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David Corfield [28]David Neil Corfield [5]
  1.  65
    Towards a Philosophy of Real Mathematics.David Corfield - 2003 - Cambridge University Press.
    In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of approaches to new thinking about the philosophy of mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing (...)
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  2.  6
    Towards a Philosophy of Real Mathematics.David Corfield - 2003 - Studia Logica 81 (2):285-289.
    In this ambitious study, David Corfield attacks the widely held view that it is the nature of mathematical knowledge which has shaped the way in which mathematics is treated philosophically, and claims that contingent factors have brought us to the present thematically limited discipline. Illustrating his discussion with a wealth of examples, he sets out a variety of new ways to think philosophically about mathematics, ranging from an exploration of whether computers producing mathematical proofs or conjectures are doing real mathematics, (...)
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  3.  49
    Duality as a Category-Theoretic Concept.David Corfield - 2017 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 59:55-61.
    In a paper published in 1939, Ernest Nagel described the role that projective duality had played in the reformulation of mathematical understanding through the turn of the nineteenth century, claiming that the discovery of the principle of duality had freed mathematicians from the belief that their task was to describe intuitive elements. While instances of duality in mathematics have increased enormously through the twentieth century, philosophers since Nagel have paid little attention to the phenomenon. In this paper I will argue (...)
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  4.  24
    Expressing ‘the Structure of’ in Homotopy Type Theory.David Corfield - 2020 - Synthese 197 (2):681-700.
    As a new foundational language for mathematics with its very different idea as to the status of logic, we should expect homotopy type theory to shed new light on some of the problems of philosophy which have been treated by logic. In this article, definite description, and in particular its employment within mathematics, is formulated within the type theory. Homotopy type theory has been proposed as an inherently structuralist foundational language for mathematics. Using the new formulation of definite descriptions, opportunities (...)
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  5.  66
    Assaying Lakatos's Philosophy of Mathematics.David Corfield - 1997 - Studies in History and Philosophy of Science Part A 28 (1):99-121.
  6. Understanding the Infinite I: Niceness, Robustness, and Realism†: Articles.David Corfield - 2010 - Philosophia Mathematica 18 (3):253-275.
    This paper treats the situation where a single mathematical construction satisfies a multitude of interesting mathematical properties. The examples treated are all infinitely large entities. The clustering of properties is termed ‘niceness’ by the mathematician Michiel Hazewinkel, a concept we compare to the ‘robustness’ described by the philosopher of science William Wimsatt. In the final part of the paper, we bring our findings to bear on the question of realism which concerns not whether mathematical entities exist as abstract objects, but (...)
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  7.  91
    Understanding the Infinite II: Coalgebra.David Corfield - 2011 - Studies in History and Philosophy of Science Part A 42 (4):571-579.
    In this paper we give an account of the rise and development of coalgebraic thinking in mathematics and computer science as an illustration of the way mathematical frameworks may be transformed. Originating in a foundational dispute as to the correct way to characterise sets, logicians and computer scientists came to see maximizing and minimizing extremal axiomatisations as a dual pair, each necessary to represent entities of interest. In particular, many important infinitely large entities can be characterised in terms of such (...)
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  8.  8
    Correction To: Expressing ‘the Structure of’ in Homotopy Type Theory.David Corfield - 2020 - Synthese 197 (2):701-701.
    The original article has been corrected. The article is published with Open Access but was missing Open Access information. This has been added.
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  9.  10
    Lautman et la réalité des mathématiques.David Corfield - 2010 - Philosophiques 37 (1):95-109.
    Cet article examine la thèse de Lautman selon laquelle la réalité des mathématiques doit être approchée par la « réalisation des idées dialectiques ». Pour ce faire, nous reprenons deux exemples que Lautman a lui-même traités. La question est de savoir si on peut ou non mieux décrire les idées dialectiques comme mathématiques, particulièrement maintenant que les moyens mathématiques d’approcher ces idées au niveau de généralisation appropriée existent. Ainsi, la théorie des catégories, inconnue de Lautman, peut donner une description très (...)
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  10.  22
    Bayesianism in Mathematics.David Corfield - 2001 - In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism. Kluwer Academic Publishers. pp. 175--201.
    A study of the possibility of casting plausible matheamtical inference in Bayesian terms.
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  11.  65
    Falsificationism and Statistical Learning Theory: Comparing the Popper and Vapnik-Chervonenkis Dimensions.David Corfield, Bernhard Schölkopf & Vladimir Vapnik - 2009 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 40 (1):51-58.
