Switch to: References

Citations of:

Thinking About Mathematics: The Philosophy of Mathematics

Oxford University Press (2000)

Add citations

You must login to add citations.
  1. Models and Representation.Roman Frigg & James Nguyen - 2017 - In Lorenzo Magnani & Tommaso Bertolotti (eds.), Springer Handbook of Model-Based Science. 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • What is the Benacerraf Problem?Justin Clarke-Doane - 2017 - In Fabrice Pataut (ed.), New Perspectives on the Philosophy of Paul Benacerraf: Truth, Objects, Infinity. Springer Verlag.
    In "Mathematical Truth", Paul Benacerraf articulated an epistemological problem for mathematical realism. His formulation of the problem relied on a causal theory of knowledge which is now widely rejected. But it is generally agreed that Benacerraf was onto a genuine problem for mathematical realism nevertheless. Hartry Field describes it as the problem of explaining the reliability of our mathematical beliefs, realistically construed. In this paper, I argue that the Benacerraf Problem cannot be made out. There simply is no intelligible problem (...)
    Download  
     
    Export citation  
     
    Bookmark   39 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Spacetime, Ontology, and Structural Realism.Edward Slowik - 2005 - International Studies in the Philosophy of Science 19 (2):147 – 166.
    This essay explores the possibility of constructing a structural realist interpretation of spacetime theories that can resolve the ontological debate between substantivalists and relationists. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of general relativity, our investigation will reveal that a structuralist approach can be beneficial to the spacetime theorist as a means of deflating some of the ontological disputes regarding similarly structured spacetimes.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • The ‘Space’ at the Intersection of Platonism and Nominalism.Edward Slowik - 2015 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 46 (2):393-408.
    This essay explores the use of platonist and nominalist concepts, derived from the philosophy of mathematics and metaphysics, as a means of elucidating the debate on spacetime ontology and the spatial structures endorsed by scientific realists. Although the disputes associated with platonism and nominalism often mirror the complexities involved with substantivalism and relationism, it will be argued that a more refined three-part distinction among platonist/nominalist categories can nonetheless provide unique insights into the core assumptions that underlie spatial ontologies, but it (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Philosophy of Mathematical Practice: A Primer for Mathematics Educators.Yacin Hamami & Rebecca Morris - forthcoming - ZDM Mathematics Education.
    In recent years, philosophical work directly concerned with the practice of mathematics has intensified, giving rise to a movement known as the philosophy of mathematical practice . In this paper we offer a survey of this movement aimed at mathematics educators. We first describe the core questions philosophers of mathematical practice investigate as well as the philosophical methods they use to tackle them. We then provide a selective overview of work in the philosophy of mathematical practice covering topics including the (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • What is Categorical Structuralism?Geoffrey Hellman - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 151--161.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Labyrinth of Continua†.Patrick Reeder - 2018 - Philosophia Mathematica 26 (1):1-39.
    This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   41 citations  
  • Nihilism Without Self-Contradiction.David Liggins - 2008 - Royal Institute of Philosophy Supplement 62:177-196.
    in Robin Le Poidevin (ed.) Being: Developments in Contemporary Metaphysics. Cambridge: Cambridge University Press. Peter van Inwagen claims that there are no tables or chairs. He also claims that sentences such as ‘There are chairs here’, which seem to imply their existence, are often true. This combination of views opens van Inwagen to a charge of self-contradiction. I explain the charge, and van Inwagen’s response to it, which involves the claim that sentences like ‘There are tables’ shift their truth-conditions between (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • Plato Was NOT A Mathematical Platonist.Elaine Landry - unknown
    Download  
     
