning by contrasting universism with a Zermelian form of multiversism. I argue that if extant justifications of reflection principles using notions of richness are acceptable for the universist, then the Zermelian can use similar justifications. However, I note that for some forms of richness argument, (...)
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  18. (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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  19. Executing Gödel's Programme in Set Theory.Neil Barton - 2017 - Dissertation, Birkbeck, University of London
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  20.  67
    Review of Tim Button's Level Theory Parts 1-3. [REVIEW]Neil Barton - forthcoming - Bulletin of Symbolic Logic.
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  21. Warrant and Objectivity.Jon Barton - 2008 - Dissertation, Kings College London
    Wright's _Truth and Objectivity_ seeks to systematise a variety of anti-realist positions. I argue that many objections to the system are avoided by transposing its talk of truth into talk of warrant. However, a problem remains about debates involving 'direction-of-fit'. -/- Dummett introduced 'anti-realism' as a philosophical view informed by mathematical intuitionism. Subsequently, the term has been associated with many debates, ancient and modern. _Truth and Objectivity_ proposes that truth admits of different characteristics; these various debates then concern which characteristics (...)
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  22. (1 other version)Set Theory and Structures.Neil Barton & Sy-David Friedman - 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. 223-253.
    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 (...)
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  23. Métaphysique analytique, métaphysique naturalisée et ontologie appliquée.Baptiste Le Bihan & Adrien Barton - 2022 - In Raphaël Künstler & Claudine Tiercelin (eds.), Métaphysique et sciences: nouveaux problèmes. Paris: Hermann.
    La pertinence de la métaphysique analytique a fait l'objet de critiques : Ladyman et Ross, par exemple, ont suggéré d'abandonner ce domaine. French et McKenzie ont défendu la métaphysique analytique en affirmant qu'elle développe des outils qui pourraient s'avérer utiles pour la philosophie de la physique. Dans cet article, nous montrons dans un premier temps que cette défense heuristique de la métaphysique peut être étendue au domaine scientifique de l'ontologie appliquée, qui utilise des théories et outils issus de la métaphysique (...)
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  24. 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 (the view that any universe of a certain kind can be extended) and actualism (the view that there are universes that cannot be extended in particular ways) face (...)
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  25. (1 other version)Peacocke’s Epiphany: A Possible Problem for Semantic Approaches to Metaphysical Necessity.Jon Barton - 2012 - Philosophia Scientiae 16 (2):99-116.
    In his _Being Known_ Peacocke sets himself the task of answering how we come to know about metaphysical necessities. He proposes a semantic principle-based conception consisting of, first, his Principles of Possibility which pro­vide necessary and sufficient conditions for a new concept 'admissibility', and second, characterizations of possibility and of necessity in terms of that new con­cept. I focus on one structural feature; viz. the recursive application involved in the specification of 'admissibility'. After sketching Peacocke’s proposal, I intro­duce a fictional (...)
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  26. Introduction.Carolin Antos, Neil Barton, Sy-David Friedman, Claudio Ternullo & John Wigglesworth - 2020 - Synthese 197 (2):469-475.
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  27. Elaine Landry,* ed. Categories for the Working Philosopher. [REVIEW]Neil Barton - 2020 - Philosophia Mathematica 28 (1):95-108.
    LandryElaine, * ed. Categories for the Working Philosopher. Oxford University Press, 2017. ISBN 978-0-19-874899-1 ; 978-0-19-106582-8. Pp. xiv + 471.
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  28. Advances in Black Holes Research.Abraham Barton (ed.) - 2014 - New York: Nova Science Publishers.
    Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermodynamics and (...)
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  29. Hotels on the Border: Cinematic Situations of Transgression and Transcendence.Melinda Campbell - 2011 - In Hyperborean Wind: Reflections on Design and the City.
