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Part IV

Published online by Cambridge University Press:  26 July 2017

Edited by
Elizabeth de Freitas ,
Nathalie Sinclair  and
Alf Coles
Elizabeth de Freitas
Affiliation:
Manchester Metropolitan University
Nathalie Sinclair
Affiliation:
Simon Fraser University, British Columbia
Alf Coles
Affiliation:
University of Bristol
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What is a Mathematical Concept? , pp. 123 - 158
Publisher: Cambridge University Press
Print publication year: 2017

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References

References

Baez, J. & Dolan, J. (2001). From finite sets to Feynman diagrams. In B. Engquist and W. Schmid (Eds.), Mathematics Unlimited – 2001 and Beyond, vol. 1, (pp. 29–50) Berlin: Springer. arXiv preprint: http://arxiv.org/abs/math/0004133.Google Scholar
Borovik, A. (2005). What is it that makes a mathematician?, www.maths.manchester.ac.uk/avb/pdf/WhatIsIt.pdf
Chang, H. (2009). We have never been whiggish (about phlogiston), Centaurus, 51(4), 239–264.CrossRefGoogle Scholar
Corfield, D. (1997). Assaying Lakatos’s philosophy of mathematics. Studies in History and Philosophy of Science Part A, 28(1), 99–121.CrossRefGoogle Scholar
Corfield, D. (1998). Beyond the methodology of mathematics research programmes. Philosophia Mathematica, 6(3), 272–301.Google Scholar
Corfield, D. (2001). The importance of mathematical onceptualisation. Studies in History and Philosophy of Science Part A, 32(3), 507–533.CrossRefGoogle Scholar
Corfield, D. (2003). Towards a philosophy ofreal mathematics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Corfield, D. (2015). Duality as a category-theoretic concept. Studies in the History and Philosophy of Modern Physics, doi:10.1016/j.shpsb.2015.07.004Google Scholar
Corfield, D. (forthcoming). Reviving the philosophy of geometry. In Landry, E. (Ed.), Categories for the working philosopher. Oxford: Oxford University Press.
Dummett, M. (1991). The logical basis of metaphysics. London: Duckworth.Google Scholar
Harper, R. (2013). Computational trinitarianism. www.doc.ic.ac.uk/gds/PLMW/harper-plmw13-talk.pdf
Harris, M. (2008). Why mathematics you may ask? In Gowers, T. et al. (Eds.), Princeton companion to mathematics (pp. 966–977). Princeton, NJ: Princeton University Press.Google Scholar
Licata, D. & Shulman, M. (2013). Calculating the fundamental group of the circle in homotopy type theory. In LICS 2013: Proceedings of the Twenty-Eighth Annual ACM/IEEE Symposium on Logic in Computer Science, pp. 223–232.CrossRef
Lurie, J. (2009a). Higher Topos theory. Princeton, NJ: Princeton University Press.Google Scholar
Lurie, J. (2009b). Derived algebraic geometry V: Structured spaces, arXiv preprint: http://arxiv.org/abs/0905.0459
Martin-Löf, P. (1984). Intuitionistic type theory. Napoli: Bibliopolis.Google Scholar
Schreiber, U. (2013). Differential cohomology in a cohesive-topos, arXiv preprint: http://arxiv.org/abs/1310.7930.
Schreiber, U. (2014). Quantization via linear homotopy types, arXiv preprint: http://arxiv.org/abs/1402.7041.
Schreiber, U. (forthcoming). Higher prequantum geometry. In G. Catren and M. Anel (Eds.), New spaces in mathematics and physics.
Shapere, D. (1987). Method in the philosophy of science and epistemology. In Nersessian, Nancy J. (Ed.), The process of science: Contemporary philosophical approaches to understanding scientific practice (pp. 1–39). Dordrecht: Martinus Nijhoff.Google Scholar
Shapere, D. (1989). Evolution and continuity in scientific change. Philosophy of Science, 56(3), 419–437.CrossRefGoogle Scholar
Shulman, M. (2015). Brouwer’s fixed-point theorem in real-cohesive homotopy type theory, arXiv preprint: http://arxiv.org/abs/1509.07584.
Shulman, M. (forthcoming). Homotopy type theory: A synthetic approach to higher equalities. In Landry, E. (Ed.), Categories for the working philosopher. Oxford University Press. arXiv preprint: http://arxiv.org/abs/1601.05035.
Tappenden, J. (1995). Extending Knowledge and ‘Fruitful Concepts’: Fregean Themes in the Foundations of Mathematics. Nous, 29(4), 427–467.CrossRefGoogle Scholar
Univalent Foundations Program (2014). Homotopy type theory.
Wilson, M. (2006). Wandering significance. Oxford: Oxford University Press.CrossRefGoogle Scholar

References

Faltings, G. (1988). p-adic Hodge theory. Journal of the American Mathematical Society, 1(1), 255–299.Google Scholar
Gabber, O. & Ramero, L. (2003). Almost ring theory. Berlin: Springer Verlag.CrossRefGoogle Scholar
Grothendieck, A. (1966). On the de Rham cohomology of algebraic varieties. Publications mathématiques de l’IHÉS, 29(1), 95–103.CrossRef
Harris, M., Lan, K., Taylor, R. & Thorne, J. (2016). On the rigid cohomology of certain Shimura varieties. Research in the Mathematical Sciences, 3(1), #37.CrossRef
McLarty, C. (2010). What does it take to prove Fermat’s last theorem? Grothendieck and the logic of number theory. The Bulletin of Symbolic Logic, 16(3), 359–377.CrossRef
Scholze, P. (2012). Perfectoid spaces. Publications mathématiques de l’IHÉS, 116(1), 245–313.CrossRef

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