Modal Structuralism with Theoretical Terms

Datos Bibliográficos

ID21461689
AutoresHeinz Andreas (0000-0002-0940-7435), Holger Andreas (University of British Columbia), Georg Schiemer (0000-0003-1197-4532, University of Vienna, autor de correspondencia)
Año2023
Volumen88
Número2
Páginas721-745
Fecha de publicación2023-02-01
Peer ReviewedSí
Open AccessSí
TipoARTICLE
RevistaErkenntnis (JOURNAL)
Identificadores de la revistaISSN: 0165-0106 • E-ISSN: 1572-8420
EditorialSpringer Science and Business Media LLC (PUBLISHER)
DOI10.1007/s10670-021-00378-w
PMID36762124
OpenAlexW3160687356
IdiomaEN
Citas recibidas2
Referencias citadas22

In this paper, we aim to explore connections between a Carnapian semantics of theoretical terms and an eliminative structuralist approach in the philosophy of mathematics. Specifically, we will interpret the language of Peano arithmetic by applying the modal semantics of theoretical terms introduced in Andreas (Synthese 174(3):367–383, 2010). We will thereby show that the application to Peano arithmetic yields a formal semantics of universal structuralism, i.e., the view that ordinary mathematical statements in arithmetic express general claims about all admissible interpretations of the Peano axioms. Moreover, we compare this application with the modal structuralism by Hellman (Mathematics without numbers: towards a modal-structural interpretation. Oxford University Press: Oxford, 1989), arguing that it provides us with an easier epistemology of statements in arithmetic

Accessibility relation · Algebra over a field · Axiom · Discrete mathematics · Epistemology · Linguistics · Modal · Modal logic · Ontology · Peano axioms · Philosophy of Mathematics · Programming language · Pure mathematics · Computer Science · Logic, Reasoning, and Knowledge · Mathematics · Philosophy · Philosophy and History of Science · Philosophy and Theoretical Science