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Profile: Christopher Pincock (Ohio State University)
  1. Christopher Pincock (web). Accounting for the Unity of Experience in Dilthey, Rickert, Bradley and Ward. In U. Feest (ed.), Historical Perspectives on Erkl. Max Planck Institute for the History of Science.
    Forthcoming in U. Feest (ed.), Historical Perspectives on Erkl.
     
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  2. Christopher Pincock, I.
    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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  3. Christopher Pincock, Scott Soames. Philosophical Analysis in the Twentieth Century_. _Volume 1: The Dawn of.
    The last twenty years have seen an explosion in books and papers on Russell’s philosophy and its contemporary significance. There is good reason to think that this will continue as the contents of the Collected Papers are digested by Russell scholars and as more specialists contribute to the history of analytic philosophy more generally. Given all this good news, it is disconcerting to find a 100 page discussion of Russell, in a well-reviewed book by a first-rate philosopher, repeating many of (...)
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  4. Chris Pincock, Conditions on the Use of the One-Dimensional Heat Equation.
    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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  5. Chris Pincock, Christopher Pincock (Pincock@Purdue.Edu) September 4, 2006 (2782 Words).
    In his carefully argued and extensively researched article “The Implications of Recent Work in the History of Analytic Philosophy” (Preston 2005a) Aaron Preston has raised what should surely be the central methodological issue for Russell studies and the history of analytic philosophy more generally.[1] That is, what are the goals of the history of analytic philosophy and by what means can we best try to meet these goals? Preston’s main conclusion is that historical investigation into the origins of analytic philosophy (...)
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  6. Chris Pincock, Derivation and Application Conditions of the One-Dimensional Heat Equation.
    Example: which mathematical truths concerning the real numbers play a role in using real numbers to represent temperature? “temperature and other scalar fields used in physics are assumed to be continuous, and this guarantees that if point x has temperature ψ(x) and point z has temperature ψ(z) and r is a real number between ψ(x) and ψ(z), then there will be a point y spatio-temporally between x and z such that ψ(y ) = r ” (Field 1980, 57).
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  7. Chris Pincock, Reviewed By.
    Christopher Pincock, Department of Philosophy, Purdue University, West Lafayette, IN 47907, USA This volume presents seventeen essays (not eleven, as the publisher inexplicably claims) by a diverse group of philosophers that arose out of a conference in Florence in 1999. As its title indicates, the focus of the conference was the contemporary significance of the topics, methods and innovations of the logical empiricists. This has led to a nicely balanced collection that combines careful historical study with an eye on current (...)
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  8. Chris Pincock, Reply to Soames.
    Christopher Pincock April 24, 2006 My goal in reviewing Soames’ book was to help readers of this journal evaluate his contribution to the history of analytic philosophy, with a special focus on his discussion of Russell.[1] Soames charges both that I misrepresent the contents of his book and that I make mistakes in the interpretation of various aspects of Russell’s philosophy. If I had committed any errors of the former sort, I would certainly apologize and thank Soames for bringing such (...)
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  9. Chris Pincock, -2098, Usa.
    In her preface to this collection of 11 new essays on Ramsey, Frápolli clarifies the nonhistorical orientation of the volume: ‘Our way of honoring Ramsey has been to think with him and, wherever possible, to go beyond that, putting his ideas to work and seeing how far they can reach’ (ix). This certainly makes sense for the topics of many of these essays, building as they do on Ramsey’s rich contributions to economics and reliabilist epistemology as well as on his (...)
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  10. Christopher Pincock, Comments on Scott Soames, Philosophical Analysis in the Twentieth Century, Volume I.
    Scott Soames has given us a clear, engaging but ultimately unsatisfying introduction to the history of analytic philosophy. Based on Soames’ impressive work in the philosophy of language, when these two volumes appeared I had high hopes that he would be successful. There is certainly a need for an introductory survey of the history of analytic philosophy. Currently, there is no resource for the beginning student or the amateur historian that will summarize our current understanding of the origins and development (...)
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  11. Christopher Pincock, Mathematical Contributions to Scientific Explanation.
    After reviewing some different indispensability arguments, I distinguish several different ways in which mathematics can make an important contribution to a scientific explanation. Once these contributions are highlighted it will be possible to see that indispensability arguments have little chance of convincing us of the existence of abstract objects, even though they may give us good reason to accept the truth of some mathematical claims. However, in the concluding part of this paper, I argue that even though there is a (...)
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  12. Christopher Pincock, Philosophy of Mathematics.
    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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  13. Christopher Pincock, The Applicability of Mathematics.
    Depending on how it is clarified, the applicability of mathematics can lie anywhere on a spectrum from the completely trivial to the utterly mysterious. At the one extreme, it is obvious that mathematics is used outside of mathematics in cases which range from everyday calculations like the attempt to balance one s checkbook through the most demanding abstract modeling of subatomic particles. The techniques underlying these applications are perfectly clear to those who have mastered them and there seems to be (...)
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  14. Christopher Pincock, The Value of Mathematics for Scientific Representation.
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  15. Sandra Lapointe & Christopher Pincock (eds.) (forthcoming). Innovations in the History of Analytical Philosophy. Palgrave-Macmillan.
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  16. Chris Pincock (forthcoming). Modeling Reality. Synthese.
    Abstract: 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 in the absence of a fundamental theory. This framework (...)
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  17. Christopher Pincock (forthcoming). Abstract Explanations in Science. British Journal for the Philosophy of Science:axu016.
