Bertran-San-Millán, Joan (2022) Peano's Structuralism and the Birth of Formal Languages. [Preprint]
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Abstract
Recent historical studies have investigated the first proponents of methodological structuralism in late nineteenth-century mathematics. In this paper, I shall attempt to answer the question of whether Peano can be counted amongst the early structuralists. I shall focus on Peano's understanding of the primitive notions and axioms of geometry and arithmetic. First, I shall argue that the undefinability of the primitive notions of geometry and arithmetic led Peano to the study of the relational features of the systems of objects that compose these theories. Second, I shall claim that, in the context of independence arguments, Peano developed a schematic understanding of the axioms which, despite diverging in some respects from Dedekind's construction of arithmetic, should be considered structuralist. From this stance I shall argue that this schematic understanding of the axioms anticipates the basic components of a formal language.
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| Item Type: | Preprint | ||||||
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| Keywords: | Peano structuralism formal languages independence proofs symbolisation | ||||||
| Subjects: | Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic |
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| Depositing User: | Joan Bertran-San-Millán | ||||||
| Date Deposited: | 05 Aug 2022 17:00 | ||||||
| Last Modified: | 05 Aug 2022 17:00 | ||||||
| Item ID: | 21013 | ||||||
| Official URL: | https://link.springer.com/article/10.1007/s11229-0... | ||||||
| DOI or Unique Handle: | 10.1007/s11229-022-03782-z | ||||||
| Subjects: | Specific Sciences > Mathematics > History of Philosophy Specific Sciences > Mathematics > History Specific Sciences > Mathematics > Logic |
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| Date: | July 2022 | ||||||
| URI: | https://philsci-archive.pitt.edu/id/eprint/21013 |
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Peano's Structuralism and the Birth of Formal Languages. (deposited 02 Jul 2022 15:15)
- Peano's Structuralism and the Birth of Formal Languages. (deposited 05 Aug 2022 17:00) [Currently Displayed]
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