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Peano's Structuralism and the Birth of Formal Languages

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
Creators:
CreatorsEmailORCID
Bertran-San-Millán, Joanjbertran@fc.ul.pt0000-0001-6874-2228
Keywords: Peano structuralism formal languages independence proofs symbolisation
Subjects: Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Depositing User: Joan Bertran-San-Millán
Date Deposited: 02 Jul 2022 15:15
Last Modified: 02 Jul 2022 15:15
Item ID: 20832
Subjects: Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > History
Specific Sciences > Mathematics > Logic
Date: 2022
URI: http://philsci-archive.pitt.edu/id/eprint/20832

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