Banner Portal
Making the mathematical world
PDF (English)


Construtivismo social
Dependente da prática
Julian Cole
John Searle

Como Citar

SCHMIDT, J. V. . Making the mathematical world: on julian cole’s institutional account of mathematics. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 45, n. 4, p. 36–78, 2023. Disponível em: Acesso em: 25 set. 2023.


Even though it is obvious that mathematics involves social activities, this rather trivial fact is rarely considered as important for its subject matter, mostly due to its undesired ontological consequences. An attempted solution for this tension was developed by Julian Cole’s institutional account of mathematics, named Practice- Dependent Realism. In the present paper, Cole’s account is evaluated, and its lights and shadows assessed concerning the ontological problem that he seeks to solve. I argue that his institutional account, although failing in delivering a sufficient ontological account of mathematics, still opens an important linguistic route for explaining its practice.

PDF (English)


BENACERRAF, P. “What Numbers Could not Be”. The Philosophical Review. 74, 1, pp.47-73, 1965.

CLARKE-DOANE, Justin. Morality and Mathematics. Oxford: Oxford University Press, 2020.

CLARKE-DOANE. Mathematics and Metaphilosophy. Cambridge: Cambridge University Press. Forthcoming.

COLE, J. “Mathematical Domains: Social Constructs?” In: GOLD, B. & SIMONS, R. (Eds). Proof and Other Dilemmas: Mathematics and Philosophy. Mathematics Association of America, 2008.

COLE, J. “Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics.”Australasian Journal of Philosophy. 87, 4, pp.589-608, 2009.

COLE, J. “Towards an Institutional Account of the Objectivity, Necessity, and Atemporality of Mathematics.” Philosophia Mathematica. 21, 1, 08, pp.9-36, 2013.

COLE, J. “Social Construction, Mathematics, and the Collective Imposition of Function onto Reality” Erkenntnis. 80, 6, p.1101-1124. 2015.

DIETERLE, J. “Social Construction in the Philosophy of Mathematics: A Critical Evaluation of Julian Cole’s Theory.” Philosophia Mathematica. 18, 3, pp.311-328, 2010.

ERNEST, P. Social Constructivism as a Philosophy of Mathematics. Albany: State University of New York Press, 1998.

EWALD, W. B. From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford: Oxford University Press, 1996.

FREGE, G. Die Grundlagen der Arithmetik: Eine logisch mathematische Untersuchung über den Begriff der Zahl. Breslau: Verlag, 1884. Transl. by J. Austin, Oxford: Blackwell, 1953.

HARDY, G. H. A Mathematician’s Apology. Cambridge: Cambridge University Press, 1992.

HERSH, R. What is Mathematics, Really? Oxford: Oxford University Press, 1997.

KITCHER, P. The Nature of Mathematical Knowledge. Oxford: Oxford University Press, 1984.

LAKATOS, I. Proofs and Refutations: The Logic of Mathematical Discovery. Cambridge: Cambridge University Press, 1976.

LINNEBO, Ø. "Platonism in the Philosophy of Mathematics", The Stanford Encyclopedia of Philosophy, Spring 2018. Edward N. Zalta (ed.), URL =

LOGAN, S. A. “The Semantics of Social Constructivism”. Synthese 192, 8, pp.2577-2598, 2015.

MANCOSU, P., (Ed.) The Philosophy of Mathematical Practice. Oxford: Oxford University Press, 2008.

PUTNAM, H. “Philosophy of Mathematics: Why Nothing Works” In: PUTNAM, H. Words and Life. Harvard: Harvard University Press, 1995. pp.499-512.

QUINE, W. V. “Truth by Convention”. In: Philosophical essays for Alfred North Whitehead. New York: Longman, Green, & Company Inc, 1936. pp.90-124.

RUFFINO, M., SAN MAURO, L., and VENTURI, G. “At Least one Black Sheep: Pragmatics and the Language of Mathematics” Journal of Pragmatics. 160, pp.114- 110, 2020.

RUFFINO, M., SAN MAURO, L., and VENTURI, G. “Speech Acts in Mathematics”. Synthese, 198, 10, pp.10063-10087, 2021.

RUSSELL, B. & WHITEHEAD, A. N. Principia Mathematica. Volume 1. Cambridge: Cambridge University Press, 1910.

SEARLE, J. “A Taxonomy of Illocutionary Acts.” In: SEARLE, J. Expression and Meaning: Studies in the Theory of Speech Acts. Cambridge: Cambridge University Press, 1979.

SEARLE, J. The Construction of Social Reality. New York: The Free Press, 1995.

SEARLE, J. Making the Social World: The Structure of Human Civilization. Oxford: Oxford University Press, 2010.

SHAPIRO, S. Philosophy of Mathematics: Structure and Ontology. Oxford: Oxford University Press, 1997.

SHAPIRO, S. “We hold these Truths to be Self-Evident: but what do we mean by that?” The Review of Symbolic Logic. v.2, n.1. pp.175-206. 2009.

Creative Commons License
Este trabalho está licenciado sob uma licença Creative Commons Attribution 4.0 International License.

Copyright (c) 2022 Manuscrito: Revista Internacional de Filosofia


Não há dados estatísticos.