|Abstract||Some philosophers of mathematics argue that the role of mathematical models in science is merely representational: when scientists use mathematical models they only believe that they are adequate representations of the physical phenomenon under investigation. Others disagree with this view and argue that mathematical models also serve as genuine explanations in science. Consequently, the application of mathematical models in science cannot be treated instrumentally and we ought to be realists about mathematics. I advance two reasons to reject realist conclusion: genuine mathematical explanations are indistinguishable from spurious ones. And, for mathematical models to be explanatory, they have to be “bottom-level”; I deny that we can know which explanations (if any) are bottom level in science. I contend that what plays the explanatory role is the impure function that links physical structures to mathematical structures.|
|Keywords||No keywords specified (fix it)|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Jay Odenbaugh (2005). Idealized, Inaccurate but Successful: A Pragmatic Approach to Evaluating Models in Theoretical Ecology. Biology and Philosophy 20 (2-3):231-255.
Axel Gelfert (2011). Mathematical Formalisms in Scientific Practice: From Denotation to Model-Based Representation. Studies in History and Philosophy of Science 42 (2):272-286.
Karlis Podnieks & John Tabak, The Nature of Mathematics – an Interview with Professor Karlis Podnieks.
Alan Baker (2009). Mathematical Explanation in Science. British Journal for the Philosophy of Science 60 (3):611-633.
Christian Hennig (2010). Mathematical Models and Reality: A Constructivist Perspective. Foundations of Science 15 (1).
Davide Rizza (2011). Magicicada, Mathematical Explanation and Mathematical Realism. Erkenntnis 74 (1):101-114.
Michael J. White (1992). The Continuous and the Discrete: Ancient Physical Theories From a Contemporary Perspective. Oxford University Press.
Alan Baker (2005). Are There Genuine Mathematical Explanations of Physical Phenomena? Mind 114 (454):223-238.
Added to index2009-01-28
Total downloads13 ( #88,037 of 549,701 )
Recent downloads (6 months)3 ( #25,807 of 549,701 )
How can I increase my downloads?