Mathematical Practice, Fictionalism and Social Ontology

Topoi 42 (1):211-220 (2022)
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From the perspective of mathematical practice, I examine positions claiming that mathematical objects are introduced by human agents. I consider in particular mathematical fictionalism and a recent position on social ontology formulated by Cole (2013, 2015). These positions are able to solve some of the challenges that non-realist positions face. I argue, however, that mathematical entities have features other than fictional characters and social institutions. I emphasise that the way mathematical objects are introduced is different and point to the multifaceted role that relations and interconnections play in this context. Finally, I argue that mathematical entities can be considered to be pragmatically real.



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Realism, Mathematics, and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Knowledge and Social Imagery.David Bloor - 1979 - British Journal for the Philosophy of Science 30 (2):195-199.
Fiction and Metaphysics.Amie Thomasson - 1999 - Journal of Aesthetics and Art Criticism 60 (2):190-192.
Mathematical Knowledge and the Interplay of Practices.José Ferreirós - 2015 - Princeton, USA: Princeton University Press.
Groundwork for a Fallibilist Account of Mathematics.Silvia De Toffoli - 2021 - Philosophical Quarterly 7 (4):823-844.

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