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186Carnap's logical structure of the worldPhilosophy Compass 4 (6): 951-961. 2009.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 wh…Read more
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45Torsten Wilholt, Zahl und Wirklichkeit: Eine philosophische Untersuchung über die Anwendbarkeit der Mathematik [Number and Reality: A Philosophical Investigation of the Applicability of Mathematics]. Paderborn: Mentis, 2004. Pp. 309. ISBN 3-89785-368-X (review)Philosophia Mathematica 13 (3): 329-337. 2005.
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10Accounting for the unity of experience in Dilthey, Rickert, Bradley and WardIn U. Feest (ed.), Historical Perspectives on Erklaren and Verstehen, Springer. pp. 187-206. 2010.Forthcoming in U. Feest (ed.), Historical Perspectives on Erkl.
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35Review of Matthew B. Ostrow, Wittgenstein's Tractatus: A Dialectical Interpretation (review)Notre Dame Philosophical Reviews 2003 (1). 2003.
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92On Batterman's 'On the Explanatory Role of Mathematics in Empirical Science'British Journal for the Philosophy of Science 62 (1). 2011.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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26Logicism and Principia Mathematica [review of William Demopoulos, Logicism and Its Philosophical Legacy (review)Russell: The Journal of Bertrand Russell Studies 35 (1): 82-87. 2015.In lieu of an abstract, here is a brief excerpt of the content:82 Reviews c:\users\arlene\documents\rj issues\type3501\rj 3501 061 red.docx 2015-07-10 4:07 PM LOGICISM BEYOND PRINCIPIA MATHEMATICA Chris Pincock Philosophy / Ohio State U. Columbus, oh 43210–1365, usa [email protected] William Demopoulos. Logicism and Its Philosophical Legacy. Cambridge: Cambridge U. P., 2013. Pp. xii, 272. isbn: 9781107029804.£60.00; us$104.99 (hb). his book brings together eight previously published essays along…Read more
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91Exploring the boundaries of conceptual evaluationPhilosophia Mathematica 18 (1): 106-121. 2010.This is a critical notice of Mark Wilson's Wandering Significance.
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16David Corfield, Towards a Philosophy of Real Mathematics. Cambridge: Cambridge University Press , 300 pp., $70.00 (review)Philosophy of Science 72 (4): 632-634. 2005.
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8Towards a Philosophy of Applied MathematicsIn Otávio Bueno & Øystein Linnebo (eds.), New Waves in Philosophy of Mathematics, Palgrave-macmillan. 2009.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 …Read more
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Preston on the Illusory Character of Analytic Philosophy (review)The Bertrand Russell Society Quarterly 136. 2007.
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43Sorin Bangu. The Applicability of Mathematics in Science: Indispensability and Ontology. Basingstoke: Palgrave Macmillan, 2012. ISBN 978-0-230-28520-0 . Pp. xiii + 252 (review)Philosophia Mathematica 22 (3): 401-412. 2014.
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72Mathematical models of biological patterns: Lessons from Hamilton’s selfish herdBiology and Philosophy 27 (4): 481-496. 2012.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 wh…Read more
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86How to avoid inconsistent idealizationsSynthese 191 (13): 2957-2972. 2014.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 oc…Read more
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43Comments on A. Casullo’s Essays on a priori knowledge and justificationPhilosophical Studies 173 (6): 1687-1694. 2016.
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230A Role for Mathematics in the Physical SciencesNoûs 41 (2): 253-275. 2007.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 math…Read more
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18Review of Nikolay Milkov, A Hundred Years of English Philosophy (review)Notre Dame Philosophical Reviews 2004 (10). 2004.
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46Overextending Partial Structures: Idealization and AbstractionPhilosophy of Science 72 (5): 1248-1259. 2005.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 i…Read more
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119Mathematics and Scientific RepresentationOxford University Press USA. 2012.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 scientific re…Read more
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73Fictions in Science: Philosophical Essays on Modeling and Idealization (review)International Studies in the Philosophy of Science 25 (2). 2011.International Studies in the Philosophy of Science, Volume 25, Issue 2, Page 196-199, June 2011
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15Carnap and the Unity of Science: 1921–1928In Thomas Bonk (ed.), Language, Truth and Knowledge, Kluwer Academic Publishers. pp. 87--96. 2003.
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97Russell’s Influence On Carnap’s AufbauSynthese 131 (1): 1-37. 2002.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…Read more
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47Innovations in the History of Analytical PhilosophyPalgrave-Macmillan. 2017.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 p…Read more
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70Mathematics, Science, and Confirmation TheoryPhilosophy of Science 77 (5): 959-970. 2010.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 intr…Read more
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48Ian Hacking why is there philosophy of mathematics at all? (review)British Journal for the Philosophy of Science 67 (3): 907-912. 2016.
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85A reserved reading of Carnap's aufbauPacific Philosophical Quarterly 86 (4). 2005.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 discipl…Read more
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25Review of Sajahan Miah, Russell's Theory of Perception (1905-1919) (review)Notre Dame Philosophical Reviews 2007 (3). 2007.
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68Platonism, Naturalism, and Mathematical Knowledge, by James Robert Brown (review)Mind 123 (492): 1174-1177. 2014.
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