    We compare Karl Popper’s ideas concerning the falsifiability of a theory with similar notions from the part of statistical learning theory known as VC-theory . Popper’s notion of the dimension of a theory is contrasted with the apparently very similar VC-dimension. Having located some divergences, we discuss how best to view Popper’s work from the perspective of statistical learning theory, either as a precursor or as aiming to capture a different learning activity.
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  12.  41
    Foundations of Bayesianism.David Corfield & Jon Williamson (eds.) - 2001 - Kluwer Academic Publishers.
    The volume includes important criticisms of Bayesian reasoning and also gives an insight into some of the points of disagreement amongst advocates of the ...
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  13.  27
    Modal Homotopy Type Theory.David Corfield - unknown
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  14.  9
    Argumentation and the Mathematical Process.David Corfield - 2002 - In G. Kampis, L.: Kvasz & M. Stöltzner (eds.), Appraising Lakatos: Mathematics, Methodology and the Man. Kluwer Academic Publishers. pp. 115--138.
  15.  15
    The Form and Function of Duality in Modern Mathematics.Ralf Krömer & David Corfield - unknown
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  16.  62
    Reflections on Michael Friedman's Dynamics of Reason.David Corfield - unknown
    Friedman's rich account of the way the mathematical sciences ideally are transformed affords mathematics a more influential role than is common in the philosophy of science. In this paper I assess Friedman's position and argue that we can improve on it by pursuing further the parallels between mathematics and science. We find a richness to the organisation of mathematics similar to that Friedman finds in physics.
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  17.  22
    The Importance of Mathematical Conceptualisation.David Corfield - 2001 - Studies in History and Philosophy of Science Part A 32 (3):507-533.
    Mathematicians typically invoke a wide range of reasons as to why their research is valuable. These reveal considerable differences between their personal images of mathematics. One of the most interesting of these concerns the relative importance accorded to conceptual reformulation and development compared with that accorded to the achievement of concrete results. Here I explore the conceptualists' claim that the scales are tilted too much in favour of the latter. I do so by taking as a case study the debate (...)
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  18.  45
    Some Implications of the Adoption of Category Theory for Philosophy.David Corfield - unknown
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  19. Varieties of Justification in Machine Learning.David Corfield - 2010 - Minds and Machines 20 (2):291-301.
    Forms of justification for inductive machine learning techniques are discussed and classified into four types. This is done with a view to introduce some of these techniques and their justificatory guarantees to the attention of philosophers, and to initiate a discussion as to whether they must be treated separately or rather can be viewed consistently from within a single framework.
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  20.  11
    Commentaire sur Emmanuel Barot : Lautman.David Corfield - 2010 - Philosophiques 37 (1):207-211.
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  21.  41
    Introduction: Bayesianism Into the 21st Century.Jon Williamson & David Corfield - 2001 - In David Corfield & Jon Williamson (eds.), Foundations of Bayesianism. Kluwer Academic Publishers. pp. 1--16.
    Bayesian theory now incorporates a vast body of mathematical, statistical and computational techniques that are widely applied in a panoply of disciplines, from artificial intelligence to zoology. Yet Bayesians rarely agree on the basics, even on the question of what Bayesianism actually is. This book is about the basics e about the opportunities, questions and problems that face Bayesianism today.
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  22.  34
    Martin H. Krieger. Doing Mathematics: Convention, Subject, Calculation, Analogy. Singapore: World Scientific Publishing, 2003. Pp. XVIII + 454. ISBN 981-238-2003 (Cloth); 981-238-2062 (Paperback). [REVIEW]David Corfield - 2005 - Philosophia Mathematica 13 (1):106-111.
  23.  13
    Conceptual Mathematics: A First Introduction to Categories.David Corfield - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (2):359-366.
  24.  26
    Conceptual Mathematics: A First Introduction to Categories.David Corfield - 2002 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33 (2):359-366.
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  25.  12
    Projection and Projectability.David Corfield - unknown
    The problem of dataset shift can be viewed in the light of the more general problems of induction, in particular the question of what it is about some objects' features or properties which allow us to project correlations confidently to other times and other places.
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  26.  8
    Complementarity and Convergence in the Philosophies of Mathematics and Physics.David Corfield - 2006 - Metascience 15 (2):363-366.
  27.  4
    Narrative and the Rationality of Mathematics.David Corfield - unknown
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  28. Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy.David Corfield - 2020 - Oxford University Press.
    Modal Homotopy Type Theory: The Prospect of a New Logic for Philosophy provides a reasonably gentle introduction to this new logic, thoroughly motivated by intuitive explanations of the need for all of its component parts, and illustrated through innovative applications of the calculus.
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