Структурализм и идентичность математических объектов

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M. Resnik

Abstract

The paper deals with the nature of mathematics from the point of view so called mathematical structuralism. The author proposes specific analysis of mathematical objects, and within the particular — relativistic standpoint — justify that mathematics is the science of patterns. He responded for the objections toward mathematical structuralism.

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Статьи

References

Benacerraf, Paul, “What numbers could not, be” originally published in the Philosophical Review in 1965, reprinted in Benacerraf and Putnam, Philosophy of Mathematics, Cambridge: Cambridge University Press, 1983.
Keranen, Jukka, “The Identity Problem for Realist Structuralism,” Philosophia Mathematica (2001)
Keranen, Jukka, “The Identity Problem for Realist Structuralism II: A Reply to Shapiro” in MacBride (2006)
Ladyman, James, “On the Identity and Diversity of Objects in a Structure” Unpublished.
MacBride, Fraser, Identity and Modality, Oxford: Clarendon Press, 2006.
Quine, W.V., “Grades of Discriminability” in W. V. Quine, Theories and Things, Cambridge, Mass: Harvard, 1981.
Resnik, Michael D., “Mathematics as a Science of Patterns: Ontology and Reference,” Nous 15, (1981)
Resnik, Michael D-, Mathematics as a Science of Patterns, Oxford: Clarendon Press, 1997.
Shapiro, Stewart, “Structure and Identity” in MacBride (2006).
Shapiro, Stewart, “The Governance of Identity” in MacBride (2006).