    Export citation  
     
    Bookmark  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   34 citations  
  • 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 (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  • Indispensability, Causation and Explanation.Sorin Bangu - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):219-232.
    When considering mathematical realism, some scientific realists reject it, and express sympathy for the opposite view, mathematical nominalism; moreover, many justify this option by invoking the causal inertness of mathematical objects. The main aim of this note is to show that the scientific realists’ endorsement of this causal mathematical nominalism is in tension with another position some of them also accept, the doctrine of methodological naturalism. By highlighting this conflict, I intend to tip the balance in favor of a rival (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Dependencia e indeterminación en la lógica de segundo orden.Lucas Rosenblatt - 2011 - Cuadernos de Filosofía 57:31-50.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   37 citations  
  • A primazia das relações sobre as essências: as forças como entidades matemáticas nos Principia de Newton.Eduardo Salles de Oliveira Barra - 2010 - Scientiae Studia 8 (4):547-569.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   1 citation  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Explaining Simulated Phenomena. A Defense of the Epistemic Power of Computer Simulations.Juan M. Durán - 2013 - Dissertation, University of Stuttgart
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Mathematics and Statistics in the Social Sciences.Stephan Hartmann & Jan Sprenger - 2011 - In Ian C. Jarvie & Jesus Zamora-Bonilla (eds.), The SAGE Handbook of the Philosophy of Social Sciences. Sage Publications. pp. 594-612.
    Download  
     
    Export citation  
     
    Bookmark  
  • Carnap’s Early Semantics.Georg Schiemer - 2013 - Erkenntnis 78 (3):487-522.
    This paper concerns Carnap’s early contributions to formal semantics in his work on general axiomatics between 1928 and 1936. Its main focus is on whether he held a variable domain conception of models. I argue that interpreting Carnap’s account in terms of a fixed domain approach fails to describe his premodern understanding of formal models. By drawing attention to the second part of Carnap’s unpublished manuscript Untersuchungen zur allgemeinen Axiomatik, an alternative interpretation of the notions ‘model’, ‘model extension’ and ‘submodel’ (...)
    Download  
     
    Export citation  
     
    Bookmark   8 citations  
  • The Philosophy of Mathematics and the Independent 'Other'.Penelope Rush - unknown
    Download  
     
    Export citation  
     
    Bookmark  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   15 citations  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   22 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Structuralism and Meta-Mathematics.Simon Friederich - 2010 - Erkenntnis 73 (1):67 - 81.
    The debate on structuralism in the philosophy of mathematics has brought into focus a question about the status of meta-mathematics. It has been raised by Shapiro (2005), where he compares the ongoing discussion on structuralism in category theory to the Frege-Hilbert controversy on axiomatic systems. Shapiro outlines an answer according to which meta-mathematics is understood in structural terms and one according to which it is not. He finds both options viable and does not seem to prefer one over the other. (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • Varieties of Finitism.Manuel Bremer - 2007 - Metaphysica 8 (2):131-148.
    I consider here several versions of finitism or conceptions that try to work around postulating sets of infinite size. Restricting oneself to the so-called potential infinite seems to rest either on temporal readings of infinity (or infinite series) or on anti-realistic background assumptions. Both these motivations may be considered problematic. Quine’s virtual set theory points out where strong assumptions of infinity enter into number theory, but is implicitly committed to infinity anyway. The approaches centring on the indefinitely large and the (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Dowód matematyczny z punktu widzenia formalizmu matematycznego. Część II.Krzysztof Wójtowicz - 2007 - Roczniki Filozoficzne 55 (2):139-153.
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark  
  • 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.
    Download  
     
    Export citation  
     
    Bookmark   16 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   19 citations  
  • Information, Meaning, and Error in Biology.Lucy A. K. Kumar - 2014 - Biological Theory 9 (1):1-11.
    Whether “information” exists in biology, and in what sense, has been a topic of much recent discussion. I explore Shannon, Dretskean, and teleosemantic theories, and analyze whether or not they are able to give a successful naturalistic account of information—specifically accounts of meaning and error—in biological systems. I argue that the Shannon and Dretskean theories are unable to account for either, but that the teleosemantic theory is able to account for meaning. However, I argue that it is unable to account (...)
    Download  
     
