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Christopher Pincock [66]Chris Pincock [17]Christoper Pincock [1]Chris John Pincock [1]
  1.  51
    Mathematics and Scientific Representation.Christopher Pincock - 2012 - Oxford and New York: Oxford University Press USA.
    Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a (...)
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  2. Abstract Explanations in Science.Christopher Pincock - 2014 - British Journal for the Philosophy of Science 66 (4):857-882.
    This article focuses on a case that expert practitioners count as an explanation: a mathematical account of Plateau’s laws for soap films. I argue that this example falls into a class of explanations that I call abstract explanations.explanations involve an appeal to a more abstract entity than the state of affairs being explained. I show that the abstract entity need not be causally relevant to the explanandum for its features to be explanatorily relevant. However, it remains unclear how to unify (...)
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  3. A Role for Mathematics in the Physical Sciences.Chris Pincock - 2007 - Noûs 41 (2):253-275.
    Conflicting accounts of the role of mathematics in our physical theories can be traced to two principles. Mathematics appears to be both (1) theoretically indispensable, as we have no acceptable non-mathematical versions of our theories, and (2) metaphysically dispensable, as mathematical entities, if they existed, would lack a relevant causal role in the physical world. I offer a new account of a role for mathematics in the physical sciences that emphasizes the epistemic benefits of having mathematics around when we do (...)
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  4. A new perspective on the problem of applying mathematics.Christopher Pincock - 2004 - Philosophia Mathematica 12 (2):135-161.
    This paper sets out a new framework for discussing a long-standing problem in the philosophy of mathematics, namely the connection between the physical world and a mathematical domain when the mathematics is applied in science. I argue that considering counterfactual situations raises some interesting challenges for some approaches to applications, and consider an approach that avoids these challenges.
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  5. The Unsolvability of The Quintic: A Case Study in Abstract Mathematical Explanation.Christopher Pincock - 2015 - Philosophers' Imprint 15.
    This paper identifies one way that a mathematical proof can be more explanatory than another proof. This is by invoking a more abstract kind of entity than the topic of the theorem. These abstract mathematical explanations are identified via an investigation of a canonical instance of modern mathematics: the Galois theory proof that there is no general solution in radicals for fifth-degree polynomial equations. I claim that abstract explanations are best seen as describing a special sort of dependence relation between (...)
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  6. Concrete Scale Models, Essential Idealization, and Causal Explanation.Christopher Pincock - 2022 - British Journal for the Philosophy of Science 73 (2):299-323.
    This paper defends three claims about concrete or physical models: these models remain important in science and engineering, they are often essentially idealized, in a sense to be made precise, and despite these essential idealizations, some of these models may be reliably used for the purpose of causal explanation. This discussion of concrete models is pursued using a detailed case study of some recent models of landslide generated impulse waves. Practitioners show a clear awareness of the idealized character of these (...)
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  7.  90
    A Defense of Truth as a Necessary Condition on Scientific Explanation.Christopher Pincock - 2021 - Erkenntnis 88 (2):621-640.
    How can a reflective scientist put forward an explanation using a model when they are aware that many of the assumptions used to specify that model are false? This paper addresses this challenge by making two substantial assumptions about explanatory practice. First, many of the propositions deployed in the course of explaining have a non-representational function. In particular, a proposition that a scientist uses and also believes to be false, i.e. an “idealization”, typically has some non-representational function in the practice, (...)
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  8.  88
    How to avoid inconsistent idealizations.Christopher Pincock - 2014 - Synthese 191 (13):2957-2972.
    Idealized scientific representations result from employing claims that we take to be false. It is not surprising, then, that idealizations are a prime example of allegedly inconsistent scientific representations. I argue that the claim that an idealization requires inconsistent beliefs is often incorrect and that it turns out that a more mathematical perspective allows us to understand how the idealization can be interpreted consistently. The main example discussed is the claim that models of ocean waves typically involve the false assumption (...)
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  9.  54
    Overextending partial structures: Idealization and abstraction.Christopher Pincock - 2005 - Philosophy of Science 72 (5):1248-1259.
    The partial structures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model‐theoretic techniques in the philosophy of science. (...)
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  10.  49
    Overextending Partial Structures: Idealization and Abstraction.Chris Pincock - 2005 - Philosophy of Science 72 (5):1248-1259.
    The partial structures program of da Costa, French and others offers a unified framework within which to handle a wide range of issues central to contemporary philosophy of science. I argue that the program is inadequately equipped to account for simple cases where idealizations are used to construct abstract, mathematical models of physical systems. These problems show that da Costa and French have not overcome the objections raised by Cartwright and Suárez to using model-theoretic techniques in the philosophy of science. (...)
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  11. Modeling reality.Christopher Pincock - 2011 - Synthese 180 (1):19 - 32.
    My aim in this paper is to articulate an account of scientific modeling that reconciles pluralism about modeling with a modest form of scientific realism. The central claim of this approach is that the models of a given physical phenomenon can present different aspects of the phenomenon. This allows us, in certain special circumstances, to be confident that we are capturing genuine features of the world, even when our modeling occurs independently of a wholly theoretical motivation. This framework is illustrated (...)
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  12.  48
    Mathematical explanations of the rainbow.Christopher Pincock - 2011 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 42 (1):13-22.
    Explanations of three different aspects of the rainbow are considered. The highly mathematical character of these explanations poses some interpretative questions concerning what the success of these explanations tells us about rainbows. I develop a proposal according to which mathematical explanations can highlight what is relevant about a given phenomenon while also indicating what is irrelevant to that phenomenon. This proposal is related to the extensive work by Batterman on asymptotic explanation with special reference to Batterman’s own discussion of the (...)
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  13.  74
    Mathematical models of biological patterns: Lessons from Hamilton’s selfish herd.Christopher Pincock - 2012 - Biology and Philosophy 27 (4):481-496.
    Mathematical models of biological patterns are central to contemporary biology. This paper aims to consider what these models contribute to biology through the detailed consideration of an important case: Hamilton’s selfish herd. While highly abstract and idealized, Hamilton’s models have generated an extensive amount of research and have arguably led to an accurate understanding of an important factor in the evolution of gregarious behaviors like herding and flocking. I propose an account of what these models are able to achieve and (...)
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  14.  92
    Mathematical Idealization.Chris Pincock - 2007 - Philosophy of Science 74 (5):957-967.
    Mathematical idealizations are scientific representations that result from assumptions that are believed to be false, and where mathematics plays a crucial role. I propose a two stage account of how to rank mathematical idealizations that is largely inspired by the semantic view of scientific theories. The paper concludes by considering how this approach to idealization allows for a limited form of scientific realism. ‡I would like to thank Robert Batterman, Gabriele Contessa, Eric Hiddleston, Nicholaos Jones, and Susan Vineberg for helpful (...)
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  15.  95
    On Batterman's 'On the Explanatory Role of Mathematics in Empirical Science'.Christopher Pincock - 2011 - British Journal for the Philosophy of Science 62 (1):211 - 217.
    This discussion note of (Batterman [2010]) clarifies the modest aims of my 'mapping account' of applications of mathematics in science. Once these aims are clarified it becomes clear that Batterman's 'completely new approach' (Batterman [2010], p. 24) is not needed to make sense of his cases of idealized mathematical explanations. Instead, a positive proposal for the explanatory power of such cases can be reconciled with the mapping account.
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  16.  74
    Mathemetical Explanation.Christopher Pincock & Paolo Mancosu - 2012 - Oxford Bibliographies in Philosophy.
  17.  64
    Russell’s Influence On Carnap’s Aufbau.Christopher Pincock - 2002 - Synthese 131 (1):1-37.
    This paper concerns the debate on the nature of Rudolf Carnap'sproject in his 1928 book The Logical Structure of the Worldor Aufbau. Michael Friedman and Alan Richardson haveinitiated much of this debate. They claim that the Aufbauis best understood as a work that is firmly grounded inneo-Kantian philosophy. They have made these claims in oppositionto Quine and Goodman's ``received view'' of the Aufbau. Thereceived view sees the Aufbau as an attempt to carry out indetail Russell's external world program. I argue (...)
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  18. Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - In Ø. Linnebo O. Bueno (ed.), New Waves in Philosophy of Mathematics. Palgrave-Macmillan.
    Most contemporary philosophy of mathematics focuses on a small segment of mathematics, mainly the natural numbers and foundational disciplines like set theory. While there are good reasons for this approach, in this paper I will examine the philosophical problems associated with the area of mathematics known as applied mathematics. Here mathematicians pursue mathematical theories that are closely connected to the use of mathematics in the sciences and engineering. This area of mathematics seems to proceed using different methods and standards when (...)
     
