Mathematics. A science of patterns?

Synthese 112 (3):379-402 (1997)
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Abstract

The present article aims at showing that it is possible to construct a realist philosophy of mathematics which commits one neither to dream the dreams of Platonism nor to reduce the word ''realism'' to mere noise. It is argued that mathematics is a science of patterns, where patterns are not objects (or properties of objects), but aspects, or aspects of aspects, etc. of objects. (The notion of aspect originates from ideas sketched by Wittgenstein in the Philosophical Investigations.)

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Citations of this work

Three varieties of mathematical structuralism.Geoffrey Hellman - 2001 - Philosophia Mathematica 9 (2):184-211.
Non-uniqueness as a non-problem.Mark Balaguer - 1998 - Philosophia Mathematica 6 (1):63-84.
Haecceities and Mathematical Structuralism.Christopher Menzel - 2018 - Philosophia Mathematica 26 (1):84-111.

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References found in this work

The logical basis of metaphysics.Michael Dummett - 1991 - Cambridge, Mass.: Harvard University Press.
Critique of Pure Reason.I. Kant - 1787/1998 - Philosophy 59 (230):555-557.
Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Principia Mathematica.A. N. Whitehead & B. Russell - 1927 - Annalen der Philosophie Und Philosophischen Kritik 2 (1):73-75.
Representation and Reality.H. Putnam - 1990 - Tijdschrift Voor Filosofie 52 (1):168-168.

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