{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T18:19:34Z","timestamp":1759774774529},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2015,3,20]],"date-time":"2015-03-20T00:00:00Z","timestamp":1426809600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2015,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In an earlier paper in this <jats:sc>journal<\/jats:sc> I provided detailed motivation for the constructive and relevant system of <jats:italic>Core Logic<\/jats:italic>; explained its main features; and established that, even though Cut is not a rule <jats:italic>of<\/jats:italic> the system, nevertheless Cut is admissible for it, and indeed with potential epistemic gain. If \u03a0 is a proof of the sequent \u0394 : <jats:italic>A<\/jats:italic>, and \u03a3 is a proof of the sequent \u0413, <jats:italic>A<\/jats:italic> : <jats:italic>\u03b8<\/jats:italic>, then there is a computable reduct [\u03a0, \u03a3] of some <jats:italic>subsequent<\/jats:italic> of the \u2018overall target sequent\u2019 \u0394, \u0413 : <jats:italic>\u03b8<\/jats:italic>. In the constructive case the potential epistemic gain consists in the possibility that the subsequent in question be a <jats:italic>proper<\/jats:italic> subsequent of \u0394, \u0413 : <jats:italic>\u03b8<\/jats:italic>, and indeed even <jats:italic>logically stronger<\/jats:italic> than \u0394, \u0413 : <jats:italic>\u03b8<\/jats:italic>.<\/jats:p><jats:p>In this paper it is established that Cut is likewise admissible for <jats:italic>Classical<\/jats:italic> Core Logic, which is obtained from Core Logic by adding a suitably relevantized form of the rule of Classical Dilemma. In the classical case there is an additional feature of potential epistemic gain: the proof [\u03a0, \u03a3] might have a <jats:italic>lower degree of non-constructivity<\/jats:italic> than do \u03a0 and \u03a3.<\/jats:p>","DOI":"10.1017\/s1755020315000088","type":"journal-article","created":{"date-parts":[[2015,3,20]],"date-time":"2015-03-20T10:31:47Z","timestamp":1426847507000},"page":"236-256","source":"Crossref","is-referenced-by-count":15,"title":["CUT FOR CLASSICAL CORE LOGIC"],"prefix":"10.1017","volume":"8","author":[{"given":"NEIL","family":"TENNANT","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2015,3,20]]},"reference":[{"key":"S1755020315000088_ref10","unstructured":"Tennant N . (forthcoming). Inferentialism, logicism, harmony, and a counterpoint. In Miller A. , editor. Essays for Crispin Wright: Logic, Language and Mathematics, pp. XXX\u2013XXX. Volume 2 of a two-volume Festschrift for Crispin Wright, co-edited with Coliva, A. Oxford: Oxford University Press."},{"key":"S1755020315000088_ref9","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020315000040"},{"key":"S1755020315000088_ref7","volume-title":"Autologic","author":"Tennant","year":"1992"},{"key":"S1755020315000088_ref2","doi-asserted-by":"publisher","DOI":"10.1093\/analys\/22.6.130"},{"key":"S1755020315000088_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020311000360"},{"key":"S1755020315000088_ref11","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020311000311"},{"key":"S1755020315000088_ref4","volume-title":"Natural Deduction: A Proof-Theoretical Study","author":"Prawitz","year":"1965"},{"key":"S1755020315000088_ref1","volume-title":"Entailment: The Logic of Relevance and Necessity","volume":"I","author":"Anderson","year":"1975"},{"key":"S1755020315000088_ref3","first-page":"68","volume-title":"The Collected Papers of Gerhard Gentzen","author":"Gentzen","year":"1935"},{"key":"S1755020315000088_ref5","doi-asserted-by":"publisher","DOI":"10.1080\/00048402.2010.528781"},{"key":"S1755020315000088_ref6","volume-title":"Natural Logic","author":"Tennant","year":"1978"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020315000088","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,20]],"date-time":"2019-04-20T20:18:47Z","timestamp":1555791527000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020315000088\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,3,20]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["S1755020315000088"],"URL":"https:\/\/doi.org\/10.1017\/s1755020315000088","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,3,20]]}}}