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.)
The philosophical importance of this contribution is mainly in the successfulness of the attempt made to justify a view of mathematics which, holding on to a Tarskian/Aristotelian conception of mathematical truth, does not involve the postulation of entities which are beyond the bounds of experience.
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Oliveri, G. Mathematics. A Science of Patterns?. Synthese 112, 379–402 (1997). https://doi.org/10.1023/A:1004906107430
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DOI: https://doi.org/10.1023/A:1004906107430