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Thinking about Mathematics

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Tijdschrift Voor Filosofie 63 (1):189-190 (2001)

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  1. Pluralism and the Absence of Truth.Jeremy Wyatt - 2014 - Dissertation, University of Connecticut
    In this dissertation, I argue that we should be pluralists about truth and in turn, eliminativists about the property Truth. Traditional deflationists were right to suspect that there is no such property as Truth. Yet there is a plurality of pluralities of properties which enjoy defining features that Truth would have, were it to exist. So although, in this sense, truth is plural, Truth is non-existent. The resulting account of truth is indebted to deflationism as the provenance of the suspicion (...)
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  • Frege’s Puzzle and Arithmetical Formalism. Putting Things in Context.Sorin Costreie - 2013 - History and Philosophy of Logic 34 (3):207-224.
    The paper discusses the emergence of Frege's puzzle and the introduction of the celebrated distinction between sense and reference in the context of Frege's logicist project. The main aim of the paper is to show that not logicism per se is mainly responsible for this introduction, but Frege's constant struggle against formalism. Thus, the paper enlarges the historical context, and provides a reconstruction of Frege's philosophical development from this broader perspective.
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  • Non-Ontological Structuralism†.Michael Resnik - 2019 - Philosophia Mathematica 27 (3):303-315.
    ABSTRACT Historical structuralist views have been ontological. They either deny that there are any mathematical objects or they maintain that mathematical objects are structures or positions in them. Non-ontological structuralism offers no account of the nature of mathematical objects. My own structuralism has evolved from an early sui generis version to a non-ontological version that embraces Quine’s doctrine of ontological relativity. In this paper I further develop and explain this view.
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  • Modal Structuralism and Theism.Silvia Jonas - forthcoming - In Fiona Ellis (ed.), New Models of Religious Understanding. Oxford: Oxford University Press.
    Drawing an analogy between modal structuralism about mathematics and theism, I o er a structuralist account that implicitly de nes theism in terms of three basic relations: logical and metaphysical priority, and epis- temic superiority. On this view, statements like `God is omniscient' have a hypothetical and a categorical component. The hypothetical component provides a translation pattern according to which statements in theistic language are converted into statements of second-order modal logic. The categorical component asserts the logical possibility of the (...)
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  • Sixteen Days.Barry Smith & Berit Brogaard - 2003 - Journal of Medicine and Philosophy 28 (1):45 – 78.
    When does a human being begin to exist? We argue that it is possible, through a combination of biological fact and philosophical analysis, to provide a definitive answer to this question. We lay down a set of conditions for being a human being, and we determine when, in the course of normal fetal development, these conditions are first satisfied. Issues dealt with along the way include: modes of substance-formation, twinning, the nature of the intra-uterine environment, and the nature of the (...)
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  • Independence of the Grossone-Based Infinity Methodology From Non-Standard Analysis and Comments Upon Logical Fallacies in Some Texts Asserting the Opposite.Yaroslav Sergeyev - 2019 - Foundations of Science 24 (1):153-170.
    This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...)
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  • Plato Was NOT A Mathematical Platonist.Elaine Landry - unknown
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  • Fiction and Scientific Representation.Roman Frigg - 2010 - In .
    Understanding scientific modelling can be divided into two sub-projects: analysing what model-systems are, and understanding how they are used to represent something beyond themselves. The first is a prerequisite for the second: we can only start analysing how representation works once we understand the intrinsic character of the vehicle that does the representing. Coming to terms with this issue is the project of the first half of this chapter. My central contention is that models are akin to places and characters (...)
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  • Ipotesi del Continuo.Claudio Ternullo - 2017 - Aphex 16.
    L’Ipotesi del Continuo, formulata da Cantor nel 1878, è una delle congetture più note della teoria degli insiemi. Il Problema del Continuo, che ad essa è collegato, fu collocato da Hilbert, nel 1900, fra i principali problemi insoluti della matematica. A seguito della dimostrazione di indipendenza dell’Ipotesi del Continuo dagli assiomi della teoria degli insiemi, lo status attuale del problema è controverso. In anni più recenti, la ricerca di una soluzione del Problema del Continuo è stata anche una delle ragioni (...)
