Miláns del Bosch, Lorenzo and Pérez-Escobar, José Antonio (2026) Mathematical properties of natural worlds. [Preprint]
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Abstract
Debates on the ontology of mathematics often pit Platonism against nominalist and formalist views. We develop an hylomorphic alternative within Aristotelian realism by asking whether mathematical structure can be shown to belong to natural reality itself. To explore this issue, we construct a thought experiment improving on Marc Lange’s story of Mother’s challenge of equally distributing 23 strawberries among her three daughters. Our though experiment is based on a toy-world containing squares, circles, and a linear attraction force, without mathematical primitive entities, and its design avoids the criticisms that Lange’s idea received, especially in regards to the role of causality versus modality acting at the core of Mother’s challenge (the two cannot be readily demarcated, and thus the example underdetermines ontological interpretations). The toy-word’s final configurations consist of chains of circles attached to each square. Observation of the possible worlds generated by this model yields a taxonomy of cases in which the truth value of the claim that all final chains have the same length is assessed. On that basis, we formulate the hypothesis that a structural relation between the sizes of the pluralities of circles and squares constrains the system’s accessible states. This relation, already present in the possible worlds, can be regimented as divisibility between the cardinalities of circles and squares: when divisibility fails, equal-length chains are structurally impossible, whereas when it holds, such outcomes are possible. As a result, we have possible worlds with inherent mathematical properties that were not set into the system by hand. Within its limits, our thought experiment overcomes the underdetermination of the ontology of mathematics in worldly states of affairs, and we show that the found mathematical properties of the possible worlds restrict physical possibilities, supporting a hylomorphic and Structurally Aristotelian Realistic reading of the ontology of mathematics.
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| Item Type: | Preprint | |||||||||
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| Keywords: | Ontology of mathematics, Aristotelian Realism, Plural Quantification, Hylomorphism | |||||||||
| Subjects: | Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics |
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| Depositing User: | Dr. Lorenzo Miláns del Bosch | |||||||||
| Date Deposited: | 06 Jun 2026 16:24 | |||||||||
| Last Modified: | 06 Jun 2026 16:24 | |||||||||
| Item ID: | 29949 | |||||||||
| Subjects: | Specific Sciences > Mathematics > Ontology Specific Sciences > Mathematics |
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| Date: | May 2026 | |||||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/29949 |
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