TL;DR
This paper explores how Fine's theory of arbitrary objects can be applied to mathematical structuralism, viewing structures as systems of arbitrary objects to deepen understanding of mathematical entities.
Contribution
It introduces a novel perspective by integrating Fine's theory with structuralism, proposing that mathematical structures can be seen as systems of arbitrary objects.
Findings
Mathematical structures can be modeled as systems of arbitrary objects.
The approach offers new insights into the nature of mathematical entities.
It bridges Fine's theory with structuralist philosophy of mathematics.
Abstract
In this article ideas from Kit Fine's theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generic mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine's sense.
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Taxonomy
TopicsPhilosophy and Theoretical Science · History and Theory of Mathematics · Philosophy and History of Science