Publication
Peano’s structuralism and the birth of formal languages
| dc.contributor.author | Bertran-San-Millán, Joan | |
| dc.date.accessioned | 2022-09-14T13:25:48Z | |
| dc.date.available | 2022-09-14T13:25:48Z | |
| dc.date.issued | 2022 | |
| dc.description.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. | pt_PT |
| dc.description.version | info:eu-repo/semantics/acceptedVersion | pt_PT |
| dc.identifier.doi | 10.1007/s11229-022-03782-z | pt_PT |
| dc.identifier.uri | http://hdl.handle.net/10451/54465 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.relation | The Formalisation of Logic in the late XIX and early XX centuries | |
| dc.relation | Center for Philosophy of Sciences of the University of Lisbon | |
| dc.subject | Peano | pt_PT |
| dc.subject | Formal languages | pt_PT |
| dc.subject | Structuralism | pt_PT |
| dc.subject | Independence proofs | pt_PT |
| dc.subject | Symbolisation | pt_PT |
| dc.title | Peano’s structuralism and the birth of formal languages | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | The Formalisation of Logic in the late XIX and early XX centuries | |
| oaire.awardTitle | Center for Philosophy of Sciences of the University of Lisbon | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/CEEC IND 3ed/2020.03291.CEECIND%2FCP1605%2FCT0001/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00678%2F2020/PT | |
| oaire.citation.issue | 4 | pt_PT |
| oaire.citation.title | Synthese | pt_PT |
| oaire.citation.volume | 200 | pt_PT |
| oaire.fundingStream | CEEC IND 3ed | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
| relation.isProjectOfPublication | 1a23d6da-0e07-4b91-8f18-fbcfc82c26d5 | |
| relation.isProjectOfPublication | 5eea26e2-4c2c-4982-8813-f6862001cc27 | |
| relation.isProjectOfPublication.latestForDiscovery | 5eea26e2-4c2c-4982-8813-f6862001cc27 |
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