On Representations of Intended Structures in Foundational Theories

Barton, Neil; Müller, Moritz; Prunescu, Mihai

On Representations of Intended Structures in Foundational Theories

Dateien

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Datum

2022

Autor:innen

Barton, Neil

Müller, Moritz

Prunescu, Mihai

Angaben zur Forschungsförderung

European Union (EU): 648276

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Philosophie

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Journal of Philosophical Logic. Springer. 2022, 51(2), pp. 283-296. ISSN 0022-3611. eISSN 1573-0433. Available under: doi: 10.1007/s10992-021-09628-2

Zusammenfassung

Often philosophers, logicians, and mathematicians employ a notion of intended structure when talking about a branch of mathematics. In addition, we know that there are foundational mathematical theories that can find representatives for the objects of informal mathematics. In this paper, we examine how faithfully foundational theories can represent intended structures, and show that this question is closely linked to the decidability of the theory of the intended structure. We argue that this sheds light on the trade-off between expressive power and meta-theoretic properties when comparing first-order and second-order logic.

Fachgebiet (DDC)

100 Philosophie

Zitieren

ISO 690

BARTON, Neil, Moritz MÜLLER, Mihai PRUNESCU, 2022. On Representations of Intended Structures in Foundational Theories. In: Journal of Philosophical Logic. Springer. 2022, 51(2), pp. 283-296. ISSN 0022-3611. eISSN 1573-0433. Available under: doi: 10.1007/s10992-021-09628-2

BibTex

@article{Barton2022-04Repre-54556,
  year={2022},
  doi={10.1007/s10992-021-09628-2},
  title={On Representations of Intended Structures in Foundational Theories},
  number={2},
  volume={51},
  issn={0022-3611},
  journal={Journal of Philosophical Logic},
  pages={283--296},
  author={Barton, Neil and Müller, Moritz and Prunescu, Mihai}
}

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Universitätsbibliographie

Nein

Begutachtet

Ja