{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,13]],"date-time":"2024-09-13T18:10:13Z","timestamp":1726251013487},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2023,6,3]],"date-time":"2023-06-03T00:00:00Z","timestamp":1685750400000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,9,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>G\u00f6del\u2019s Incompleteness Theorems suggest that no single formal system can capture the entirety of one\u2019s mathematical beliefs, while pointing at a hierarchy of systems of increasing logical strength that make progressively more explicit those implicit assumptions. This notion of implicit commitment motivates directly or indirectly several research programmes in logic and the foundations of mathematics; yet there hasn\u2019t been a direct logical analysis of the notion of implicit commitment itself. In a recent paper, we carried out an initial assessment of this project by studying necessary conditions for implicit commitments; from seemingly weak assumptions on implicit commitments of an arithmetical system $S$, it can be derived that a uniform reflection principle for $S$\u2014stating that all numerical instances of theorems of $S$ are true\u2014must be contained in $S$\u2019s implicit commitments. This study gave rise to unexplored research avenues and open questions. This paper addresses the main ones. We generalize this basic framework for implicit commitments along two dimensions: in terms of iterations of the basic implicit commitment operator, and via a study of implicit commitments of theories in arbitrary first-order languages, not only couched in an arithmetical language.<\/jats:p>","DOI":"10.1093\/logcom\/exad025","type":"journal-article","created":{"date-parts":[[2023,6,9]],"date-time":"2023-06-09T16:16:58Z","timestamp":1686327418000},"page":"1136-1158","source":"Crossref","is-referenced-by-count":0,"title":["Implicit commitment in a general setting"],"prefix":"10.1093","volume":"34","author":[{"given":"Mateusz","family":"\u0141e\u0141yk","sequence":"first","affiliation":[{"name":"Faculty of Philosophy , University of Warsaw, Krakowskie Przedmie\u015bcie 3, 00-927 Warsaw"}]},{"given":"Carlo","family":"Nicolai","sequence":"additional","affiliation":[{"name":"Department of Philosophy King's College London Strand Campus WC2R 2LS London , United Kingdom"}]}],"member":"286","published-online":{"date-parts":[[2023,6,2]]},"reference":[{"key":"2024091304305123400_ref1","doi-asserted-by":"crossref","DOI":"10.1017\/9781316717196","volume-title":"Admissible Sets and Structures","author":"Barwise","year":"2017"},{"key":"2024091304305123400_ref2","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1070\/RM2005v060n02ABEH000823","article-title":"Reflection principles and provability algebras in formal arithmetic","volume":"60","author":"Beklemishev","year":"2005","journal-title":"Russian Mathematical Surveys"},{"key":"2024091304305123400_ref3","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/978-3-319-22156-4_9","article-title":"Proof theoretic analysis by iterated reflection","volume-title":"Turing\u2019s Revolution","author":"Beklemishev","year":"2015"},{"key":"2024091304305123400_ref4","doi-asserted-by":"crossref","first-page":"569","DOI":"10.1070\/RM9843","article-title":"Reflection calculus and conservativity spectra","volume":"73","author":"Beklemishev","year":"2018","journal-title":"Russian Mathematical Surveys"},{"key":"2024091304305123400_ref5","doi-asserted-by":"crossref","first-page":"103093","DOI":"10.1016\/j.apal.2022.103093","article-title":"Reflection algebras and conservation results for theories of iterated truth","volume":"173","author":"Beklemishev","year":"2022","journal-title":"Annals of Pure and Applied Logic"},{"volume-title":"Bounded Arithmetic","year":"1986","author":"Buss","key":"2024091304305123400_ref6"},{"key":"2024091304305123400_ref7","doi-asserted-by":"crossref","DOI":"10.1017\/9781108178600","volume-title":"The Epistemic Lightness of Truth: Deflationism and Its Logic","author":"Cie\u015bli\u0144ski","year":"2017"},{"key":"2024091304305123400_ref8","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1093\/philmat\/nku026","article-title":"Arithmetical reflection and the provability of soundness","volume":"23","author":"Dean","year":"2015","journal-title":"Philosophia Mathematica"},{"key":"2024091304305123400_ref9","doi-asserted-by":"crossref","DOI":"10.1017\/9781316717219","volume-title":"Constructibility","author":"Devlin","year":"2017"},{"key":"2024091304305123400_ref10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2269764","article-title":"Systems of predicative analysis","volume":"29","author":"Feferman","year":"1964","journal-title":"Journal of Symbolic Logic"},{"key":"2024091304305123400_ref11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2274902","article-title":"Reflecting on incompleteness","volume":"56","author":"Feferman","year":"1991","journal-title":"Journal of Symbolic Logic"},{"key":"2024091304305123400_ref12","doi-asserted-by":"crossref","first-page":"259","DOI":"10.2307\/2964649","article-title":"Transfinite recursive progressions of axiomatic theories","volume":"27","author":"Feferman","year":"1962","journal-title":"Journal of Symbolic Logic"},{"key":"2024091304305123400_ref13","doi-asserted-by":"crossref","first-page":"2631","DOI":"10.1093\/logcom\/exx023","article-title":"Iterated reflection over full disquotational truth","volume":"27","author":"Fischer","year":"2017","journal-title":"Journal of Logic and Computation"},{"key":"2024091304305123400_ref14","article-title":"Lecture Notes in Logic","volume-title":"Inexhaustibility. 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