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  19. Russell's Last (And Best) Multiple-Relation Theory of Judgement.Christopher Pincock - 2008 - Mind 117 (465):107 - 139.
    Russell's version of the multiple-relation theory from the "Theory of Knowledge" manuscript is presented and defended against some objections. A new problem, related to defining truth via correspondence, is reconstructed from Russell's remarks and what we know of Wittgenstein's objection to Russell's theory. In the end, understanding this objection in terms of correspondence helps to link Russell's multiple-relation theory to his later views on propositions.
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  20.  91
    A reserved reading of Carnap's aufbau.Christopher Pincock - 2005 - Pacific Philosophical Quarterly 86 (4):518–543.
    The two most popular approaches to Carnap's 1928 Aufbau are the empiricist reading of Quine and the neo-Kantian readings of Michael Friedman and Alan Richardson. This paper presents a third "reserved" interpretation that emphasizes Carnap's opposition to traditional philosophy and consequent naturalism. The main consideration presented in favor of the reserved reading is Carnap's work on a physical construction system. I argue that Carnap's construction theory was an empirical scientific discipline and that the basic relations of its construction systems need (...)
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  21. Philosophy of Mathematics.Christopher Pincock - 2011 - In Steven French & Juha Saatsi (eds.), Continuum Companion to the Philosophy of Science. Continuum. pp. 314-333.
    For many philosophers of science, mathematics lies closer to logic than it does to the ordinary sciences like physics, biology and economics. While this view may account for the relative neglect of the philosophy of mathematics by philosophers of science, it ignores at least two pressing questions about mathematics that philosophers of science need to be able to answer. First, do the similarities between mathematics and science support the view that mathematics is, after all, another science? Second, does the central (...)
     
