{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T14:38:42Z","timestamp":1759847922080},"reference-count":22,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":5215,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1999,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In a 1969 paper, Quine coined the term \u2018limits of decision\u201d. This term evidently refers to limits on the logical vocabulary of a logic, beyond which satisfiability is no longer decidable. In the same paper, Quine showed that not only monadic formulas, but homogeneous <jats:italic>k<\/jats:italic> -adic formulas for arbitrary <jats:italic>k<\/jats:italic> lie on the decidable side of the limits of decision. But the precise location of the limits of decision has remained an open question. The present paper answers that question. It addresses the question of decidability of those sublogics of first-order logic that are defined in terms of their logical vocabularies. A complete answer is obtained, thus locating exactly Quine's limits of decision.<\/jats:p>","DOI":"10.2307\/2586789","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T14:03:57Z","timestamp":1146924237000},"page":"1439-1466","source":"Crossref","is-referenced-by-count":6,"title":["Quine's \u2018limits of decision\u2019"],"prefix":"10.1017","volume":"64","author":[{"given":"William C.","family":"Purdy","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200012676_ref017","first-page":"157","volume-title":"Proceedings of the 14th International Congress of Philosophy, vol. III, University of Vienna, 1969","author":"Quine","year":"1981"},{"key":"S0022481200012676_ref006","volume-title":"A mathematical introduction to logic","author":"Enderton","year":"1972"},{"key":"S0022481200012676_ref013","volume-title":"Combinatorial optimization","author":"Papadimitriou","year":"1982"},{"key":"S0022481200012676_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4489-7"},{"key":"S0022481200012676_ref005","volume-title":"Mathematical logic","author":"Ebbinghaus","year":"1984"},{"key":"S0022481200012676_ref015","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1305\/ndjfl\/1040067318","article-title":"Decidability of fluted logic with identity","volume":"37","author":"Purdy","year":"1996","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S0022481200012676_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-3296-4_8"},{"key":"S0022481200012676_ref021","volume-title":"Methods of logic","author":"Quine","year":"1982"},{"key":"S0022481200012676_ref016","first-page":"608","volume":"61","author":"Purdy","year":"1996","journal-title":"Fluted formulas and the limits of decidability"},{"key":"S0022481200012676_ref018","first-page":"343","article-title":"Variables explained away","volume":"104","author":"Quine","year":"1960","journal-title":"Proceedings of the American Philosophical Society"},{"key":"S0022481200012676_ref003","volume-title":"The decision problem: Solvable classes of quantificational formulas","author":"Dreben","year":"1979"},{"key":"S0022481200012676_ref014","volume-title":"Proceedings of the workshop on variable-free semantics, University of Osnabrueck, September 12\u201313, 1996","author":"Purdy"},{"key":"S0022481200012676_ref004","volume-title":"Finite model theory","author":"Ebbinghaus","year":"1995"},{"key":"S0022481200012676_ref012","volume-title":"The logic of natural language","author":"Noah","year":"1982"},{"key":"S0022481200012676_ref019","volume-title":"The ways of paradox and other essays","author":"Quine","year":"1976"},{"key":"S0022481200012676_ref020","first-page":"649","volume":"46","author":"Quine","year":"1981","journal-title":"Predicate functors revisited"},{"key":"S0022481200012676_ref022","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-3763-5_2"},{"key":"S0022481200012676_ref011","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093883255"},{"key":"S0022481200012676_ref008","volume-title":"Logic, language-games and information","author":"Hintikka","year":"1973"},{"key":"S0022481200012676_ref001","volume-title":"An introduction to mathematical logic and type theory","author":"Andrews","year":"1986"},{"key":"S0022481200012676_ref010","volume-title":"Elements of the theory of computation","author":"Lewis","year":"1981"},{"key":"S0022481200012676_ref009","volume-title":"Unsolvable classes of quantificational formulas","author":"Lewis","year":"1979"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200012676","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,9]],"date-time":"2019-05-09T15:57:26Z","timestamp":1557417446000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200012676\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,12]]},"references-count":22,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1999,12]]}},"alternative-id":["S0022481200012676"],"URL":"https:\/\/doi.org\/10.2307\/2586789","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,12]]}}}