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Alan Baker [32]Alan Rh Baker [1]Alan Richard Baker [1]
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Alan Baker
Swarthmore College
  1. Are There Genuine Mathematical Explanations of Physical Phenomena?Alan Baker - 2005 - Mind 114 (454):223-238.
    Many explanations in science make use of mathematics. But are there cases where the mathematical component of a scientific explanation is explanatory in its own right? This issue of mathematical explanations in science has been for the most part neglected. I argue that there are genuine mathematical explanations in science, and present in some detail an example of such an explanation, taken from evolutionary biology, involving periodical cicadas. I also indicate how the answer to my title question impacts on broader (...)
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  2. Mathematical Explanation in Science.Alan Baker - 2009 - British Journal for the Philosophy of Science 60 (3):611-633.
    Does mathematics ever play an explanatory role in science? If so then this opens the way for scientific realists to argue for the existence of mathematical entities using inference to the best explanation. Elsewhere I have argued, using a case study involving the prime-numbered life cycles of periodical cicadas, that there are examples of indispensable mathematical explanations of purely physical phenomena. In this paper I respond to objections to this claim that have been made by various philosophers, and I discuss (...)
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  3. Science-Driven Mathematical Explanation.Alan Baker - 2012 - Mind 121 (482):243-267.
    Philosophers of mathematics have become increasingly interested in the explanatory role of mathematics in empirical science, in the context of new versions of the Quinean ‘Indispensability Argument’ which employ inference to the best explanation for the existence of abstract mathematical objects. However, little attention has been paid to analysing the nature of the explanatory relation involved in these mathematical explanations in science (MES). In this paper, I attack the only articulated account of MES in the literature (an account sketched by (...)
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  4. Indexing and Mathematical Explanation.Alan Baker & Mark Colyvan - 2011 - Philosophia Mathematica 19 (3):323-334.
    We discuss a recent attempt by Chris Daly and Simon Langford to do away with mathematical explanations of physical phenomena. Daly and Langford suggest that mathematics merely indexes parts of the physical world, and on this understanding of the role of mathematics in science, there is no need to countenance mathematical explanation of physical facts. We argue that their strategy is at best a sketch and only looks plausible in simple cases. We also draw attention to how frequently Daly and (...)
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  5. Simplicity.Alan Baker - 2008 - Stanford Encyclopedia of Philosophy.
  6.  88
    Parsimony and Inference to the Best Mathematical Explanation.Alan Baker - 2016 - Synthese 193 (2).
    Indispensability-based arguments for mathematical platonism are typically motivated by drawing an analogy between abstract mathematical objects and concrete scientific posits. In this paper, I argue that mathematics can sometimes help to reduce our concrete ontological, ideological, and structural commitments. My focus is on optimization explanations, and in particular the case study involving periodical cicadas. I argue that in this case, stronger mathematical apparatus yields explanations that have fewer concrete commitments. The nominalist cannot accept these more parsimonious explanations without embracing the (...)
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  7. Experimental Mathematics.Alan Baker - 2008 - Erkenntnis 68 (3):331-344.
    The rise of the field of “ experimental mathematics” poses an apparent challenge to traditional philosophical accounts of mathematics as an a priori, non-empirical endeavor. This paper surveys different attempts to characterize experimental mathematics. One suggestion is that experimental mathematics makes essential use of electronic computers. A second suggestion is that experimental mathematics involves support being gathered for an hypothesis which is inductive rather than deductive. Each of these options turns out to be inadequate, and instead a third suggestion is (...)
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  8.  44
    Mathematical Spandrels.Alan Baker - 2017 - Australasian Journal of Philosophy 95 (4):779-793.
    The aim of this paper is to open a new front in the debate between platonism and nominalism by arguing that the degree of explanatory entanglement of mathematics in science is much more extensive than has been hitherto acknowledged. Even standard examples, such as the prime life cycles of periodical cicadas, involve a penumbra of mathematical features whose presence can only be explained using relatively sophisticated mathematics. I introduce the term ‘mathematical spandrel’ to describe these penumbral properties, and focus on (...)
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  9. The Indispensability Argument and Multiple Foundations for Mathematics.Alan Baker - 2003 - Philosophical Quarterly 53 (210):49–67.
    One recent trend in the philosophy of mathematics has been to approach the central epistemological and metaphysical issues concerning mathematics from the perspective of the applications of mathematics to describing the world, especially within the context of empirical science. A second area of activity is where philosophy of mathematics intersects with foundational issues in mathematics, including debates over the choice of set-theoretic axioms, and over whether category theory, for example, may provide an alternative foundation for mathematics. My central claim is (...)
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  10.  46
    Mathematics and Explanatory Generality.Alan Baker - 2017 - Philosophia Mathematica 25 (2):194-209.
    According to one popular nominalist picture, even when mathematics features indispensably in scientific explanations, this mathematics plays only a purely representational role: physical facts are represented, and these exclusively carry the explanatory load. I think that this view is mistaken, and that there are cases where mathematics itself plays an explanatory role. I distinguish two kinds of explanatory generality: scope generality and topic generality. Using the well-known periodical-cicada example, and also a new case study involving bicycle gears, I argue that (...)
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  11. Mathematical Induction and Explanation.Alan Baker - 2010 - Analysis 70 (4):681-689.
  12. Mathematics, Indispensability and Scientific Progress.Alan Baker - 2001 - Erkenntnis 55 (1):85-116.
  13. Science and Mathematics: The Scope and Limits of Mathematical Fictionalism. [REVIEW]Christopher Pincock, Alan Baker, Alexander Paseau & Mary Leng - 2012 - 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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  14.  58
    Non-Deductive Methods in Mathematics.Alan Baker - 2010 - Stanford Encyclopedia of Philosophy.
