{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T12:27:38Z","timestamp":1776083258446,"version":"3.50.1"},"reference-count":51,"publisher":"Duke University Press","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,4,1]]},"abstract":"<jats:p>This paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn\u2019t arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the \u03bb-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a diagrammatic representation and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification and demonstrate various equivalences between the diagrammatic and logical representations and a fragment of the \u03bb-calculus.<\/jats:p>","DOI":"10.1215\/00318108-10294409","type":"journal-article","created":{"date-parts":[[2023,5,30]],"date-time":"2023-05-30T20:16:04Z","timestamp":1685477764000},"page":"173-238","source":"Crossref","is-referenced-by-count":11,"title":["A Theory of Structured Propositions"],"prefix":"10.1215","volume":"132","author":[{"given":"Andrew","family":"Bacon","sequence":"first","affiliation":[{"name":"University of Southern California"}]}],"member":"73","published-online":{"date-parts":[[2023,4,1]]},"reference":[{"key":"2023053020154412700_cit001","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-015-9934-4","volume-title":"An Introduction to Mathematical Logic and Type Theory: To Truth through Proof","author":"Andrews","year":"2002"},{"issue":"5","key":"2023053020154412700_cit002","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1007\/s10992-017-9447-9","article-title":"The Broadest Necessity","volume":"47","author":"Bacon","year":"2018","journal-title":"Journal of Philosophical Logic"},{"issue":"6","key":"2023053020154412700_cit003","doi-asserted-by":"crossref","first-page":"1017","DOI":"10.1007\/s10992-019-09505-z","article-title":"Substitution Structures","volume":"48","author":"Bacon","year":"2019","journal-title":"Journal of Philosophical Logic"},{"issue":"4","key":"2023053020154412700_cit004","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1215\/00318108-8540944","article-title":"Logical Combinatorialism","volume":"129","author":"Bacon","year":"2020","journal-title":"Philosophical Review"},{"key":"2023053020154412700_cit005","doi-asserted-by":"crossref","volume-title":"A Philosophical Introduction to Higher-order Logics","author":"Bacon","DOI":"10.4324\/9781003039181"},{"issue":"4\u20135","key":"2023053020154412700_cit006","first-page":"46","article-title":"Higher-Order Free Logic and the Prior-Kaplan Paradox","author":"Bacon","year":"2016","journal-title":"Canadian Journal of Philosophy"},{"issue":"1","key":"2023053020154412700_cit007","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1111\/phpr.12454","article-title":"The Logic of Opacity","volume":"99","author":"Bacon","year":"2019","journal-title":"Philosophy and Phenomenological Research"},{"issue":"4","key":"2023053020154412700_cit008","doi-asserted-by":"crossref","first-page":"1121","DOI":"10.1007\/s11098-020-01486-z","article-title":"The Fundamental and the Brute","volume":"178","author":"Bader","year":"2021","journal-title":"Philosophical Studies"},{"issue":"12","key":"2023053020154412700_cit009","doi-asserted-by":"crossref","first-page":"685","DOI":"10.2307\/2027014","article-title":"The Prince and the Phone Booth: Reporting Puzzling Beliefs","volume":"86","author":"Crimmins","year":"1989","journal-title":"Journal of Philosophy"},{"issue":"3","key":"2023053020154412700_cit010","doi-asserted-by":"crossref","first-page":"509","DOI":"10.2307\/2370619","article-title":"Grundlagen der kombinatorischen Logik","volume":"52","author":"Curry","year":"1930","journal-title":"American Journal of Mathematics"},{"key":"2023053020154412700_cit011","doi-asserted-by":"crossref","unstructured":"De Bruijn Nicolaas Govert . 1972. \u201cLambda Calculus Notation with Nameless Dummies, a Tool for Automatic Formula Manipulation, with Application to the Church-Rosser Theorem.\u201d In Indagationes Mathematicae (Proceedings), vol. 75, 381\u201392. 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