{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:06Z","timestamp":1740123906050,"version":"3.37.3"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2019,2,4]],"date-time":"2019-02-04T00:00:00Z","timestamp":1549238400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Philos Logic"],"published-print":{"date-parts":[[2019,10]]},"DOI":"10.1007\/s10992-019-09500-4","type":"journal-article","created":{"date-parts":[[2019,2,4]],"date-time":"2019-02-04T01:05:07Z","timestamp":1549242307000},"page":"885-908","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Burali-Forti as a Purely Logical Paradox"],"prefix":"10.1007","volume":"48","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1653-6611","authenticated-orcid":false,"given":"Graham","family":"Leach-Krouse","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,2,4]]},"reference":[{"issue":"6","key":"9500_CR1","doi-asserted-by":"publisher","first-page":"130","DOI":"10.1093\/analys\/22.6.130","volume":"22","author":"ND Belnapv","year":"1962","unstructured":"Belnapv, N.D. (1962). Tonk, plonk and plink. Analysis, 22(6), 130.","journal-title":"Analysis"},{"key":"9500_CR2","unstructured":"Barwise, J, & Feferman, S. (Eds.). (1985). Model-theoretic logics. Perspectives in mathematical logic. New York: Springer."},{"key":"9500_CR3","unstructured":"Cardone, F., & Hindley, J.R. (2009). Lambda-calculus and combinators in the 20th century. In Gabbay, D.M., & Woods, J. (Eds.) Logic from Russell to church, volume 5 of Handbook of the History of Logic. New York: Elsevier."},{"key":"9500_CR4","volume-title":"Frege: philosophy of language","author":"M Dummett","year":"1973","unstructured":"Dummett, M. (1973). Frege: philosophy of language. London: Duckworth. OCLC: 845425340."},{"key":"9500_CR5","volume-title":"The logical basis of metaphysics. Number 1976 in The William James Lectures","author":"M Dummett","year":"1994","unstructured":"Dummett, M. (1994). The logical basis of metaphysics. Number 1976 in The William James Lectures. Cambridge: Harvard University Press. Mass, 3. print edition. OCLC: 176860499."},{"key":"9500_CR6","unstructured":"Gentzen, G. (1969). The Collected Papers of Gerhard Gentzen. North Holland."},{"key":"9500_CR7","unstructured":"Girard, J.-Y. (1971). Une Extension De L\u2019Interpretation De G\u00f6del a L\u2019Analyse, Et Son Application a L\u2019Elimination Des Coupures Dans L\u2019Analyse Et La Theorie Des Types. In Studies in logic and the foundations of mathematics, (Vol. 63 pp. 63\u201392): Elsevier."},{"key":"9500_CR8","unstructured":"Girard, J.-Y. (1990). The system F of variable types, 15 years later. In Huet, G. (Ed.) Logical Foundations of Functional Programming (pp. 87\u2013126). Boston: Addison-Wesley Longman Publishing Co., Inc."},{"key":"9500_CR9","doi-asserted-by":"crossref","unstructured":"Klement, K.C. (2010). Russell, his paradoxes, and Cantor\u2019s theorem: part I philosophy compass.","DOI":"10.1111\/j.1747-9991.2009.00271.x"},{"key":"9500_CR10","doi-asserted-by":"publisher","first-page":"123","DOI":"10.4064\/fm-99-2-123-132","volume":"99","author":"H Kotlarski","year":"1978","unstructured":"Kotlarski, H. (1978). Some remarks on well-ordered models. Fundamenta Mathematicae, 99, 123\u2013132.","journal-title":"Fundamenta Mathematicae"},{"key":"9500_CR11","first-page":"134","volume-title":"Lecture Notes in Mathematics","author":"F. William Lawvere","year":"1969","unstructured":"Lawvere, F. (1969). Diagonal arguments and cartesian closed categories. Category theory."