A Theory of Structured Propositions

Bibliographic Data

ID10700952
AuthorsAndrew Bacon (University of Southern California, corresponding author)
Year2023
Volume132
Issue2
Pages173-238
Publication date2023-04-01
Peer ReviewedYes
Open AccessNo
TypeARTICLE
VenueThe Philosophical Review (JOURNAL)
Journal identifiersISSN: 0031-8108 • E-ISSN: 1558-1470
PublisherDuke University Press (PUBLISHER • US)
DOI10.1215/00318108-10294409
OpenAlexW4381295101
LanguageEN
Citations received5
References cited39

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’t arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the λ-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 λ-calculus

Algebra over a field · Algorithm · Arithmetic · Calculus (dental) · Diagrammatic reasoning · Epistemology · Fragment (logic) · Logical consequence · Notation · Programming language · Pure mathematics · Representation (politics) · Computer Science · Logic, programming, and type systems · Logic, Reasoning, and Knowledge · Mathematics · Philosophy · Philosophy and Theoretical Science

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