Switch to: References

Add citations

You must login to add citations.
  1. Aspects of Mathematical Explanation: Symmetry, Unity, and Salience.Marc Lange - 2014 - Philosophical Review 123 (4):485-531.
    Unlike explanation in science, explanation in mathematics has received relatively scant attention from philosophers. Whereas there are canonical examples of scientific explanations, there are few examples that have become widely accepted as exhibiting the distinction between mathematical proofs that explain why some mathematical theorem holds and proofs that merely prove that the theorem holds without revealing the reason why it holds. This essay offers some examples of proofs that mathematicians have considered explanatory, and it argues that these examples suggest a (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   35 citations  
  • Road Work Ahead: Heavy Machinery on the Easy Road.M. Colyvan - 2012 - Mind 121 (484):1031-1046.
    In this paper I reply to Jody Azzouni, Otávio Bueno, Mary Leng, David Liggins, and Stephen Yablo, who offer defences of so-called ‘ easy road ’ nominalist strategies in the philosophy of mathematics.
    Direct download (8 more)  
     
    Export citation  
     
    Bookmark   44 citations  
  • 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 (...)
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   37 citations  
  • The Prospects for a Monist Theory of Non-Causal Explanation in Science and Mathematics.Alexander Reutlinger, Mark Colyvan & Karolina Krzyżanowska - forthcoming - Erkenntnis:1-21.
    We explore the prospects of a monist account of explanation for both non-causal explanations in science and pure mathematics. Our starting point is the counterfactual theory of explanation (CTE) for explanations in science, as advocated in the recent literature on explanation. We argue that, despite the obvious differences between mathematical and scientific explanation, the CTE can be extended to cover both non-causal explanations in science and mathematical explanations. In particular, a successful application of the CTE to mathematical explanations requires us (...)
    Direct download (3 more)  
    Translate
     
     
    Export citation  
     
    Bookmark   4 citations  
  • Pluralists About Pluralism? Versions of Explanatory Pluralism in Psychiatry.Jeroen Van Bouwel - 2014 - In M. C. Galavotti, D. Dieks, W. J. Gonzalez, S. Hartmann, Th Uebel & M. Weber (eds.), New Directions in Philosophy of Science (The Philosophy of Science in a European Perspective Series). Springer. pp. 105-119.
    In this contribution, I comment on Raffaella Campaner’s defense of explanatory pluralism in psychiatry (in this volume). In her paper, Campaner focuses primarily on explanatory pluralism in contrast to explanatory reductionism. Furthermore, she distinguishes between pluralists who consider pluralism to be a temporary state on the one hand and pluralists who consider it to be a persisting state on the other hand. I suggest that it would be helpful to distinguish more than those two versions of pluralism – different understandings (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Causal Explanation and Ontological Commitment.Mark Colyvan - 1999 - In Uwe Meixner Peter Simons (ed.), Metaphysics in the Post-Metaphysical Age. Austrian Ludwig Wittgenstein Society. pp. 1--141.
  • Indispensability Arguments in the Philosophy of Mathematics.Mark Colyvan - 2008 - Stanford Encyclopedia of Philosophy.
    One of the most intriguing features of mathematics is its applicability to empirical science. Every branch of science draws upon large and often diverse portions of mathematics, from the use of Hilbert spaces in quantum mechanics to the use of differential geometry in general relativity. It's not just the physical sciences that avail themselves of the services of mathematics either. Biology, for instance, makes extensive use of difference equations and statistics. The roles mathematics plays in these theories is also varied. (...)
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   47 citations