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  15.  71
    Complexity Unfavoured.Alan Baker - 2008 - Analysis 68 (1):85–88.
  16. Drinking Discretely: Parsons's Old Peculiar.Alan Baker - 2007 - Analysis 67 (4):318–321.
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  17.  72
    No Reservations Required? Defending Anti-Nominalism.Alan Baker - 2010 - Studia Logica 96 (2):127-139.
    In a 2005 paper, John Burgess and Gideon Rosen offer a new argument against nominalism in the philosophy of mathematics. The argument proceeds from the thesis that mathematics is part of science, and that core existence theorems in mathematics are both accepted by mathematicians and acceptable by mathematical standards. David Liggins (2007) criticizes the argument on the grounds that no adequate interpretation of “acceptable by mathematical standards” can be given which preserves the soundness of the overall argument. In this discussion (...)
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  18.  45
    Complexity, Networks, and Non-Uniqueness.Alan Baker - 2013 - Foundations of Science 18 (4):687-705.
    The aim of the paper is to introduce some of the history and key concepts of network science to a philosophical audience, and to highlight a crucial—and often problematic—presumption that underlies the network approach to complex systems. Network scientists often talk of “the structure” of a given complex system or phenomenon, which encourages the view that there is a unique and privileged structure inherent to the system, and that the aim of a network model is to delineate this structure. I (...)
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  19. Is There a Problem of Induction for Mathematics?Alan Baker - 2007 - In M. Potter (ed.), Mathematical Knowledge. Oxford University Press. pp. 57-71.
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  20.  75
    Are the Laws of Nature Deductively Closed?Alan Baker - 1999 - In H. Sankey (ed.), Causation and Laws of Nature. Kluwer Academic Press. pp. 91--109.
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  21. Malebranche on Laws of Nature and God’s General Volitions.Alan Baker - 2004 - Logical Analysis and History of Philosophy 7.
    According to Malebranche’s occasionalism, all cases of causation in the world are due to the action of God’s will. These actions are divided into "particular volitions" and "general volitions". There has been sharp disagreement in the secondary literature concerning the nature of general volitions, for Malebranche. One side claims that general volitions are volitions of wide scope which cover a multiplicity of potential situations. The other side claims that general volitions are specific but fall under the scope of broader laws (...)
     
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  22.  26
    Russell Marcus. Autonomy Platonism and the Indispensability Argument.Alan Baker - 2016 - Philosophia Mathematica 24 (3):422-424.
  23.  43
    Christopher Pincockmathematics and Scientific Representation.Alan Baker - 2015 - British Journal for the Philosophy of Science 66 (3):695-699.
  24.  45
    Malebranche's Occasionalism.Alan Baker - 2005 - American Catholic Philosophical Quarterly 79 (2):251-272.
    The core thesis of Malebranche’s doctrine of occasionalism is that God is the sole true cause, where a true cause is one that has the power to initiate change and for which the mind perceives a necessary connection between it and its effects. Malebranche gives two separate arguments for his core thesis, T, based on necessary connection and on divine power respectively. The standard view is that these two arguments are necessary to establish T. I argue for a reinterpretation of (...)
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  25.  14
    Robert Arthur Donkin 1928-2006.Alan Rh Baker - 2011 - In Proceedings of the British Academy, Volume 172, Biographical Memoirs of Fellows, X. pp. 115.
    Robin Donkin was an exceptional scholar in the field of historical geography, particularly concerning Latin America and the domestication of plants and animals globally. His early research was on the effect of the Cistercians on medieval landscape, and he held posts at the University of Edinburgh and the University of Brimingham. Donkin then lectured in Latin American geography at the University of Cambridge. He was a Fellow of Jesus College, Cambridge and was elected as a Fellow of the British Academy (...)
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  26.  58
    Putting Expectations in Order.Alan Baker - 2007 - Philosophy of Science 74 (5):692-700.
    In their paper, “Vexing Expectations,” Nover and Hájek (2004) present an allegedly paradoxical betting scenario which they call the Pasadena Game (PG). They argue that the silence of standard decision theory concerning the value of playing PG poses a serious problem. This paper provides a threefold response. First, I argue that the real problem is not that decision theory is “silent” concerning PG, but that it delivers multiple conflicting verdicts. Second, I offer a diagnosis of the problem based on the (...)
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  27.  20
    A Medley of Philosophy of Mathematics.Alan Baker - 2010 - Metascience 19 (2):221-224.
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  28.  20
    The Foundations of Mathematics in the Theory of Sets.Alan Baker - 2002 - Australasian Journal of Philosophy 80 (4):533-534.
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  29.  33
    Book Review: Charles S. Chihara. A Structural Account of Mathematics. [REVIEW]Alan Baker - 2006 - Notre Dame Journal of Formal Logic 47 (3):435-442.
  30.  3
    Malebranche’s Occasionalism: A Strategic Reinterpretation.Alan Baker - 2005 - American Catholic Philosophical Quarterly 79 (2):251-272.
    The core thesis of Malebranche’s doctrine of occasionalism is that God is the sole true cause, where a true cause is one that has the power to initiate change and for which the mind perceives a necessary connection between it and its effects. Malebranche gives two separate arguments for his core thesis, T, based on necessary connection and on divine power respectively. The standard view is that these two arguments are necessary to establish T. I argue for a reinterpretation of (...)
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  31. Complex Thinking: The Emergence of Everything?Alan Baker - 2006 - The Baltic International Yearbook of Cognition, Logic and Communication 2.
     
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  32. Indispensibility and the Multiple Reducibility of Mathematical Objects.Alan Baker - manuscript
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  33. Maximizing Principles and Mathematical Methodology.Alan Baker - 2002 - Logique Et Analyse 45.