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  22. Carnap's logical structure of the world.Chris Pincock - 2009 - Philosophy Compass 4 (6):951-961.
    This article aims to give an overview of Carnap's 1928 book Logical Structure of the World or Aufbau and the most influential interpretations of its significance. After giving an outline of the book in Section 2 , I turn to the first sustained interpretations of the book offered by Goodman and Quine in Section 3 . Section 4 explains how this empirical reductionist interpretation was largely displaced by its main competitor. This is the line of interpretation offered by Friedman and (...)
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  23.  26
    The derivation of Poiseuille’s law: heuristic and explanatory considerations.Christopher Pincock - 2021 - Synthese 199 (3-4):11667-11687.
    This paper illustrates how an experimental discovery can prompt the search for a theoretical explanation and also how obtaining such an explanation can provide heuristic benefits for further experimental discoveries. The case considered begins with the discovery of Poiseuille’s law for steady fluid flow through pipes. The law was originally supported by careful experiments, and was only later explained through a derivation from the more basic Navier–Stokes equations. However, this derivation employed a controversial boundary condition and also relied on a (...)
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  24.  24
    Defending a Realist Stance.Christopher Pincock - 2024 - International Studies in the Philosophy of Science 37 (1-2):1-15.
    Should the scientific realist admit that their realism involves what Chakravartty has called an epistemic stance? I argue that the realist should accept the need for a realist stance that licenses the use of inference to the best explanation. However, unlike Chakravartty, I maintain that the realist should insist that their realist stance is rationally obligatory. This requires an anti-voluntarism about stances that involves theoretical reasons for adopting one stance rather than another. I present one account of what these reasons (...)
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  25. Conditions on the Use of the One-dimensional Heat Equation.Chris Pincock - unknown
    This paper explores the conditions under which scientists are warranted in adding the one-dimensional heat equation to their theories and then using the equation to describe particular physical situations. Summarizing these derivation and application conditions motivates an account of idealized scientific representation that relates the use of mathematics in science to interpretative questions about scientific theories.
     
