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Semantics without Toil? Brady and Rush Meet Hallden

In: Organon F, vol. 26, no. 3
Lloyd Humberstone


Year, pages: 2019, 340 - 404
Language: eng
Nonclassical logic, semantic completeness, homophonic model theory, Hallden completeness, choice of meta-logic.
Article type: Research Article
Document type: Research Article
About article:
The present discussion takes up an issue raised in Section 5 of Ross Brady and Penelope Rush’s paper ‘Four Basic Logical Issues’ concerning the (claimed) triviality – in the sense of automatic availability – of soundness and completeness results for a logic in a metalanguage employing at least as much logical vocabulary as the object logic, where the metalogical behaviour of the common logical vocabulary is as in the object logic. We shall see – in Propositions 4.5–4.7 – that this triviality claim faces difficulties in the face of Hallden incompleteness, for essentially the same reasons that Hallden thought this phenomenon raised semantic difficulties for the modal logics of C. I. Lewis exhibiting it. To counter any inclination to dismiss the phenomenon as providing at best a marginal range of counterexamples to the triviality claim, a Postscript assembles some reminders of the extent of – and the varied considerations favouring – Hallden incompleteness.
How to cite:
ISO 690:
Humberstone, L. 2019. Semantics without Toil? Brady and Rush Meet Hallden. In Organon F, vol. 26, no.3, pp. 340-404. 1335-0668. DOI: https://doi.org/10.31577/orgf.2019.26303

Humberstone, L. (2019). Semantics without Toil? Brady and Rush Meet Hallden. Organon F, 26(3), 340-404. 1335-0668. DOI: https://doi.org/10.31577/orgf.2019.26303
About edition:
Publisher: Institute of Philosophy of the Slovak Academy of Sciences, Institute of Philosophy of the Czech Academy of Sciences
Published: 24. 8. 2019
Lloyd Humberstone