Modal Structuralism and Reflection

Roberts, Sam

Modal Structuralism and Reflection

Dateien

Roberts_2-1sve2a0zfnqcl1.pdfGröße: 328.5 KBDownloads: 176

Datum

2019

Open Access-Veröffentlichung

Open Access Green

Sammlungen

Philosophie

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

The Review of Symbolic Logic. Cambridge University Press. 2019, 12(4), pp. 823-860. ISSN 1755-0203. eISSN 1755-0211. Available under: doi: 10.1017/S1755020318000138

Zusammenfassung

Modal structuralism promises an interpretation of set theory that avoids commitment to abstracta. This article investigates its underlying assumptions. In the first part, I start by highlighting some shortcomings of the standard axiomatisation of modal structuralism, and propose a new axiomatisation I call MSST (for Modal Structural Set Theory). The main theorem is that MSST interprets exactly Zermelo set theory plus the claim that every set is in some inaccessible rank of the cumulative hierarchy. In the second part of the article, I look at the prospects for supplementing MSST with a modal structural reflection principle, as suggested in Hellman (2015). I show that Hellman’s principle is inconsistent (Theorem 5.32), and argue that modal structural reflection principles in general are either incompatible with modal structuralism or extremely weak

Fachgebiet (DDC)

100 Philosophie

Schlagwörter

structuralism, modal structuralism, set theory, modal logic, plural logic, large cardinals, reflection principles

Zitieren

ISO 690

ROBERTS, Sam, 2019. Modal Structuralism and Reflection. In: The Review of Symbolic Logic. Cambridge University Press. 2019, 12(4), pp. 823-860. ISSN 1755-0203. eISSN 1755-0211. Available under: doi: 10.1017/S1755020318000138

BibTex

@article{Roberts2019Modal-53566,
  year={2019},
  doi={10.1017/S1755020318000138},
  title={Modal Structuralism and Reflection},
  number={4},
  volume={12},
  issn={1755-0203},
  journal={The Review of Symbolic Logic},
  pages={823--860},
  author={Roberts, Sam}
}

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