{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T06:25:58Z","timestamp":1775975158903,"version":"3.50.1"},"reference-count":8,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":23676,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1949,5,16]]},"abstract":"<jats:p>The present note introduces a constructible interpretation for the logical connectives of number theory which is divergent from that of the intuitionists. Under the intuitionistic interpretation, the principle of excluded middle and certain other classically acceptable principles of logic must be rejected. Under the present interpretation, while some classical principles may be reinstated, other principles, acceptable both classically and intuitionistically, may be shown to be invalid. Among these is the principle of contradiction.<\/jats:p>","DOI":"10.2307\/2268973","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T15:04:01Z","timestamp":1146927841000},"page":"16-26","source":"Crossref","is-referenced-by-count":357,"title":["Constructible falsity"],"prefix":"10.1017","volume":"14","author":[{"given":"David","family":"Nelson","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200073126_ref002","volume-title":"On undecidable propositions of formal mathematical systems","author":"G\u00f6del","year":"1934"},{"key":"S0022481200073126_ref003","first-page":"42","volume-title":"Sitzungsberichte der Preussischen Akademie der Wissenschaften","author":"Heyting","year":"1930"},{"key":"S0022481200073126_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1943-0007371-8"},{"key":"S0022481200073126_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01565439"},{"key":"S0022481200073126_ref001","first-page":"34","article-title":"Zur intuitionistischen Arithmetik und Zahlentheorie","volume":"4","author":"G\u00f6del","year":"1931","journal-title":"Ergebnisse eines mathematischen Kolloquiums"},{"key":"S0022481200073126_ref005","first-page":"150","volume":"3","author":"Kleene","year":"1938","journal-title":"On notation for ordinal numbers"},{"key":"S0022481200073126_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1947-0025420-1"},{"key":"S0022481200073126_ref007","first-page":"109","volume":"10","author":"Kleene","year":"1945","journal-title":"On the interpretation of intuitionistic number theory"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200073126","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,8]],"date-time":"2019-06-08T06:33:00Z","timestamp":1559975580000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200073126\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1949,5,16]]},"references-count":8,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1949,5,16]]}},"alternative-id":["S0022481200073126"],"URL":"https:\/\/doi.org\/10.2307\/2268973","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1949,5,16]]}}}