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• W1567404991 abstract "DialecticaVolume 63, Issue 4 p. 381-395 Vectors and Beyond: Geometric Algebra and its Philosophical Significance Peter SIMONS, Peter SIMONS Department of Philosophy, Trinity College Dublin, Dublin 2, Ireland; Email: [email protected]Search for more papers by this author Peter SIMONS, Peter SIMONS Department of Philosophy, Trinity College Dublin, Dublin 2, Ireland; Email: [email protected]Search for more papers by this author First published: 25 February 2010 https://doi.org/10.1111/j.1746-8361.2009.01214.xCitations: 2Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL References Altmann, S. 1986, Quaternions, Rotations and Double Groups, Oxford: Oxford University Press. Altmann, S. 1989, ‘Hamilton, Rodrigues, and the Quaternion Scandal’, Mathematics Magazine 62, pp. 291– 308. Altmann, S. 1992, Icons and Symmetry, Oxford: Oxford University Press. Altmann, S. and Ortiz, E. (eds.) 2005, Mathematics and Social Utopias in France: Olinde Rodrigues and his Times, Providence: American Mathematical Society. Baker, A. 2005, ‘Are there Genuine Mathematical Explanations of Physical Phenomena?’, Mind 114, pp. 223– 238. Bangu, S. I. 2008, ‘Inference to the Best Explanation and Mathematical Realism’, Synthese 160, pp. 13– 20. Batterman, R. 2002, The Devil in the Details. Asymptotic Reasoning in Explanation, Reduction, and Emergence, Oxford: Oxford University Press. Clifford, W. K. 1878, ‘Applications of Grassmann's Extensive Algebra’, American Journal of Mathematics 1, pp. 350– 358. Clifford, W. 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G. 1840, Theorie der Ebbe und Flut (dissertation), reprinted in Grassmann (1894–1911), Vol. 3. Grassmann, H. G. 1844, Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik dargestellt and durch Anwendungen auf die ubrigen Zweige der Mathematik, wie auch auf der Statik, Mechanik, die Lehre vom Magnetismus und die Krystallonomie erläutert, Leipzig: Wigand (reprinted 1878), reprinted in Grassmann (1894–1911), Vol. 1. Grassmann, H. G. 1862, Die Ausdehnungslehre: vollständig und in strenger Form bearbeitet, Berlin: Enslin, reprinted in Grassmann (1894– 1911), Vol. 1. Grassmann, H. G. 18941911, Gesammelte mathematische und physikalische Werke, in 3 vols., F. Engel, ed., Leipzig: Teubner, reprinted 1972, New York: Johnson. Grassmann, H. G. 1995, A New Branch of Mathematics. The Ausdehnungslehre of 1844 and Other Works, trans. by L. C. Kannenberg, Chicago: Open Court. Hestenes, D. 1966, Space-Time Algebra, New York: Gordon and Breach. Hestenes, D. 1986, New Foundations for Classical Mechanics, Dordrecht: Kluwer, second edition 1999. Hestenes, D. 1990, ‘The Zitterbewegung Interpretation of Quantum Mechanics’. Foundations of Physics 20, pp. 1213– 1232. Hestenes, D. 2003, Oersted Lecture 2002: ‘Reforming the Mathematical Language of Physics’, American Journal of Physics 71, pp. 104– 121. Hestenes, D. and Sobczyk, G. 1984, Clifford Algebra to Geometric Calculus: a Unified Language for Mathematics and Physics, Dordrecht: Reidel. Kline, R. R. 1992, Steinmetz: Engineer and Socialist, Baltimore: Johns Hopkins University Press. Kuipers, J. P. 2002, Quaternions and Rotation Sequences: A Primer with Applications to Orbits, Aerospace and Virtual Reality, Princeton: Princeton University Press. Lyon, A. and M. Colyvan 2007, ‘The Explanatory Power of Phase Spaces’, Philosophia Mathematica 16, pp. 227– 243. Mancosu, P. 2008, ‘Explanation in Mathematics’, in: E. N. Zalta, ed., The Stanford Encyclopedia of Philosophy (Fall 2008 Edition), URL=<http://plato.stanford.edu/archives/fall2008/entries/mathematics-explanation/>. Melia, J. 2000, ‘Weaseling Away the Indispensability Argument’, Mind 109, pp. 455– 479. Melia, J. 2002, Response to Colyvan, Mind 111, pp. 75– 79. Schrödinger, E. 1930, ‘Über die kräftefreie Bewegung in der relativistischen Quantenmechanik’, Berliner Berichte, pp. 418– 428. Schrödinger, E. 1931, ‘Zur Quantendynamik des Elektrons’, Berliner Berichte, pp. 63– 72. Steiner, M. 1998, The Applicability of Mathematics as a Philosophical Problem, Cambridge MA: Harvard University Press. Steiner, M. 2005, ‘Mathematics – Applications and Applicability’, in: S. Shapiro, ed., The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford: Oxford University Press, pp. 625– 650. Whitehead, A. N. 1898, A Treatise on Universal Algebra, with Applications, Cambridge: Cambridge University Press, reprinted New York: Hafner, 1960. Wigner, E. 1967, ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’, in: Symmetries and Reflections, Bloomington: Indiana University Press, pp. 222– 237. Citing Literature Volume63, Issue4Special Issue: The Philosophy of Vectors. Guest Editors: Philipp Keller, Stephan LeuenbergerDecember 2009Pages 381-395 ReferencesRelatedInformation" @default.
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