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  • Print publication year: 2017
  • Online publication date: July 2017

3 - Notes on the Syntax and Semantics Distinction, or Three Moments in the Life of the Mathematical Drawing

from Part II
Arana, A. (2016). Imagination in mathematics. In A. Kind (Ed.), The Routledge handbook of philosophy of imagination (pp. 463–477). Abingdon, UK: Routledge.
Austin, J. (1955/1962). How to do things with words. Oxford: Clarendon Press.
Avigad, J., Dean, E. & Mumma, J. (2009). A formal system for Euclid’s Elements. The Review of Symbolic Logic, 2(4), 700768.
Bolzano, B. (1992) Gesamtausgabe (Reihe I: Schriften, Band 13,3: Wissenschaftslehre §349–391) (Edited by J. Berg et al.). Stuttgart, Germany: Frommann-Holzboog.
Catton, P. & Montelle, C. (2012). To diagram, to demonstrate: to do, to see, and to judge in Greek geometry. Philosophia Mathematica, 20(1), 2557.
Coffa, A. (1991). The semantic tradition from Kant to Carnap: To the Vienna station. Cambridge: Cambridge University Press.
Courant, R. & Robbins, H. (1941). What is mathematics? An elementary approach to ideas and methods. Oxford: Oxford University Press.
Daston, L. & Galison, P. (1992). The image of objectivity. Representations, 40, 81128.
de Freitas, E. & Sinclair, N. (2012). Diagram, gesture, agency: Theorizing embodiment in the mathematics classroom. Educational Studies in Mathematics, 80(1/2), 133152.
Foucault, M. (1966/2009). The order of things: An archaeology of the human sciences. Abingdon, UK: Routledge.
Franks, C. (2014). Logical completeness, form, and content: An archaeology. In J. Kennedy (Ed.), Interpreting Gödel: Critical essays (pp. 78106). Cambridge: Cambridge University Press.
Freudenthal, H. (1962). The main trends of the foundations of geometry in the 19th century. In E. Nagel, P. Suppes & A. Tarski (Eds), Logic, methodology and philosophy of science (pp. 613–621). Palo Alto, CA: Stanford University Press.
Giaquinto, M. (2015). The epistemology of visual thinking in mathematics. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. (
Hilbert, D. (1899/2004). Die Grundlagen der Geometrie. In M. Hallett & U. Majer (Eds), David Hilbert’s lectures on the foundations of geometry 1891–1902 (pp. 436–525). New York: Springer.
Hilbert, D. & Cohn-Vossen, S. (1932/1952). Geometry and the imagination (trans. P. Neméyni). New York: Chelsea Publishing Co.
James, W. (1978). Pragmatism: A new name for some old ways of thinking. Cambridge, MA and London: Harvard University Press.
Jones, C. & Galison, P. (1998/2013). Introduction: Picturing science, producing art. In C. Jones & P. Galison (Eds), Picturing science, producing art (pp. 1–23). Abingdon, UK: Routledge.
Macbeth, D. (2014). Realizing reason: A narrative of truth and knowing. Oxford: Oxford University Press.
Manders, K. (1995/2008). The Euclidean diagram. In P. Mancosu (Ed.), The philosophy of mathematical practice (pp. 80–133). Oxford: Oxford University Press.
Nagel, E. (1939). The formation of modern conceptions of formal logic in the development of geometry. Osiris, 7, 142223.
Nemirovsky, R. & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies in Mathematics 70(2), 159174.
Netz, R. (1998). Greek mathematical diagrams: Their use and their meaning. For the Learning of Mathematics, 18(3), 3340.
Netz, R. (1999). The shaping of deduction in Greek mathematics: A study of cognitive history. Cambridge: Cambridge University Press.
Pallasmaa, J. (2009). The thinking hand: Existential and embodied wisdom in architecture. Chichester, UK: John Wiley & Sons.
Pasch, M. (1882). Vorlesungen über neuere Geometrie. Leipzig, Germany: Teubner.
Quine, W. (1951/1996). Two dogmas of empiricism. In A. Martinich (Eds), The philosophy of language (3rd edn, pp. 39–52). Oxford: Oxford University Press.
Roth, W.-M. (2010). Incarnation: Radicalizing the embodiment of mathematics. For the Learning of Mathematics, 30(2), 817.
Russ, S. (1980). A translation of Bolzano’s paper on the intermediate value theorem. Historia Mathematica, 7(2), 156–185.
Schlimm, D. (2010). Pasch’s philosophy of mathematics. The Review of Symbolic Logic, 3(1), 93–118.
Seidenberg, A. (1975). Did Euclid’s Elements, Book I, develop geometry axiomatically? Archive for History of Exact Sciences, 14(4), 263–295.
Shin, S. (1994). The logical status of diagrams. Cambridge: Cambridge University Press.
Shin, S., Lemon, O. & Mumma, J. (2014). Diagrams. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. (
Tarski, A. (1983, 2nd edn). Logic, semantics, metamathematics: Papers from 1923 to 1938. Indianapolis, IN: Hackett Publishing Co.
Tarski, A. & Vaught, R. (1958). Arithmetical extensions of relational systems. Compositio Mathematica, 13, 81–102.