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  1. The Enhanced Indispensability Argument: Representational Versus Explanatory Role of Mathematics in Science.Juha Saatsi - 2011 - British Journal for the Philosophy of Science 62 (1):143-154.
    The Enhanced Indispensability Argument (Baker [ 2009 ]) exemplifies the new wave of the indispensability argument for mathematical Platonism. The new wave capitalizes on mathematics' role in scientific explanations. I will criticize some analyses of mathematics' explanatory function. In turn, I will emphasize the representational role of mathematics, and argue that the debate would significantly benefit from acknowledging this alternative viewpoint to mathematics' contribution to scientific explanations and knowledge.
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  • Word and Object.Henry W. Johnstone - 1961 - Philosophy and Phenomenological Research 22 (1):115-116.
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  • The Indispensability of Mathematics.Mark Colyvan - 2001 - Oxford, England: Oxford University Press.
    This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
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  • Mathematics and Aesthetic Considerations in Science.Mark Colyvan - 2002 - Mind 111 (441):69-74.
  • 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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  • 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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  • Where Mathematics Comes From How the Embodied Mind Brings Mathematics Into Being.George Lakoff & Rafael E. Núñez - 2000
  • Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - Oxford, England and New York, NY, USA: Oxford University Press.
    Many philosophers claim to be naturalists, but there is no common understanding of what naturalism is. Maddy proposes an austere form of naturalism called 'Second Philosophy', using the persona of an idealized inquirer, and she puts this method into practice in illuminating reflections on logical truth, philosophy of mathematics, and metaphysics.
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  • Second Philosophy: A Naturalistic Method.Penelope Maddy - 2007 - Oxford, England and New York, NY, USA: Oxford University Press.
    Many philosophers these days consider themselves naturalists, but it's doubtful any two of them intend the same position by the term. In Second Philosophy, Penelope Maddy describes and practices a particularly austere form of naturalism called "Second Philosophy". Without a definitive criterion for what counts as "science" and what doesn't, Second Philosophy can't be specified directly ("trust only the methods of science" for example), so Maddy proceeds instead by illustrating the behaviors of an idealized inquirer she calls the "Second Philosopher". (...)
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  • Scientific Realism and Mathematical Nominalism: A Marriage Made in Hell.Mark Colyvan - unknown
    The Quine-Putnam Indispensability argument is the argument for treating mathematical entities on a par with other theoretical entities of our best scientific theories. This argument is usually taken to be an argument for mathematical realism. In this chapter I will argue that the proper way to understand this argument is as putting pressure on the viability of the marriage of scientific realism and mathematical nominalism. Although such a marriage is a popular option amongst philosophers of science and mathematics, in light (...)
     
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  • Platonism, Naturalism, and Mathematical Knowledge.James Robert Brown - 2011 - Routledge.
    This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does (...)
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  • The Question of Ontology.Kit Fine - 2009 - In David Chalmers, David Manley & Ryan Wasserman (eds.), Metametaphysics: New Essays on the Foundations of Ontology. Oxford University Press. pp. 157--177.
  • Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
     
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  • Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2000 - Philosophical Quarterly 50 (198):120-123.
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