},{"key":"9500_CR12","doi-asserted-by":"crossref","unstructured":"Martin, RL. (1977). On a puzzling classical validity. The Philosophical Review.","DOI":"10.2307\/2184563"},{"issue":"6","key":"9500_CR13","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1007\/BF00265253","volume":"25","author":"V McGee","year":"1996","unstructured":"McGee, V. (1996). Logical Operations. Journal of Philosophical Logic, 25(6), 567\u2013580.","journal-title":"Journal of Philosophical Logic"},{"issue":"3","key":"9500_CR14","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1016\/0315-0860(81)90070-7","volume":"8","author":"GH Moore","year":"1981","unstructured":"Moore, G.H., & Garciadiego, A. (1981). Burali-Forti\u2019s paradox: a reappraisal of its origins. Historia Mathematica, 8(3), 319\u2013350.","journal-title":"Historia Mathematica"},{"issue":"1","key":"9500_CR15","first-page":"37","volume":"19","author":"D Mirimanoff","year":"1917","unstructured":"Mirimanoff, D. (1917). Les antinomies de Russell et de Burali-Forti et le probl\u00e8me fondamental de la th\u00e9orie des ensembles. L\u2019Enseignement Math\u00e9matique, 19(1), 37\u201352.","journal-title":"L\u2019Enseignement Math\u00e9matique"},{"key":"9500_CR16","unstructured":"Michael, P. (2004). Set theory and its philosophy: a critical introduction. Oxford University Press."},{"issue":"1-2","key":"9500_CR17","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1007\/BF00660889","volume":"27","author":"Dag Prawitz","year":"1974","unstructured":"Prawitz, D. (1974). On the idea of a general proof theory. Synthese, 27(1\/2,).","journal-title":"Synthese"},{"key":"9500_CR18","volume-title":"Natural deduction: a proof-theoretical study. Dover books on mathematics","author":"D Prawitz","year":"2006","unstructured":"Prawitz, D. (2006). Natural deduction: a proof-theoretical study. Dover books on mathematics. Mineola: Dover Publications. Dover ed edition. OCLC: ocm61296001."},{"issue":"2","key":"9500_CR19","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1093\/analys\/21.2.38","volume":"21","author":"AN Prior","year":"1960","unstructured":"Prior, A.N. (1960). The runabout inference-ticket. Analysis, 21(2), 38.","journal-title":"Analysis"},{"issue":"409","key":"9500_CR20","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1093\/mind\/103.409.25","volume":"103","author":"GG Priest","year":"1994","unstructured":"Priest, G.G. (1994). The structure of the paradoxes of self-reference. Mind, 103(409), 25\u201334.","journal-title":"Mind"},{"key":"9500_CR21","unstructured":"Ramsey, F.P. (1925). The foundations of mathematics. In The foundations of mathematics and other logical essays (pp. 1\u201361). Routledge & Kegan Paul LTD."},{"key":"9500_CR22","unstructured":"Restall, G. (1994). On logics without contraction. PhD thesis, Department of Philosophy University of Queensland."},{"issue":"01","key":"9500_CR23","doi-asserted-by":"publisher","first-page":"1","DOI":"10.2307\/2267550","volume":"7","author":"B Rosser","year":"1942","unstructured":"Rosser, B. (1942). The Burali-Forti paradox. The Journal of Symbolic Logic, 7(01), 1\u201317.","journal-title":"The Journal of Symbolic Logic"},{"issue":"1","key":"9500_CR24","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1112\/plms\/s2-4.1.29","volume":"s2-4","author":"B Russell","year":"1907","unstructured":"Russell, B. (1907). On some difficulties in the theory of transfinite numbers and order types. Proceedings of the London Mathematical Society, s2-4(1), 29\u201353.","journal-title":"Proceedings of the London Mathematical Society"},{"key":"9500_CR25","volume-title":"Introduction to mathematical philosophy","author":"B Russell","year":"1920","unstructured":"Russell, B. (1920). Introduction to mathematical philosophy. London: Allen & Unwin."},{"key":"9500_CR26","unstructured":"Steinberger, F. (2009). Harmony and logical inferentialism. PhD thesis, University of Cambridge, Hughes Hall."},{"issue":"4","key":"9500_CR27","doi-asserted-by":"publisher","first-page":"617","DOI":"10.1080\/00048402.2010.528781","volume":"89","author":"F Steinberger","year":"2011","unstructured":"Steinberger, F. (2011). What harmony could and could not be? Australasian Journal of Philosophy, 89(4), 617\u2013639.","journal-title":"Australasian Journal of Philosophy"},{"issue":"6","key":"9500_CR28","doi-asserted-by":"publisher","first-page":"980","DOI":"10.1090\/S0002-9904-1966-11611-7","volume":"72","author":"WW Tait","year":"1966","unstructured":"Tait, W.W. (1966). A nonconstructive proof of Gentzen\u2019s