    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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  18. Christopher Pincock (2014). How to Avoid Inconsistent Idealizations. 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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  19. Christopher Pincock (2014). Sorin Bangu. The Applicability of Mathematics in Science: Indispensability and Ontology. Basingstoke: Palgrave Macmillan, 2012. ISBN 978-0-230-28520-0 (Hbk). Pp. Xiii + 252. [REVIEW] Philosophia Mathematica 22 (3):401-412.
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  20. Mark Balaguer, Elaine Landry, Sorin Bangu & Christopher Pincock (2013). Structures, Fictions, and the Explanatory Epistemology of Mathematics in Science. Metascience 22 (2):247-273.
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  21. Christopher Pincock (2013). Review of B. Linsky, The Evolution of Principia Mathematica: Bertrand Russell's Manuscripts and Notes for the Second Edition. [REVIEW] Bulletin of Symbolic Logic 9 (1):106-108.
    Review by: Christopher Pincock The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 106-108, March 2013.
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  22. Marion Vorms & Christopher Pincock (2013). Preface. Synthese 190 (2):187-188.
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  23. Christopher Pincock (2012). Mathematics and Scientific Representation. OUP USA.
    Pincock tackles this perennial question by asking how mathematics contributes to the success of our best scientific representations.
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  24. Christopher Pincock (2012). Mathematical Models of Biological Patterns: Lessons From Hamilton's Selfish Herd. Biology and Philosophy 27 (4):481-496.
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  25. Christopher Pincock, Alan Baker, Alexander Paseau & Mary Leng (2012). Science and Mathematics: The Scope and Limits of Mathematical Fictionalism. [REVIEW] Metascience 21 (2):269-294.
    Science and mathematics: the scope and limits of mathematical fictionalism Content Type Journal Article Category Book Symposium Pages 1-26 DOI 10.1007/s11016-011-9640-3 Authors Christopher Pincock, University of Missouri, 438 Strickland Hall, Columbia, MO 65211-4160, USA Alan Baker, Department of Philosophy, Swarthmore College, Swarthmore, PA 19081, USA Alexander Paseau, Wadham College, Oxford, OX1 3PN UK Mary Leng, Department of Philosophy, University of York, Heslington, York, YO10 5DD UK Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
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  26. Marion Vorms & Christopher Pincock, Models and Simulations.
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  27. Chris Pincock (2011). Mathematical Structural Realism. In Alisa Bokulich & Peter Bokulich (eds.), Scientific Structuralism.
    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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  28. Christopher Pincock (2011). Fictions in Science: Philosophical Essays on Modeling and Idealization. International Studies in the Philosophy of Science 25 (2):196 - 199.
    International Studies in the Philosophy of Science, Volume 25, Issue 2, Page 196-199, June 2011.
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  29. Christopher Pincock (2011). Mathematical Explanations of the Rainbow. Studies in History and Philosophy of Science Part B 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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  30. Christopher Pincock (2011). Modeling Reality. 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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  31. Christopher Pincock (2011). Mathematical Structural Realism. In. In Alisa Bokulich & Peter Bokulich (eds.), Scientific Structuralism. Springer Science+Business Media. 67--79.
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  32. Christopher Pincock (2011). On Batterman's 'On the Explanatory Role of Mathematics in Empirical Science'. 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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  33. Christopher Pincock (2010). Exploring the Boundaries of Conceptual Evaluation. Philosophia Mathematica 18 (1):106-121.
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  34. Christopher Pincock (2010). Mathematics, Science, and Confirmation Theory. 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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  35. Chris Pincock, Abstract Representations and Confirmation.
    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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  36. Chris Pincock (2009). Carnap's Logical Structure of the World. 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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  37. Chris Pincock (2009). From Sunspots to the Southern Oscillation: Confirming Models of Large-Scale Phenomena in Meteorology. 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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  38. Christopher Pincock (2009). Carnap's Logical Structure of the World. Philosophy Compass 4 (6):951-961.
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  39. Christopher Pincock (2009). Towards a Philosophy of Applied Mathematics. In Otávio Bueno & Øystein Linnebo (eds.), 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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  40. Chris Pincock (2008). Russell's Last (And Best) Multiple-Relation Theory of Judgement. 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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  41. Christopher Pincock (2008). Jesper Lützen. Mechanistic Images in Geometric Form: Heinrich Hertz's Principles of Mechanics. Philosophia Mathematica 16 (1):140-144.
  42. Christopher Pincock (2008). Russell's Last (And Best) Multiple-Relation Theory of Judgement. 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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  43. Chris Pincock (2007). A Role for Mathematics in the Physical Sciences. 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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  44. Chris Pincock (2007). Mathematical Idealization. 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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  45. Christopher Pincock (2007). A Role for Mathematics in the Physical Sciences. 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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  46. Christopher Pincock (2007). Mathematical Idealization. Philosophy of Science 74 (5):957-967.
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  47. Christopher Pincock (2007). Review of Sajahan Miah, Russell's Theory of Perception (1905-1919). [REVIEW] Notre Dame Philosophical Reviews 2007 (3).
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  48. Christopher Pincock (2007). The Limits of the Relative A Priori. Soochow Journal of Philosophical Studies 16:51 - 68.
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  49. Chris Pincock (2005). Overextending Partial Structures: Idealization and Abstraction. 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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  50. Christopher Pincock (2005). A Reserved Reading of Carnap's Aufbau. 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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