63 found
Order:
  1. 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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   115 citations  
  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 (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   77 citations  
  3. 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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   44 citations  
  4. 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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   17 citations  
  5. 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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  6.  85
    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, (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  7.  86
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   13 citations  
  8.  50
    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. (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   20 citations  
  9. 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 (...)
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  10.  97
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  11.  72
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  12.  92
    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.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  13.  97
    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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  14.  75
    Mathemetical Explanation.Christopher Pincock & Paolo Mancosu - 2012 - Oxford Bibliographies in Philosophy.
  15. Towards a Philosophy of Applied Mathematics.Christopher Pincock - 2009 - 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 (...)
     
    Export citation  
     
    Bookmark   7 citations  
  16. 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.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  17.  85
    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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   8 citations  
  18. Philosophy of Mathematics.Christopher Pincock - 2011 - In J. Saatsi & S. French (eds.), 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 (...)
     
    Export citation  
     
    Bookmark   5 citations  
  19.  19
    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 (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  20.  19
    Defending a Realist Stance.Christopher Pincock - forthcoming - International Studies in the Philosophy of Science: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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  21. 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 (...)
    Direct download  
     
    Export citation  
     
    Bookmark   3 citations  
  22.  91
    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.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  23.  30
    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 (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  24. 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.
  25.  81
    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 (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  26.  27
    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.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  27. The Limits of the Relative A Priori.Christopher Pincock - 2007 - Soochow Journal of Philosophical Studies 16:51 - 68.
     
    Export citation  
     
    Bookmark  
  28.  47
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  29. Accounting for the unity of experience in Dilthey, Rickert, Bradley and Ward.Christopher Pincock - 2010 - In U. Feest (ed.), Historical Perspectives on Erklaren and Verstehen. Springer. pp. 187-206.
    Forthcoming in U. Feest (ed.), Historical Perspectives on Erkl.
     
    Export citation  
     
    Bookmark  
  30.  43
    Comments on A. Casullo’s Essays on a priori knowledge and justification.Christopher Pincock - 2016 - Philosophical Studies 173 (6):1687-1694.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  31. Comments on Leiber’s “Russell and Wittgenstein”.Christopher Pincock - 2005 - The Bertrand Russell Society Quarterly 125.
     
    Export citation  
     
    Bookmark  
  32.  14
    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 (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  33.  72
    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.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  34. 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.
     
    Export citation  
     
    Bookmark  
  35.  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.
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  36.  21
    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 (...)
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  37.  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?
    No categories
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  38.  44
    Preface.Marion Vorms & Christopher Pincock - 2013 - Synthese 190 (2):187-188.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  39. Comments on Scott Soames, Philosophical Analysis in the Twentieth Century, volume I.Christopher Pincock - unknown
    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 (...)
     
    Export citation  
     
    Bookmark  
  40. 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.
     
    Export citation  
     
    Bookmark  
  41. Mathematical Contributions to Scientific Explanation.Christopher Pincock - unknown
    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 (...)
     
    Export citation  
     
    Bookmark   1 citation  
  42.  13
    On Hans-Johann Glock, What is Analytic Philosophy?Christopher Pincock - 2013 - Journal for the History of Analytical Philosophy 2 (2):6-10.
    Direct download  
     
    Export citation  
     
    Bookmark  
  43. Scott Soames. Philosophical Analysis in the Twentieth Century_. _Volume 1: The Dawn of.Christopher Pincock - unknown
    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 (...)
     
    Export citation  
     
    Bookmark  
  44. The value of mathematics for scientific representation.Christopher Pincock - manuscript
  45. Models and simulations.Marion Vorms & Christopher Pincock - unknown
     
    Export citation  
     
    Bookmark  
  46.  55
    Carnap’s Logical Structure of the World. [REVIEW]Christopher 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 Richardson which (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  47.  43
    Sorin Bangu. The Applicability of Mathematics in Science: Indispensability and Ontology. Basingstoke: Palgrave Macmillan, 2012. ISBN 978-0-230-28520-0 . Pp. xiii + 252. [REVIEW]Christopher Pincock - 2014 - Philosophia Mathematica 22 (3):401-412.
  48.  78
    Bas C. Van Fraassen * Scientific Representation: Paradoxes of Perspective. [REVIEW]Christopher Pincock - 2011 - British Journal for the Philosophy of Science 62 (3):677-682.
  49.  38
    Bernard Linsky. The Evolution of Principia Mathematica: Bertrand Russell's manuscripts and notes for the second edition. Cambridge University Press, Cambridge, 2011, vii + 407 pp. [REVIEW]Christopher Pincock - 2013 - Bulletin of Symbolic Logic 19 (1):106-108.
    Review by: Christopher Pincock The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 106-108, March 2013.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  50.  37
    Carnap Brought Home: The View from Jena. [REVIEW]Christopher Pincock - 2006 - Vienna Circle Institute Yearbook 12:213-218.
1 — 50 / 63