    Three important 20th-century American films prominently feature a hotel as the site for morally ambiguous and sexually charged events depicted in the plot: Orson Welles's Touch of Evil (1958), Alfred Hitchcock's Psycho (1960), and Joel and Ethan Coen's Barton Fink (1991). While all three films have a multiplicity of elements that present how hotel spaces open horizons displaying human behaviors both normal and abnormal, moral and immoral, secret and public, sane and insane, the paper presents an extended argument for (...)
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  30. The Priority of Intentional Action: From Developmental to Conceptual Priority.Yair Levy - forthcoming - The Philosophical Quarterly.
    Philosophical orthodoxy has it that intentional action consists in one’s intention appropriately causing a motion of one’s body, placing the latter as (conceptually and/or metaphysically) prior to the former. Here I argue that this standard schema should be reversed: acting intentionally is at least conceptually prior to intending. The argument is modelled on a Williamsonian argument for the priority of knowledge developed by Jenifer Nagel. She argues that children acquire the concept KNOWS before they acquire BELIEVES, building on this (...)
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  31. Gametogênese Animal: Espermatogênese e Ovogênese.Emanuel Isaque Cordeiro da Silva - manuscript
    GAMETOGÊNESE -/- Emanuel Isaque Cordeiro da Silva Instituto Agronômico de Pernambuco Departamento de Zootecnia – UFRPE Embrapa Semiárido -/- • _____OBJETIVO -/- Os estudantes bem informados, estão a buscando conhecimento a todo momento. O estudante de Veterinária e Zootecnia, sabe que a Reprodução é uma área de primordial importância para sua carreira. Logo, o conhecimento da mesma torna-se indispensável. No primeiro trabalho da série fisiologia reprodutiva dos animais domésticos, foi abordado de forma clara, didática e objetiva os mecanismos de diferenciação (...)
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  32. The Adversary System: Who Needs It?Edmund Byrne - 1986 - In Elliston M. Davis and F. A. (ed.), Ethics and the Legal Profession. Prometheus. pp. 204-215.
    -/- [Posted here is article as originally published (same title) in ALSA Forum VI (1982) pp. 1-17 plus rebuttal by Thomas D. Barton, pp. 18-22].
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  33. Behaviourism and Psychology.Gary Hatfield - 2003 - In Thomas Baldwin (ed.), The Cambridge history of philosophy, 1870-1945. New York: Cambridge University Press. pp. 640-48.
    Behaviorism was a peculiarly American phenomenon. As a school of psychology it was founded by John B. Watson (1878-1958) and grew into the neobehaviorisms of the 1920s, 30s and 40s. Philosophers were involved from the start, prefiguring the movement and endeavoring to define or redefine its tenets. Behaviorism expressed the naturalistic bent in American thought, which came in response to the prevailing philosophical idealism and was inspired by developments in natural science itself. There were several versions of naturalism in American (...)
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  34.  34
    Uma incursão sobre a obra de arte, a tecnologia e a pornografia.Marcos A. Ferreira - 2024 - Itaca 42:59-73.
    The aim of this article is to try to understand the role of pornography through a number of different channels, namely: the work of art and technology. To understand how the work of art passed from an erotic position to a pornographic one, with explicitly political motivations. To this end, our main references are Walter Benjamin’s work The Work of Art in the Age of Its Technical Reproducibility (1936) and Polly Barton’s Porn: An Oral History (2023). -/- O presente (...)
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  35. Un braconnage impossible : le courant de conscience de William James et la durée réelle de Bergson.Mathias Girel - 2011 - In Stéphane Madelrieux (ed.), Bergson et James, cent ans après. Paris: Puf. pp. 27-56.
    James a maintes fois célébré les rencontres philosophiques et l’on sait les efforts de James et de Bergson pour se voir, lors des passages de James en Europe. Proximité physique ne signifie évidemment pas convergence ni capillarité philosophiques, comme l’apprend à ses dépens Agathon dans le Banquet de Platon. Or, le rapprochement, mais aussi les confusions, entre la philosophie de Bergson et celle de James, voire entre « bergsonisme » et « pragmatisme », restent un passage obligé de l’étude des (...)
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