Hauptsatz for second order predicate logic. Bulletin of the American Mathematical Society, 72(6), 980\u2013984.","journal-title":"Bulletin of the American Mathematical Society"},{"key":"9500_CR29","doi-asserted-by":"publisher","first-page":"39","DOI":"10.4099\/jjm1924.23.0_39","volume":"23","author":"G Takeuti","year":"1953","unstructured":"Takeuti, G. (1953). On a generalized logical calculus. Japanese Journal of Mathematics, 23, 39\u201396.","journal-title":"Japanese Journal of Mathematics"},{"issue":"2","key":"9500_CR30","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1080\/01445348608837096","volume":"7","author":"A Tarski","year":"1986","unstructured":"Tarski, A. (1986). What are logical notions? History and Philosophy of Logic, 7(2), 143\u2013154.","journal-title":"History and Philosophy of Logic"},{"key":"9500_CR31","unstructured":"Tennant, N. Inferentialism, logicism, harmony, and a counterpoint. To appear in ed. Alex Miller, essays for Crispin Wright: logic, language and mathematics (in preparation for Oxford University Press: volume 2 of a two-volume Festschrift for Crispin Wright, co-edited with Annalisa Coliva)."},{"key":"9500_CR32","volume-title":"Natural logic","author":"N Tennant","year":"1990","unstructured":"Tennant, N. (1990). Natural logic. Edinburgh: Edinburgh University Press."},{"issue":"03","key":"9500_CR33","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1017\/S1755020311000360","volume":"5","author":"N Tennant","year":"2012","unstructured":"Tennant, N. (2012). Cut for core logic. The Review of Symbolic Logic, 5(03), 450\u2013479.","journal-title":"The Review of Symbolic Logic"},{"key":"9500_CR34","doi-asserted-by":"crossref","unstructured":"Tennant, N. (2016). Normalizability, cut eliminability and paradox. Synthese.","DOI":"10.1007\/s11229-016-1119-8"},{"key":"9500_CR35","unstructured":"Thompson, J.F. (1962). On some paradoxes. In Butler, R.J. (Ed.), Analytical philosophy (pp. 104\u2013119)."},{"issue":"4","key":"9500_CR36","doi-asserted-by":"publisher","first-page":"504","DOI":"10.2307\/2687796","volume":"7","author":"J V\u00e4\u00e4n\u00e4nen","year":"2001","unstructured":"V\u00e4\u00e4n\u00e4nen, J. (2001). Second-order logic and the foundations of mathematics. The Bulletin of Symbolic Logic, 7(4), 504\u2013520.","journal-title":"The Bulletin of Symbolic Logic"},{"issue":"3","key":"9500_CR37","doi-asserted-by":"publisher","first-page":"362","DOI":"10.2178\/bsl\/1058448677","volume":"9","author":"NS Yanofsky","year":"2003","unstructured":"Yanofsky, N.S. (2003). A universal approach to self-referential paradoxes, incompleteness and fixed points. The Bulletin of Symbolic Logic, 9(3), 362\u2013386.","journal-title":"The Bulletin of Symbolic Logic"},{"issue":"6","key":"9500_CR38","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1080\/00029890.1987.12000674","volume":"94","author":"WS Zwicker","year":"1987","unstructured":"Zwicker, W.S. (1987). Playing games with games: the hypergame paradox. The American Mathematical Monthly, 94(6), 507.","journal-title":"The American Mathematical Monthly"}],"container-title":["Journal of Philosophical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10992-019-09500-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-019-09500-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-019-09500-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T19:12:55Z","timestamp":1580757175000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10992-019-09500-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2,4]]},"references-count":38,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["9500"],"URL":"https:\/\/doi.org\/10.1007\/s10992-019-09500-4","relation":{},"ISSN":["0022-3611","1573-0433"],"issn-type":[{"type":"print","value":"0022-3611"},{"type":"electronic","value":"1573-0433"}],"subject":[],"published":{"date-parts":[[2019,2,4]]},"assertion":[{"value":"24 July 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 February 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}