Book contents
- What Is a Mathematical Concept?
- What Is a Mathematical Concept?
- Copyright page
- Contents
- Images
- Notes on Contributors
- Introduction
- Part I
- Part II
- 3 Notes on the Syntax and Semantics Distinction, or Three Moments in the Life of the Mathematical Drawing
- 4 Concepts as Generative Devices
- Part III
- Part IV
- Part V
- Part VI
- Part VII
- Part VIII
- Index
- References
3 - Notes on the Syntax and Semantics Distinction, or Three Moments in the Life of the Mathematical Drawing
from Part II
Published online by Cambridge University Press: 26 July 2017
Book contents
- What Is a Mathematical Concept?
- What Is a Mathematical Concept?
- Copyright page
- Contents
- Images
- Notes on Contributors
- Introduction
- Part I
- Part II
- 3 Notes on the Syntax and Semantics Distinction, or Three Moments in the Life of the Mathematical Drawing
- 4 Concepts as Generative Devices
- Part III
- Part IV
- Part V
- Part VI
- Part VII
- Part VIII
- Index
- References
- Type
- Chapter
- Information
- What is a Mathematical Concept? , pp. 55 - 75Publisher: Cambridge University PressPrint publication year: 2017
References
Arana, A. (2016). Imagination in mathematics. In A. Kind (Ed.), The Routledge handbook of philosophy of imagination (pp. 463–477). Abingdon, UK: Routledge.Google Scholar
Avigad, J., Dean, E. & Mumma, J. (2009). A formal system for Euclid’s Elements. The Review of Symbolic Logic, 2(4), 700–768.Google Scholar
Bolzano, B. (1992) Gesamtausgabe (Reihe I: Schriften, Band 13,3: Wissenschaftslehre §349–391) (Edited by J. Berg et al.). Stuttgart, Germany: Frommann-Holzboog.Google Scholar
Catton, P. & Montelle, C. (2012). To diagram, to demonstrate: to do, to see, and to judge in Greek geometry. Philosophia Mathematica, 20(1), 25–57.CrossRefGoogle Scholar
Coffa, A. (1991). The semantic tradition from Kant to Carnap: To the Vienna station. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Courant, R. & Robbins, H. (1941). What is mathematics? An elementary approach to ideas and methods. Oxford: Oxford University Press.Google Scholar
Daston, L. & Galison, P. (1992). The image of objectivity. Representations, 40, 81–128.CrossRefGoogle Scholar
de Freitas, E. & Sinclair, N. (2012). Diagram, gesture, agency: Theorizing embodiment in the mathematics classroom. Educational Studies in Mathematics, 80(1/2), 133–152.Google Scholar
Foucault, M. (1966/2009). The order of things: An archaeology of the human sciences. Abingdon, UK: Routledge.Google Scholar
Franks, C. (2014). Logical completeness, form, and content: An archaeology. In J. Kennedy (Ed.), Interpreting Gödel: Critical essays (pp. 78–106). Cambridge: Cambridge University Press.Google Scholar
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.Google Scholar
Giaquinto, M. (2015). The epistemology of visual thinking in mathematics. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. (https://plato.stanford.edu/archives/win2015/entries/epistemology-visual-thinking/)Google Scholar
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.Google Scholar
Hilbert, D. & Cohn-Vossen, S. (1932/1952). Geometry and the imagination (trans. P. Neméyni). New York: Chelsea Publishing Co.Google Scholar
James, W. (1978). Pragmatism: A new name for some old ways of thinking. Cambridge, MA and London: Harvard University Press.Google Scholar
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.Google Scholar
Macbeth, D. (2014). Realizing reason: A narrative of truth and knowing. Oxford: Oxford University Press.Google Scholar
Manders, K. (1995/2008). The Euclidean diagram. In P. Mancosu (Ed.), The philosophy of mathematical practice (pp. 80–133). Oxford: Oxford University Press.Google Scholar
Nagel, E. (1939). The formation of modern conceptions of formal logic in the development of geometry. Osiris, 7, 142–223.Google Scholar
Nemirovsky, R. & Ferrara, F. (2009). Mathematical imagination and embodied cognition. Educational Studies in Mathematics 70(2), 159–174.CrossRefGoogle Scholar
Netz, R. (1998). Greek mathematical diagrams: Their use and their meaning. For the Learning of Mathematics, 18(3), 33–40.Google Scholar
Netz, R. (1999). The shaping of deduction in Greek mathematics: A study of cognitive history. Cambridge: Cambridge University Press.Google Scholar
Pallasmaa, J. (2009). The thinking hand: Existential and embodied wisdom in architecture. Chichester, UK: John Wiley & Sons.Google Scholar
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.Google Scholar
Roth, W.-M. (2010). Incarnation: Radicalizing the embodiment of mathematics. For the Learning of Mathematics, 30(2), 8–17.Google Scholar
Russ, S. (1980). A translation of Bolzano’s paper on the intermediate value theorem. Historia Mathematica, 7(2), 156–185.Google Scholar
Schlimm, D. (2010). Pasch’s philosophy of mathematics. The Review of Symbolic Logic, 3(1), 93–118.Google Scholar
Seidenberg, A. (1975). Did Euclid’s Elements, Book I, develop geometry axiomatically? Archive for History of Exact Sciences, 14(4), 263–295.Google Scholar
Shin, S. (1994). The logical status of diagrams. Cambridge: Cambridge University Press.Google Scholar
Shin, S., Lemon, O. & Mumma, J. (2014). Diagrams. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy. (https://plato.stanford.edu/archives/win2014/entries/diagrams/)Google Scholar
Tarski, A. (1983, 2nd edn). Logic, semantics, metamathematics: Papers from 1923 to 1938. Indianapolis, IN: Hackett Publishing Co.Google Scholar
Tarski, A. & Vaught, R. (1958). Arithmetical extensions of relational systems. Compositio Mathematica, 13, 81–102.Google Scholar
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