What is the Difference Between a Definition and a Concept?
Science Journal of Education
Volume 4, Issue 5, October 2016, Pages: 159-168
Received: Sep. 21, 2016; Accepted: Oct. 1, 2016; Published: Oct. 27, 2016
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Michael F. Otte, University of Bielefeld, Bielefeld, Germany
Luiz G. X. de Barros, Universidade Anhanguera de São Paulo (UNIAN), São Paulo, Brasil
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Definitions are formulated in order to draw conclusions and to solve technical problems. Tinkering around as long as it takes, until something halfway interesting comes out or can be concluded. Definitions are cognitive and communicative functions in the first place. Concepts, in contrast, are like continua relations and visions of possibilities. Mathematics seems to be that area of intellectual activity, where the difference between concepts and definitions and consequently the difference between seeing something on the one hand and calculating it on the other hand, gapes apart most strongly and widely. In this article, we discuss this difference from several viewpoints.
Mathematics, Mathematics Education, Philosophy of Mathematics, Complementarity
To cite this article
Michael F. Otte, Luiz G. X. de Barros, What is the Difference Between a Definition and a Concept?, Science Journal of Education. Vol. 4, No. 5, 2016, pp. 159-168. doi: 10.11648/j.sjedu.20160405.14
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ARISTOTLE, Physics, book VI, chapter 9. Acessed on May, 25, 2015 in: http://classics.mit.edu/Aristotle/physics.6.vi.html
BARROW, J., 1992. Perche il mondo e matematico?. Roma: Editore Guis.
BATESON, G., 1980. Mind and Nature. Toronto: Bantam Books, Toronto.
BOLZANO, B., 1837: Wissenschaftslehre (WL), 4 vol., Sulzbach. Republication by W. Schultz, Leipzig 1929-31.
BYERS, W., 2007. How Mathematicians Think. Princeton UP.
DELEUZE, G. & GUATTARI, F., 1996. What is Philosophy?. Columbia University Press.
DUMMETT, M., 1991. Frege. Cambridge, MA: Harvard University Press.
FREGE, G., 1969. Funktion, Begriff, Bedeutung. Goettingen.
GREENE, D. H. & KUTH, D., 1981. Mathematics for the Analysis of Algorithms, Boston: Birkhäuser.
HAHN, H., 1988. Empirismus, Logik, Mathematik, Frankfurt: Suhrkamp.
HILBERT, D., 1964. Über das Unendliche. In: Hilbertiana, Darmstadt.
KANT, I., 1787. Critique of Pure Reason. English translation by Norman Kemp Smith, 1929. Palgrave Macmillan Pub.
KATZ, J. J., 2004. Sense, Reference and Philosophy. Oxford University Press.
KLEIN, S. B., 2014. The Two Selves, Oxford University Press
KUHN, T. S., 1996. The Structure of Scientific Revolutions. University of Chicago Press.
LAKATOS, I. (1970). Falsification and the methodology of science research programs. In Lakatos/Musgrave (Eds.), Criticism and the growth of knowledge. Cambridge UP.
LEIBNIZ, G. W., 1685. The Art of Discovery. In: (W51) Leibniz: Selections. Edited by Philip P. Wiener. New York: Charles Scribner's Sons, 1951.
LOVEJOY, A. O., 1964, The Great Chain of Being: A Study of the History of an Idea, Cambridge, Massachusetts: Harvard University Press.
MASANI, P. R., 1990. Norbert Wiener 1894–1964. Basel: Birkhäuser Verlag.
MAYR, E., 2001. What Evolution Is. New York: Basic Books.
NEWTON, I., 1729. Mathematical Principles of Natural Philosophy. Oxford University.
OTTE, M., 1994. Intuition and logic in mathematics. In: D.E. Robitaille, D. H. Wheeler and C. Kieran (eds.), Selected Lectures from the 7th International Congress on Mathematical Education, Les Presses de l’Université Laval, 271–284.
OTTE, M., 2003. Complementarity, sets and numbers. Educational Studies in Mathematics 53, 203–228.
OTTE, M. & STEINBRING, H., 1977. Probleme der Begriffsentwicklung. Didaktik der Mathematik 1, 16–25.
OTTE, M. & LENHARD, J., 2010. Two Types of Mathematization. In Bart Van Kerkhove, Jonas De Vuyst and Jean Paul Van Bendegem, Philosophical perspectives on mathematical practice. (pp. 301-330). London: College Publications, 2010.
PEIRCE, C. S. CP = Collected Papers of Charles Sanders Peirce, Volumes I-VI, ed. by Charles Hartshorne and Paul Weiß, Cambridge, Mass. (Harvard UP) 1931-1935, Volumes VII-VIII, ed. by Arthur W. Burks, Cambridge, Mass. (Harvard UP) 1958 (quoted by no. of volume and paragraph) NEM = Carolyn Eisele (ed.), The New Elements of Mathematics by Charles S. Peirce, Vol. I-IV, The Hague-Paris/Atlantic Highlands, N.J. (Mouton/Humanities Press)
PLANCK, M., 1936. The Philosophy of Physics, W.W. Norton Co.
POPPER, K., 1972. Objective Knowledge, Oxford University Press.
QUINE, W. V. O., 1974. Roots of Reference. La Salle: Open Court.
REICHENBACH, H., 1951. The Rise of Scientific Philosophy. Berkeley: University of California Press.
RORTY, R., 1979. Philosophy and the Mirror of Nature. Princeton, NJ: Princeton University Press.
RUCKER, R., 1982. Infinity and the Mind. Basel: Birkhäuser.
RUSSELL, B., 1919. Introduction to Mathematical Philosophy. London: Routledge.
SCHLICK, M., 1925. Epistemology & Modern Physics. Garland Publishing Inc.
SCHÜLING, H., 1969. Die Geschichte der axiomatischen Methode im 16. und beginnenden 17. Jahrhundert, Hildesheim.
SEARLE, J., 1980. Minds, Brains and Programs. In: Behavioral and Brain Sciences 3 (3). p. 417-457. Cambridge University Press.
SHANE, E., 2014. Turner. New York: Parkstone Press.
STEWART, M., 2006. The Courtier and the Heretic. New York: W. W. Norton.
STOLZENBERG, G., 1980. Can an Inquiry into the Foundations of Mathematics tell us anything interesting about the Mind. In: P. Watzlawik (ed.) Invented Reality, W. W. Norton Inc., pp 257-308
TUOMELA, R., 1973. Theoretical Concepts. Springer Wien.
TURNER, M., 2014, The Origin of Ideas, Oxford University Press.
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