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  • The Pursuit of Rigor: Hilbert's Axiomatic Method and the Objectivity of Mathematics.Yoshinori Ogawa - 2004 - Annals of the Japan Association for Philosophy of Science 12 (2):89-108.
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  • Dependencia e indeterminación en la lógica de segundo orden.Lucas Rosenblatt - 2011 - Cuadernos de Filosofía 57:31-50.
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  • The Epistemology of Geometry I: The Problem of Exactness.Anne Newstead & Franklin James - 2010 - Proceedings of the Australasian Society for Cognitive Science 2009.
    We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...)
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  • Everything You Always Wanted to Know About Structural Realism but Were Afraid to Ask.Roman Frigg & Ioannis Votsis - 2011 - European Journal for Philosophy of Science 1 (2):227-276.
    Everything you always wanted to know about structural realism but were afraid to ask Content Type Journal Article Pages 227-276 DOI 10.1007/s13194-011-0025-7 Authors Roman Frigg, Department of Philosophy, Logic and Scientific Method, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE UK Ioannis Votsis, Philosophisches Institut, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, Geb. 23.21/04.86, 40225 Düsseldorf, Germany Journal European Journal for Philosophy of Science Online ISSN 1879-4920 Print ISSN 1879-4912 Journal Volume Volume 1 Journal Issue Volume 1, Number 2.
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  • Indispensability and Explanation.Sorin Bangu - 2013 - British Journal for the Philosophy of Science 64 (2):255-277.
    The question as to whether there are mathematical explanations of physical phenomena has recently received a great deal of attention in the literature. The answer is potentially relevant for the ontology of mathematics; if affirmative, it would support a new version of the indispensability argument for mathematical realism. In this article, I first review critically a few examples of such explanations and advance a general analysis of the desiderata to be satisfied by them. Second, in an attempt to strengthen the (...)
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  • Explaining Simulated Phenomena. A Defense of the Epistemic Power of Computer Simulations.Juan M. Durán - 2013 - Dissertation, University of Stuttgart
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  • Mathematical Existence.Penelope Maddy - 2005 - Bulletin of Symbolic Logic 11 (3):351-376.
    Despite some discomfort with this grandly philosophical topic, I do in fact hope to address a venerable pair of philosophical chestnuts: mathematical truth and existence. My plan is to set out three possible stands on these issues, for an exercise in compare and contrast.' A word of warning, though, to philosophical purists (and perhaps of comfort to more mathematical readers): I will explore these philosophical positions with an eye to their interconnections with some concrete issues of set theoretic method.
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  • The Philosophy of Mathematics and the Independent 'Other'.Penelope Rush - unknown
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  • Disregarding the 'Hole Argument'.Bryan W. Roberts - unknown
    Jim Weatherall has suggested that Einstein's hole argument, as presented by Earman and Norton, is based on a misleading use of mathematics. I argue on the contrary that Weatherall demands an implausible restriction on how mathematics is used. The hole argument, on the other hand, is in no new danger at all.
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  • Is Structural Underdetermination Possible?Holger Lyre - 2011 - Synthese 180 (2):235 - 247.
    Structural realism is sometimes said to undermine the theory underdetermination (TUD) argument against realism, since, in usual TUD scenarios, the supposed underdetermination concerns the object-like theoretical content but not the structural content. The paper explores the possibility of structural TUD by considering some special cases from modern physics, but also questions the validity of the TUD argument itself. The upshot is that cases of structural TUD cannot be excluded, but that TUD is perhaps not such a terribly serious anti-realistic argument.
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  • The Fiction View of Models Reloaded.Roman Frigg & James Nguyen - 2016 - The Monist 99 (3):225-242.
    In this paper we explore the constraints that our preferred account of scientific representation places on the ontology of scientific models. Pace the Direct Representation view associated with Arnon Levy and Adam Toon we argue that scientific models should be thought of as imagined systems, and clarify the relationship between imagination and representation.
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  • How Models Represent.James Nguyen - 2016 - Dissertation,
    Scientific models are important, if not the sole, units of science. This thesis addresses the following question: in virtue of what do scientific models represent their target systems? In Part i I motivate the question, and lay out some important desiderata that any successful answer must meet. This provides a novel conceptual framework in which to think about the question of scientific representation. I then argue against Callender and Cohen’s attempt to diffuse the question. In Part ii I investigate the (...)
