The Fictionalist Concept of Numbers: A Critique

  • Etorobong Godwin Akpan Department of Philosophy, University of Port Harcourt
  • Victor Chizi Ihunda Department of Philosophy, University of Port Harcourt
DOI: https://doi.org/10.17605/ijie.v6i3.4184
Keywords: fictionalist, concept, numbers

Abstract

The philosophy of mathematics is primarily concerned with the meaning of ordinary mathematical sentences and the question of whether abstract mathematical objects exist, with the objectives of strengthening the mathematical theory and aiding mathematics education. On the existence of mathematical objects, positions advanced have tended to crystallise in a number of oppositions. We find Platonists who believe in the existence of abstract mathematical entities, as opposed to fictionalists who deny the existence of such entities and attempt to strip mathematics of its abstract qualities. We also find realists who believe in the objective mind-independence of mathematical truth-values, who are opposed by various types of anti-realists or fictionalists. We investigate the ontological mathematical divide between mathematical fictionalists and mathematical realists using critical analysis as our method. This conflict includes the question of the existence of abstract mathematical objects and entities, as well as their epistemological justification, if they exist at all. We further upheld mathematical realism based on its ability to prove mathematical objectivity, apodictic, a priori knowledge and promote ease in mathematics education.

References

1. Antonelli, A. (2016). Semantic Nominalism: How I Learned to Stop Worrying and Love Universals. In F. Boccuni and A. Sereni (Eds.), Objectivity, Realism, and Proof FilMat Studies in the Philosophy of Mathematics. Springer International Publishing Switzerland.
2. Balaguer, M.(2018). Fictionalism in the Philosophy of Mathematics. In Edward N. Zalta (Ed.) The Stanford Encyclopedia of Philosophy, http://plato.standford.edu/archives/fall2018/entries/fictionalism-mathematics
3. Benacerraf, P. (1983). What Numbers could not Be. In P. Benacerraf and H. Putnam (Eds.), Philosophy of Mathematics: Selected Readings (2nd ed.). London: Cambridge University Press.
4. Bueno, O. (2011). Logical and Mathematical Knowledge. In S. Bernecker and D. Pritchard (Eds.), Routledge Companion to Epistemology New York: Tailor and Francis e-Library.
5. Burgess, J. Rosen, G. (1997). A Subject with No Object, New York: Oxford University Press Field, H. (2016). Science Without Number: A Defence of Nominalism (2nd ed). Oxford: Oxford University Press.
6. Leng, M. Fictionalism in the Philosophy of Mathematics. In Internet Encyclopedia of Philosophy, ISSN 2161-0002, https://iep.utm.edu
7. Maddy, P. (1990). Realism in Mathematics. Oxford: Oxford University Press.
8. Plato. (2013) The Republic. An Electronic Classics Series Publication.
9. Shapiro, S. (2005). Philosophy of Mathematics and its Logic: Introduction. In S. Shapiro (Ed.), The Oxford Handbook of Philosophy of Mathematics and Logic(pp.3-27). Oxford University Press.
10. Shapiro, S. (2016). Mathematics in Philosophy, Philosophy in Mathematics: Three Case Studies. In F. Boccuni and A. Sereni (Eds.), Objectivity, Realism, and Proof FilMat Studies in the Philosophy of Mathematics. Springer International Publishing Switzerland.
11. Van Fraassen, B. (1980). The Scientific Image, Oxford: Clarendon Press.
Published
2023-03-27
How to Cite
[1]
Akpan, E.G. and Ihunda, V.C. 2023. The Fictionalist Concept of Numbers: A Critique. International Journal on Integrated Education. 6, 3 (Mar. 2023), 237-244. DOI:https://doi.org/10.17605/ijie.v6i3.4184.
Issue
Vol. 6 No. 3 (2023): International Journal on Integrated Education (IJIE)
Section
Articles

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