{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T03:23:58Z","timestamp":1774927438765,"version":"3.50.1"},"reference-count":27,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T00:00:00Z","timestamp":1760486400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2025,12]]},"abstract":"Abstract<\/jats:title>\n \n The paper proposes and studies new classical, type-free theories of truth and determinateness with unprecedented features. The theories are fully compositional, strongly classical (namely, their internal and external logics are both classical), and feature a\n defined<\/jats:italic>\n determinateness predicate satisfying desirable and widely agreed principles. The theories capture a conception of truth and determinateness according to which the generalizing power associated with the classicality and full compositionality of truth is combined with the identification of a natural class of sentences\u2014the determinate ones\u2014for which clear-cut semantic rules are available. Our theories can also be seen as the\n classical closures<\/jats:italic>\n of Kripke\u2013Feferman truth: their\n \n \n \n $\\omega $<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n -models, which we precisely pin down, result from including in the extension of the truth predicate the sentences that are satisfied by a Kripkean closed-off fixed-point model. The theories compare to recent theories proposed by Fujimoto and Halbach, featuring a primitive determinateness predicate. In the paper we show that our theories entail all principles of Fujimoto and Halbach\u2019s theories, and are proof-theoretically equivalent to Fujimoto and Halbach\u2019s\n \n \n \n $\\mathsf {CD}^{+}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n . We also show establish some negative results on Fujimoto and Halbach\u2019s theories: such results show that, unlike what happens in our theories, the primitive determinateness predicate prevents one from establishing clear and unrestricted semantic rules for the language with type-free truth.\n <\/jats:p>","DOI":"10.1017\/s1755020325100968","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T09:26:20Z","timestamp":1760520380000},"page":"1041-1067","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["ON CLASSICAL DETERMINATE TRUTH"],"prefix":"10.1017","volume":"18","author":[{"given":"LUCA","family":"CASTALDO","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05591te55","id-type":"ROR","asserted-by":"publisher"}],"name":"LMU 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2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}