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  • Models and Representation.Roman Frigg & James Nguyen - 2017 - In Lorenzo Magnani & Tommaso Bertolotti (eds.). pp. 49-102.
    Scientific discourse is rife with passages that appear to be ordinary descriptions of systems of interest in a particular discipline. Equally, the pages of textbooks and journals are filled with discussions of the properties and the behavior of those systems. Students of mechanics investigate at length the dynamical properties of a system consisting of two or three spinning spheres with homogenous mass distributions gravitationally interacting only with each other. Population biologists study the evolution of one species procreating at a constant (...)
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  • Intuition Between the Analytic-Continental Divide: Hermann Weyl's Philosophy of the Continuum.Janet Folina - 2008 - Philosophia Mathematica 16 (1):25-55.
    Though logical positivism is part of Kant's complex legacy, positivists rejected both Kant's theory of intuition and his classification of mathematical knowledge as synthetic a priori. This paper considers some lingering defenses of intuition in mathematics during the early part of the twentieth century, as logical positivism was born. In particular, it focuses on the difficult and changing views of Hermann Weyl about the proper role of intuition in mathematics. I argue that it was not intuition in general, but his (...)
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  • On Naturalizing the Epistemology of Mathematics.Jeffrey W. Roland - 2009 - Pacific Philosophical Quarterly 90 (1):63-97.
    In this paper, I consider an argument for the claim that any satisfactory epistemology of mathematics will violate core tenets of naturalism, i.e. that mathematics cannot be naturalized. I find little reason for optimism that the argument can be effectively answered.
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  • Dowód matematyczny z punktu widzenia formalizmu matematycznego. Część II.Krzysztof Wójtowicz - 2007 - Roczniki Filozoficzne 55 (2):139-153.
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  • Humean Perspectives on Structural Realism.Holger Lyre - 2009 - In F. Stadler (ed.), The Present Situation in the Philosophy of Science. Springer. pp. 381--397.
    The paper is a kind of opinionated review paper on current issues in the debate about Structural Realism, roughly the view that we should be committed in the structural rather than object-like content of our best current scientific theories. The major thesis in the first part of the paper is that Structural Realism has to take structurally derived intrinsic properties into account, while in the second part key elements of aligning Structural Realism with a Humean framework are outlined.
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  • Philosophy of Mathematics.Jeremy Avigad - manuscript
    The philosophy of mathematics plays an important role in analytic philosophy, both as a subject of inquiry in its own right, and as an important landmark in the broader philosophical landscape. Mathematical knowledge has long been regarded as a paradigm of human knowledge with truths that are both necessary and certain, so giving an account of mathematical knowledge is an important part of epistemology. Mathematical objects like numbers and sets are archetypical examples of abstracta, since we treat such objects in (...)
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  • From Mirror to Mirage: The Idea of Logical Space in Kant, Wittgenstein, and van Fraassen.R. Lamoureux Lucien - unknown
    This dissertation investigates the origin, intellectual development and use of a semantic variant of the idea of logical space found implicitly in Kant and explicitly in early Wittgenstein and van Fraassen. It elucidates the idea of logical space as the idea of images or pictures representative of reality organized into a logico-mathematical structure circumscribing a form of all possible worlds. Its main claim is that application of these images or pictures to reality is through a certain conception of self. The (...)
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  • What Structures Could Not Be.Jacob Busch - 2003 - International Studies in the Philosophy of Science 17 (3):211 – 225.
    James Ladyman has recently proposed a view according to which all that exists on the level of microphysics are structures "all the way down". By means of a comparative reading of structuralism in philosophy of mathematics as proposed by Stewart Shapiro, I shall present what I believe structures could not be. I shall argue that, if Ladyman is indeed proposing something as strong as suggested here, then he is committed to solving problems that proponents of structuralism in philosophy of mathematics (...)
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  • Louis Joly as a Platonist Painter?Roger Pouivet - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 337--341.
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  • ‘Whys’ and ‘Hows’ of Using Philosophy in Mathematics Education.Uffe Thomas Jankvist & Steffen Møllegaard Iversen - 2014 - Science & Education 23 (1):205-222.
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