{
  "abstract": "Gödelian incompleteness yields arithmetical sentences \\(A\\) such that \\(\\mathsf{PA}+A\\) and \\(\\mathsf{PA}+\\neg A\\) are both consistent. Are such extensions equally legitimate? I propose graded epistemic arithmetical non-pluralism: justification for choosing between them varies with the set-theoretic strength of \\(A\\). I defend \\(\\mathsf{PA}+\\mathsf{Con}(\\mathsf{PA})\\) and show that Friedman's concrete incompleteness results pose a serious challenge to non-pluralism about first-order arithmetic. Resolving the selection problem for such sentences turns on justifying large cardinals. Defending graded non-pluralism thus engages Gödel's programme and the justification of very large cardinals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22797",
  "author_total": 1,
  "authors": [
    {
      "name": "Yong Cheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b8t9419dy2nc2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22797",
  "fulltext_url": null,
  "id": "b8t9419dy2nc2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22797",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.HO"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214058654",
  "pdf_url": "https://arxiv.org/pdf/2609.22797",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b8t9419dy2nc2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2609.22797",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22797"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "The Limits of Arithmetical Pluralism: Incompleteness, Large Cardinals, and Graded Non-Pluralism",
  "title_text": "The Limits of Arithmetical Pluralism: Incompleteness, Large Cardinals, and Graded Non-Pluralism",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/b8t9419dy2nc2",
  "venue": "arXiv",
  "versions": []
}