{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T04:05:54Z","timestamp":1648958754204},"reference-count":13,"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":11424,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,12]]},"abstract":"<jats:p>Quine has shown that set theory may be based on inclusion and abstraction [1937], [1953]. He quantifies over (or abstracts upon) sets of all kinds, of course, including sets of sets. Here I confine Quine's approach to quantification over (abstraction upon) individuals alone, or at any rate their unit classes. Forsaking quantification over sets undercuts Quine's definition of negation, however. Smullyan sketches a first-order restriction of Quine's approach with no bound class variables for which inclusion and abstraction alone are adequate logical primitives [1957, n. 10]. However, the definition of negation requires more than one element in the universe of discourse. This requirement is met for Smullyan because he is doing arithmetic. Here, on the other hand, I presuppose only that the universe is nonempty. Accordingly, I assume a third primitive notion, the empty class. I will show that this threefold basis suffices both for classical first-order logic and for a version of \u201cfree\u201d many-sorted logic. The monadic fragment, which I call Boolean logic with abstraction, is intermediate in strength between Boolean class logic and Lesniewski's Ontology. It affords a novel perspective on descriptions, particularly in their generic use.<\/jats:p>","DOI":"10.2307\/2273099","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:01:43Z","timestamp":1146938503000},"page":"793-808","source":"Crossref","is-referenced-by-count":0,"title":["First-order logic based on inclusion and abstraction"],"prefix":"10.1017","volume":"47","author":[{"given":"John","family":"Bacon","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120004367X_ref012","first-page":"55","volume":"22","author":"Smullyan","year":"1957","journal-title":"Languages in which self reference is possible"},{"key":"S002248120004367X_ref011","first-page":"229","volume-title":"Philosophical perspectives","author":"Sellars","year":"1967"},{"key":"S002248120004367X_ref006","volume-title":"Grundgesetze der Arithmetik","volume":"1","author":"Frege","year":"1983"},{"key":"S002248120004367X_ref003","volume-title":"Introduction to mathematical logic","volume":"1","author":"Church","year":"1956"},{"key":"S002248120004367X_ref010","first-page":"94","volume-title":"From a logical point of view: 9 logico-philosophlcal essays","author":"Quine","year":"1953"},{"key":"S002248120004367X_ref002","first-page":"197","article-title":"The untenability of genera","volume":"17","author":"Bacon","year":"1974","journal-title":"Logique et Analyse"},{"key":"S002248120004367X_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF00423086"},{"key":"S002248120004367X_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02120669"},{"key":"S002248120004367X_ref008","first-page":"111","article-title":"\u00dcber die Grundlagen der Ontologie","volume":"23","author":"Le\u015bniewski","year":"1930","journal-title":"Comptes Rendus des S\u00e9ances de la Soci\u00e9t\u00e9 des Sciences et des Lettres de Varsovie, Classe iii"},{"key":"S002248120004367X_ref004","volume-title":"Symbolic logic: an introduction","author":"Fitch","year":"1952"},{"key":"S002248120004367X_ref005","first-page":"66","volume-title":"Funktion, Begriff, Bedeutung: f\u00fcnf logische Studien","author":"Frege","year":"1966"},{"key":"S002248120004367X_ref009","first-page":"145","volume":"2","author":"Quine","year":"1937","journal-title":"Logic based on inclusion and abstraction"},{"key":"S002248120004367X_ref013","volume-title":"Symbolic logic: an introduction","author":"Thomason","year":"1970"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120004367X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T16:18:38Z","timestamp":1558714718000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120004367X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,12]]},"references-count":13,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1982,12]]}},"alternative-id":["S002248120004367X"],"URL":"https:\/\/doi.org\/10.2307\/2273099","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,12]]}}}