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  26.  75
    Mathematical Structural Realism.Christopher Pincock - 2011 - In Alisa Bokulich & Peter Bokulich (eds.), Scientific Structuralism. Springer Science+Business Media. pp. 67--79.
    Epistemic structural realists have argued that we are in a better epistemic position with respect to the structural claims made by our theories than the non-structural claims. Critics have objected that we cannot make the structure/non-structure distinction precise. I respond that a focus on mathematical structure leads to a clearer understanding of this debate. Unfortunately for the structural realist, however, the contribution that mathematics makes to scientific representation undermines any general confidence we might have in the structural claims made by (...)
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  27.  96
    Exploring the boundaries of conceptual evaluation.Christopher Pincock - 2010 - Philosophia Mathematica 18 (1):106-121.
    This is a critical notice of Mark Wilson's Wandering Significance.
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  28.  32
    Richard Semon and Russell’s Analysis of Mind.Christopher Pincock - 2006 - Russell: The Journal of Bertrand Russell Studies 26 (2):101-125.
    Russell’s study of the biologist and psychologist Richard Semon is traced to contact with the experimental psychologist Adolf Wohlgemuth and dated to the summer of 1919. This allows a new interpretation of when Russell embraced neutral monism and presents a case-study in Russell’s use of scientific results for philosophical purposes. Semon’s distinctive notion of mnemic causation was used by Russell to clarify both how images referred to things and how the existence of images could be reconciled with a neutral monist (...)
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  29. Logical Empiricism.Christopher Pincock - 2016 - In Herman Cappelen, Tamar Gendler & John Hawthorne (eds.), The Oxford Handbook of Philosophical Methodology. Oxford, United Kingdom: Oxford University Press.
    At different times logical empiricists engaged one another in debates about the proper problems and methods for philosophy or its successor discipline. The most pressing problem focused on how to coordinate the abstract statements of the sciences with what can be experienced and tested. While the new logic was the main tool for coordination for Moritz Schlick, Hans Reichenbach, and Rudolf Carnap, there was no agreement on the nature of logic or its role in coordination. Otto Neurath and Philipp Frank (...)
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  30.  16
    Carnap and the Unity of Science: 1921–1928.Chris Pincock - 2003 - In Thomas Bonk (ed.), Language, Truth and Knowledge: Contributions to the Philosophy of Rudolf Carnap. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 87--96.
  31. Structures, fictions, and the explanatory epistemology of mathematics in science: Christopher Pincock: Mathematics and scientific representation. New York: Oxford University Press, 2012, 330pp, $65.00 HB.Mark Balaguer, Elaine Landry, Sorin Bangu & Christopher Pincock - 2013 - Metascience 22 (2):247-273.
  32.  29
    The Collected Works of Rudolf Carnap, Volume 1: Early Writings, edited by A. W. Carus, Michael Friedman, Wolfgang Kienzler, Alan Richardson & Sven Schlotter, general editor Richard Creath, with editorial assistance from Steve Awodey, Dirk Schlimm & Richard Zach.Christopher Pincock - 2022 - Mind 131 (521):317-326.
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  33.  74
    Explanatory Relevance and Contrastive Explanation.Christopher Pincock - 2018 - Philosophy of Science.
    A pluralist about explanation posits many explanatory relevance relations, while an invariantist denies any substantial role for context in fixing genuine explanation. This article summarizes one approach to combining pluralism and invariantism that emphasizes the contrastive nature of explanation. If explanations always take contrasts as their objects and contrasts come in types, then the role for the context in which an explanation is given can be minimized. This approach is illustrated using a classic debate between natural theology and natural selection (...)
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  34. The Limits of the Relative A Priori.Christopher Pincock - 2007 - Soochow Journal of Philosophical Studies 16:51 - 68.
     
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  35.  49
    Innovations in the History of Analytical Philosophy.Sandra Lapointe & Christopher Pincock - 2017 - London, United Kingdom: Palgrave-Macmillan.
    This book offers new perspectives on the history of analytical philosophy, surveying recent scholarship on the philosophical study of mind, language, logic and reality over the course of the last 200 years. Each chapter contributes to a broader engagement with a wider range of figures, topics and disciplines outside of philosophy than has been traditionally associated with the history of analytical philosophy. The book acquaints readers with new aspects of analytical philosophy’s revolutionary past while engaging in a much needed methodological (...)
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  36.  11
    Russel and logical empiricism.Christopher Pincock & Eric Fayet - unknown
    Christopher Pincock analyses the evolution of the Russellian theory of induction and compares it to Reichenbach's.
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  37.  23
    Reichenbach, Russell and scientific realism.Christopher Pincock - 2021 - Synthese 199 (3-4):8485-8506.
    This paper considers how to best relate the competing accounts of scientific knowledge that Russell and Reichenbach proposed in the 1930s and 1940s. At the heart of their disagreements are two different accounts of how to best combine a theory of knowledge with scientific realism. Reichenbach argued that a broadly empiricist epistemology should be based on decisions. These decisions or “posits” informed Reichenbach’s defense of induction and a corresponding conception of what knowledge required. Russell maintained that a scientific realist must (...)
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  38.  11
    Which universal phenomena are emergent?Christopher Pincock & Eric Fayet - unknown
    Christopher Pincock discusses the nature of the explanation of the universality of certain natural phenomena, such as critical phenomena. Under what conditions can they be called emergent?
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  39. Accounting for the unity of experience in Dilthey, Rickert, Bradley and Ward.Christopher Pincock - 2007 - In U. Feest (ed.), Historical Perspectives on Erkl. Max Planck Institute for the History of Science. pp. 187-206.
    Forthcoming in U. Feest (ed.), Historical Perspectives on Erkl.
     
