{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T08:46:06Z","timestamp":1777538766644,"version":"3.51.4"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":2146,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[2008,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper deals with the problem of giving a principled characterization of the class of logical constants. According to the so-called Tarski\u2013Sher thesis, an operation is logical iff it is invariant under permutation. In the model-theoretic tradition, this criterion has been widely accepted as giving a necessary condition for an operation to be logical. But it has been also widely criticized on the account that it counts too many operations as logical, failing thus to provide a sufficient condition.<\/jats:p><jats:p>Our aim is to solve this problem of overgeneration by modifying the invariance criterion. We introduce a general notion of invariance under a similarity relation and present the connection between similarity relations and classes of invariant operations. The next task is to isolate a similarity relation well-suited for a definition of logicality. We argue that the standard arguments in favor of invariance under permutation, which rely on the generality and the formality of logic, should be modified. The revised arguments are shown to support an alternative to Tarski's criterion, according to which an operation is logical iff it is invariant under potential isomorphism.<\/jats:p>","DOI":"10.2178\/bsl\/1208358843","type":"journal-article","created":{"date-parts":[[2008,4,16]],"date-time":"2008-04-16T19:49:36Z","timestamp":1208375376000},"page":"29-68","source":"Crossref","is-referenced-by-count":59,"title":["Logicality and Invariance"],"prefix":"10.1017","volume":"14","author":[{"given":"Denis","family":"Bonnay","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600001815_ref022","volume-title":"The bounds of logic","author":"Sher","year":"1991"},{"key":"S1079898600001815_ref023","doi-asserted-by":"publisher","DOI":"10.1080\/01445348608837096"},{"key":"S1079898600001815_ref017","first-page":"717","volume-title":"Model-theoretic logics","author":"Makowski","year":"1985"},{"key":"S1079898600001815_ref016","unstructured":"MacFarlane J.G. [2000], What does itmean to say that logic is formal, Ph.D.Dissertation, University of Pittsburgh."},{"key":"S1079898600001815_ref021","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1093\/oso\/9780198236542.003.0005","volume-title":"Philosophy of Mathematics Today: Proceedings of an International Conference in Munich","author":"Shapiro","year":"1998"},{"key":"S1079898600001815_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059538"},{"key":"S1079898600001815_ref015","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044481714-3\/50020-5"},{"key":"S1079898600001815_ref010","first-page":"29","article-title":"Persistent and invariant formulas for outer extensions","volume":"20","author":"Feferman","year":"1968","journal-title":"Compositio Mathematica"},{"key":"S1079898600001815_ref018","doi-asserted-by":"publisher","DOI":"10.1007\/BF00265253"},{"key":"S1079898600001815_ref002","first-page":"25","volume-title":"Model-theoretic logics","author":"Barwise","year":"1985"},{"key":"S1079898600001815_ref005","unstructured":"Bonnay D. [2006], Qu'est-ce qu'une constante logique?, Ph.D. Dissertation, University Paris 1."},{"key":"S1079898600001815_ref007","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093635154"},{"key":"S1079898600001815_ref019","doi-asserted-by":"crossref","first-page":"12","DOI":"10.4064\/fm-44-1-12-36","article-title":"On a generalization of quantifiers","volume":"44","author":"Mostowski","year":"1957","journal-title":"Fundamenta Mathematicae"},{"key":"S1079898600001815_ref013","first-page":"77","volume-title":"Model-theoretic logics","author":"Flum","year":"1985"},{"key":"S1079898600001815_ref009","volume-title":"The concept of logical consequence","author":"Etchemendy","year":"1999"},{"key":"S1079898600001815_ref012","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1305\/ndjfl\/1039096304","article-title":"Logic, logics, and logicism","volume":"40","author":"Feferman","year":"1999","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S1079898600001815_ref001","first-page":"5","volume-title":"Model theory","volume":"8","author":"Barwise","year":"1973"},{"key":"S1079898600001815_ref008","volume-title":"The logical basis of metaphysics","author":"Dummett","year":"1991"},{"key":"S1079898600001815_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF00350139"},{"key":"S1079898600001815_ref024","first-page":"599","volume-title":"Model-theoretic logics","author":"V\u00e4\u00e4n\u00e4nen","year":"1985"},{"key":"S1079898600001815_ref004","first-page":"420","volume-title":"Reflections on the foundations of mathematics: Essays in honor of Solomon Feferman","volume":"15","author":"van Benthem","year":"2002"},{"key":"S1079898600001815_ref014","volume-title":"The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory","volume":"3","author":"G\u00f6del","year":"1940"},{"key":"S1079898600001815_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-006-9034-y"},{"key":"S1079898600001815_ref020","doi-asserted-by":"crossref","DOI":"10.4159\/9780674042445","volume-title":"Philosophy of logic","author":"Quine","year":"1986"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600001815","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,25]],"date-time":"2024-02-25T05:22:23Z","timestamp":1708838543000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600001815\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,3]]},"references-count":24,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,3]]}},"alternative-id":["S1079898600001815"],"URL":"https:\/\/doi.org\/10.2178\/bsl\/1208358843","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,3]]}}}