Research: Christopher Pincock

Last update: July 28, 2008

Publications

• Articles
  • Mathematical Idealization
    Philosophy of Science (Proceedings) 74 (2007): 957-967.
    Abstract: 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.
  • Russell's Last (and Best) Multiple-relation Theory of Judgment
    Mind 117 (2008): 107-140.
    Abstract: 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.
  • Carnap, Russell and the External World
    In M. Friedman & R. Creath (eds.), Cambridge Companion to Carnap, 2008, 106-128.
    Abstract: After summarizing and criticizing Quine’s own somewhat self-serving reconstruction of the Russell-Carnap relationship, I turn to the more subtle proposal first offered by Demopoulos and Friedman in their paper "Bertrand Russell’s The Analysis of Matter: Its Historical Context and Contemporary Interest." The link noted by Demopoulos and Friedman then frames my survey of the later developments of Carnap and Russell. Here we find Russell filling out his proposals from the 1920s in a fairly straightforward manner, while Carnap adopts a series of increasingly radical proposals to overcome the problems of traditional philosophy. From where Carnap ends up in the 1950 paper "Empiricism, Semantics and Ontology," Russell’s views on experience, language and metaphysics look outdated and confused.
  • A Role for Mathematics in the Physical Sciences
    Nous 41 (2007): 253-275.
    Abstract: 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 science. This account successfully reconciles theoretical indispensability and metaphysical dispensability and has important consequences for both advocates and critics of indispensability arguments for platonism about mathematics.
  • The Limits of the Relative A Priori
    Soochow Journal of Philosophical Studies (Taiwan) 16 (2007): 51-68.
    Abstract: I consider Friedman's notion of relative a priori justification and conclude that even though Friedman's specific proposal does not work, a closely related notion has some chance of success.
  • Accounting for the Unity of Experience in Dilthey, Rickert, Bradley and Ward
    In U. Feest (ed.), Historical Perspectives on Erklären and Verstehen, Max Planck Institute for the History of Science, Preprint 324, 2007, 175-192.
  • Richard Semon and Russell's Analysis of Mind
    Russell 26 (2006): 101-125.
    Abstract: 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.
  • Overextending Partial Structures: Idealization and Abstraction
    Philosophy of Science (Proceedings) 72 (2005): 1248-1259.
    Abstract: 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. However, my concerns arise independently of the more controversial assumptions that Cartwright and Suárez have employed.
    
  • A Reserved Reading of Carnap's Aufbau
    Pacific Philosophical Quarterly 86 (2005): 518-543. (Published version available online.)
    Abstract: 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. The main consideration presented in favor of the reserved reading is Carnap's work on a physical construction system. Once we detach Carnap's project from the more usual philosophical movements, his aims and failures come into sharper focus.
  • Conditions on the Use of the One-dimensional Heat Equation
    In G. Sica (ed.), Essays on the Foundations of Mathematics and Logic, Vol. 2, Polimetrica, 2005, 67-79.
    Abstract: 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.
    Beamer Presentation (May, 2005: Society for Exact Philosophy Meeting, Toronto)
  • A New Perspective on the Problem of Applying Mathematics
    Philosophia Mathematica 12 (2004): 135-161.
    Abstract: 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 that 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.
  • A Revealing Flaw in Colyvan's Indispensability Argument
    Philosophy of Science 71 (2004), 61-79.
    Abstract: Mark Colyvan uses applications of mathematics to argue that mathematical entities exist. I claim that his argument is invalid based on the assumption that a certain way of thinking about applications, called `the mapping account', is correct. My main contention is that successful applications depend only on there being appropriate structural relations between physical situations and the mathematical domain. As a variety of non-realist interpretations of mathematics deliver these structural relations, indispensability arguments are invalid.
  • Carnap and the Unity of Science: 1921-1928
    In T. Bonk (ed.), Language, Truth and Knowledge: Contributions to the Philosophy of Rudolf Carnap, Vienna Circle Institute Library, Volume 2, Kluwer, 2003, pp. 87-96.
  • Russell's Influence on Carnap's Aufbau
    Synthese 131 (2002), 1-37.
    Abstract: This paper concerns the debate on the nature of Rudolf Carnap's project in his 1928 book The Logical Structure of the World or Aufbau. Michael Friedman and Alan Richardson have initiated much of this debate. They claim that the Aufbau is best understood as a work that is firmly grounded in neo-Kantian philosophy. They have made these claims in opposition to Quine and Goodman's "received view" of the Aufbau. The received view sees the Aufbau as an attempt to carry out in detail Russell's external world program. I argue that both sides of this debate have made errors in their interpretation of Russell. These errors have led these interpreters to misunderstand the connection between Russell's project and Carnap's project. Russell in fact exerted a crucial influence on Carnap in the 1920s. This influence is complicated, however, due to the fact that Russell and Carnap disagreed on many philosophical issues. I conclude that interpretations of the Aufbau that ignore Russell's influence are incomplete.
• Reviews and Critical Notices
  • Review of Luetzen, Mechanistic Images in Geometric Form: Heinrich Hertz's Principles of Mechanics
    Philosophia Mathematica 16 (2008): 140-144.
  • Preston on the Illusory Character of Analytic Philosophy
    Forthcoming, Bertrand Russell Society Quarterly
  • Review of Miah, Russell's Theory of Perception (1905-1919), Continuum, 2006.
    Notre Dame Philosophical Reviews, 2007.03.08.
  • Reply to Soames
    Russell 26 (summer 2006): 77-86. (Here is what I am replying to. See below for the related exchange at the 2006 Pacific APA.)
  • Review of S. Soames, Philosophical Analysis in the Twentieth Century, Princeton, 2003.
    Russell 25 (winter 2005-2006): 167-172.
  • Review of Frápolli (ed.), F. P. Ramsey: Critical Reassessments, Continuum, 2005.
    History and Philosophy of Logic 27 (2006): 81-82.
  • Review of Corfield, Towards a Philosophy of Real Mathematics, Cambridge University Press, 2003.
    Philosophy of Science 72 (2005): 632-634.
  • Critical Notice for Torsten Wilholt, Zahl und Wirklichkeit [Number and Reality], Mentis, 2004.
    Philosophia Mathematica 13 (2005): 329-337. (Published version available online.)
  • Review of Awodey and Klein (eds.), Carnap Brought Home: The View from Jena, Open Court, 2004.
    M. Galavotti (ed.), Cambridge and Vienna. Ramsey and the Vienna Circle. Institute Vienna Circle Yearbook 12, Kluwer, 2005, 213-218.
  • Review of Milkov, A Hundred Years of English Philosophy, Kluwer, 2003.
    Notre Dame Philosophical Reviews, 2004.10.06.
  • Review of Parrini, Salmon and Salmon (eds.), Logical Empiricism: Historical and Contemporary Perspectives, University of Pittsburgh Press, 2003.
    F. Stadler (ed.), Induction and Deduction in the Sciences, Institute Vienna Circle Yearbook 11, Kluwer, 2004, 331-334.
  • Review of Wittgenstein & Waismann, The Voices of Wittgenstein: The Vienna Circle, G. Baker (ed.), Routledge, 2003.
    History and Philosophy of Logic 25 (2004): 156-157.
  • Review of M. Ostrow, Wittgenstein's Tractatus: A Dialectical Interpretation, Cambridge, 2002.
    Notre Dame Philosophical Reviews, 2003.01.14.
  • Review of E. Reck (ed.), From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy, Oxford, 2002.
    History and Philosophy of Logic 23 (2002): 297-300.