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  40.  44
    Comments on A. Casullo’s Essays on a priori knowledge and justification.Christopher Pincock - 2016 - Philosophical Studies 173 (6):1687-1694.
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  41. Comments on Leiber’s “Russell and Wittgenstein”.Christopher Pincock - 2005 - The Bertrand Russell Society Quarterly 125.
     
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  42.  35
    From sunspots to the Southern Oscillation: confirming models of large-scale phenomena in meteorology.Chris Pincock - 2009 - Studies in History and Philosophy of Science Part A 40 (1):45-56.
    Forthcoming, Studies in the History and Philosophy of Science Abstract: The epistemic problem of assessing the support that some evidence confers on a hypothesis is considered using an extended example from the history of meteorology. In this case, and presumably in others, the problem is to develop techniques of data analysis that will link the sort of evidence that can be collected to hypotheses of interest. This problem is solved by applying mathematical tools to structure the data and connect it (...)
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  43.  15
    From sunspots to the Southern Oscillation: confirming models of large-scale phenomena in meteorology.Christopher Pincock - 2009 - Studies in History and Philosophy of Science Part A 40 (1):45-56.
    The epistemic problem of assessing the support that some evidence confers on a hypothesis is considered using an extended example from the history of meteorology. In this case, and presumably in others, the problem is to develop techniques of data analysis that will link the sort of evidence that can be collected to hypotheses of interest. This problem is solved by applying mathematical tools to structure the data and connect them to the competing hypotheses. I conclude that mathematical innovations provide (...)
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  44.  73
    Mathematics, Science, and Confirmation Theory.Christopher Pincock - 2010 - Philosophy of Science 77 (5):959-970.
    This paper begins by distinguishing intrinsic and extrinsic contributions of mathematics to scientific representation. This leads to two investigations into how these different sorts of contributions relate to confirmation. I present a way of accommodating both contributions that complicates the traditional assumptions of confirmation theory. In particular, I argue that subjective Bayesianism does best accounting for extrinsic contributions, while objective Bayesianism is more promising for intrinsic contributions.
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  45. Mathematical Structural Realism.Chris Pincock - 2011 - In Alisa Bokulich & Peter Bokulich (eds.), Scientific Structuralism. Springer Science+Business Media.
    Epistemic structural realists have argued that we are in a better epistemic position with respect to the structural claims made by our theories than the non-structural claims. Critics have objected that we cannot make the structure/non-structure distinction precise. I respond that a focus on mathematical structure leads to a clearer understanding of this debate. Unfortunately for the structural realist, however, the contribution that mathematics makes to scientific representation undermines any general confidence we might have in the structural claims made by (...)
     
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  46. Part II. Does mathematical explanation require mathematical truth?: Mathematical explanation requires mathematical truth.Christopher Pincock - 2020 - In Shamik Dasgupta, Brad Weslake & Ravit Dotan (eds.), Current Controversies in Philosophy of Science. London: Routledge.
     
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  47.  44
    Preface.Marion Vorms & Christopher Pincock - 2013 - Synthese 190 (2):187-188.
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  48. I.Christopher Pincock - unknown
    Most contemporary philosophy of mathematics focuses on a small segment of mathematics, mainly the natural numbers and foundational disciplines like set theory. While there are good reasons for this approach, in this paper I will examine the philosophical problems associated with the area of mathematics known as applied mathematics.
     
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  49. A priori contributions to scientific knowledge.Chris Pincock - unknown
    This paper presents two different kinds a priori entitlements and argues that both are necessary to account for scientific knowledge. On the one hand, there are formal a priori entitlements whose existence is grounded in conditions on concept possession. On the other hand, there are material a priori entitlements that an agent accrues in virtue of practical reasoning. The discussion aims to reconcile the strengths of Christopher Peacocke’s and Michael Friedman’s recent work on the a priori, while overcoming the weaknesses (...)
     
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  50.  42
    Abstract representations and confirmation.Chris Pincock - unknown
    Many philosophers would concede that mathematics contributes to the abstractness of some of our most successful scientific representations. Still, it is hard to know what this abstractness really comes to or how to make a link between abstractness and success. I start by explaining how mathematics can increase the abstractness of our representations by distinguishing two kinds of abstractness. First, there is an abstract representation that eschews causal content. Second, there are families of representations with a common mathematical core that (...)
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