    Export citation  
     
    Bookmark   2 citations  
  • 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 (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Indispensability and the Problem of Compatible Explanations: A Reply to ‘Should Scientific Realists Be Platonists?’.Josh Hunt - 2016 - Synthese 193 (2):451-467.
    Alan Baker’s enhanced indispensability argument supports mathematical platonism through the explanatory role of mathematics in science. Busch and Morrison defend nominalism by denying that scientific realists use inference to the best explanation to directly establish ontological claims. In response to Busch and Morrison, I argue that nominalists can rebut the EIA while still accepting Baker’s form of IBE. Nominalists can plausibly require that defenders of the EIA establish the indispensability of a particular mathematical entity. Next, I argue that IBE cannot (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Deferentialism.Chris Daly & David Liggins - 2011 - Philosophical Studies 156 (3):321-337.
    There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism , as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems (...)
    Download  
    Translate
     
     
    Export citation  
     
    Bookmark   13 citations  
  • How to Be a Minimalist About Sets.Luca Incurvati - 2012 - Philosophical Studies 159 (1):69-87.
    According to the iterative conception of set, sets can be arranged in a cumulative hierarchy divided into levels. But why should we think this to be the case? The standard answer in the philosophical literature is that sets are somehow constituted by their members. In the first part of the paper, I present a number of problems for this answer, paying special attention to the view that sets are metaphysically dependent upon their members. In the second part of the paper, (...)
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • Program Verification and Functioning of Operative Computing Revisited: How About Mathematics Engineering? [REVIEW]Uri Pincas - 2011 - Minds and Machines 21 (2):337-359.
    The issue of proper functioning of operative computing and the utility of program verification, both in general and of specific methods, has been discussed a lot. In many of those discussions, attempts have been made to take mathematics as a model of knowledge and certitude achieving, and accordingly infer about the suitable ways to handle computing. I shortly review three approaches to the subject, and then take a stance by considering social factors which affect the epistemic status of both mathematics (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Pluralism × 3: Truth, Logic, Metaphysics.Nikolaj Jang Lee Linding Pedersen - 2014 - Erkenntnis 79 (S2):259-277.
    This paper offers a discussion of metaphysical pluralism, alethic pluralism, and logical pluralism. According to the metaphysical pluralist, there are several ways of being. According to the alethic pluralist, there are several ways of being true, and according to the logical pluralist, there are several ways of being valid. Each of these three forms of pluralism will be considered on its own, but the ambition of the paper is to explore possible connections between them. My primary objective is to present (...)
    Download  
     
    Export citation  
     
    Bookmark   12 citations  
  • David Bostock: Philosophy of Mathematics: An Introduction: Wiley-Blackwell, Oxford, 2009, 332 Pp, BPD 55.00, ISBN: 978-1405189927 , BPD 20.99, ISBN: 978-1-4051-8991-0. [REVIEW]Holger A. Leuz - 2011 - Erkenntnis 74 (3):425-428.
    Download  
     
    Export citation  
     
    Bookmark  
  • Computing as a Science: A Survey of Competing Viewpoints. [REVIEW]Matti Tedre - 2011 - Minds and Machines 21 (3):361-387.
    Since the birth of computing as an academic discipline, the disciplinary identity of computing has been debated fiercely. The most heated question has concerned the scientific status of computing. Some consider computing to be a natural science and some consider it to be an experimental science. Others argue that computing is bad science, whereas some say that computing is not a science at all. This survey article presents viewpoints for and against computing as a science. Those viewpoints are analyzed against (...)
    Download  
     
    Export citation  
     
    Bookmark   13 citations  
  • Conjoining Mathematical Empiricism with Mathematical Realism: Maddy’s Account of Set Perception Revisited.Alex Levine - 2005 - Synthese 145 (3):425-448.
    Penelope Maddy's original solution to the dilemma posed by Benacerraf in his 'Mathematical Truth' was to reconcile mathematical empiricism with mathematical realism by arguing that we can perceive realistically construed sets. Though her hypothesis has attracted considerable critical attention, much of it, in my view, misses the point. In this paper I vigorously defend Maddy's account against published criticisms, not because I think it is true, but because these criticisms have functioned to obscure a more fundamental issue that is well (...)
    Download  
     
    Export citation  
     
    Bookmark