Preprints

• From Sunspots to the Southern Oscillation: Confirming Models of Large-Scale Phenomena in Meteorology
  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 to the competing hypotheses. I conclude that mathematical innovations provide crucial epistemic links between evidence and theories precisely because the evidence and theories are mathematically described.
• Mathematical Structural Realism
  Forthcoming in A. Bokulich & P. Bokulich (eds.), Scientific Structuralism, Boston Studies in the Philosophy of Science, Springer.
  Abstract: 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 our theories. Thinking about the role of mathematics in science may also complicate other versions of realism.

Work in Progress

• Book Project: The Value of Mathematics for Scientific Representation (updates here)
• Mathematics and Scientific Representation (Pittsburgh Lunchtime Colloquium)
  Abstract: One widespread, if not entirely universal, aspect of successful scientific representation is its mathematical character. Unfortunately, philosophers of science have paid little attention to the different sorts of contributions that mathematics makes and it proves a challenge to even formulate the issue in a useful way. Here I make a start on this task by posing the problem in a specific form and considering some potential solutions.
• The Value of Mathematics for Scientific Confirmation (PSA 2008 Symposium)
  Abstract: In some cases of scientific confirmation we can assign the boost in confirmation to an agent's belief in a mathematical theorem. Two examples are the application of statistics to data and the solution of an equation that was previously intractable. This raises a puzzle concerning how believing something that is necessarily true can help to give an agent a reason to believe something that is contingent. This puzzle is developed for two leading approaches to confirmation: subjective Bayesianism and Norton's "material" theory of induction. The paper concludes by proposing an alternative approach to confirmation based on an analysis of the content of the statements of applied mathematics.
• Idealization and Mathematical Tractability (2009 Central APA, Group Session)
• A Recipe for Avoiding Inconsistent Idealizations
  Contribution to a proposed volume Is Science Inconsistent?
• A Priori Contributions to Scientific Knowledge
  Abstract: 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 of their respective proposals.
• Towards a Philosophy of Applied Mathematics
  Forthcoming in O. Bueno & O. Linnebo (eds.), New Waves in Philosophy of Mathematics, Palgrave Macmillan.
  Abstract: 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 compared to much of mathematics. I argue that applied mathematics can contribute to the philosophy of mathematics and our understanding of mathematics as a whole.
• Modeling Reality
  Presented at Models and Simulations 2
  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 is illustrated using models from contemporary meteorology.

'Classics' from the Archives

• Author Meets Critics: Scott Soames, Philosophical Analysis in the Twentieth Century, Pacific APA (2006)
  My comments on volume 1. Other comments were by Michael Kremer, Paul Horwich and Thomas Hurka.
  Here are Soames' comments from the conference. See above for the related exchange in Russell.

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Contact me with your feedback at pincock@purdue.edu.