{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:18:11Z","timestamp":1774624691916,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,10,25]],"date-time":"2018-10-25T00:00:00Z","timestamp":1540425600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100012366","name":"Institute of Advanced Studies, University of Bristol","doi-asserted-by":"publisher","award":["IAS Benjamin Meaker Visiting Professorship"],"award-info":[{"award-number":["IAS Benjamin Meaker Visiting Professorship"]}],"id":[{"id":"10.13039\/100012366","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Philos Logic"],"published-print":{"date-parts":[[2019,8]]},"DOI":"10.1007\/s10992-018-9490-1","type":"journal-article","created":{"date-parts":[[2018,10,25]],"date-time":"2018-10-25T05:34:53Z","timestamp":1540445693000},"page":"685-707","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Reasoning about Arbitrary Natural Numbers from a Carnapian Perspective"],"prefix":"10.1007","volume":"48","author":[{"given":"Leon","family":"Horsten","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6386-5632","authenticated-orcid":false,"given":"Stanislav O.","family":"Speranski","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,10,25]]},"reference":[{"issue":"1","key":"9490_CR1","doi-asserted-by":"publisher","first-page":"47","DOI":"10.2307\/2183530","volume":"74","author":"P Benacerraf","year":"1965","unstructured":"Benacerraf, P. (1965). What numbers could not be. Philosophical Review, 74 (1), 47\u201373. \n                              https:\/\/doi.org\/10.2307\/2183530\n                              \n                           .","journal-title":"Philosophical Review"},{"issue":"2","key":"9490_CR2","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1093\/philmat\/4.2.184","volume":"4","author":"P Benacerraf","year":"1996","unstructured":"Benacerraf, P. (1996). Recantation or any old \u03c9-sequence would do after all. Philosophia Mathematica, 4 (2), 184\u2013189. \n                              https:\/\/doi.org\/10.1093\/philmat\/4.2.184\n                              \n                           .","journal-title":"Philosophia Mathematica"},{"key":"9490_CR3","volume-title":"Meaning and necessity. A Study in semantics and modal logic (3rd edn)","author":"R Carnap","year":"1956","unstructured":"Carnap, R. (1956). Meaning and necessity. A Study in semantics and modal logic (3rd edn). Chicago: University of Chicago Press."},{"key":"9490_CR4","volume-title":"Reasoning with arbitrary objects","author":"K Fine","year":"1985","unstructured":"Fine, K. (1985). Reasoning with arbitrary objects. Oxford: Blackwell."},{"issue":"1","key":"9490_CR5","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1007\/BF00542649","volume":"14","author":"K Fine","year":"1985","unstructured":"Fine, K. (1985). Natural deduction and arbitrary objects. Journal of Philosophical Logic, 14(1), 57\u2013107. \n                              https:\/\/doi.org\/10.1007\/BF00542649\n                              \n                           .","journal-title":"Journal of Philosophical Logic"},{"issue":"12","key":"9490_CR6","doi-asserted-by":"publisher","first-page":"599","DOI":"10.2307\/2564641","volume":"95","author":"K Fine","year":"1998","unstructured":"Fine, K. (1998). Cantorian abstraction: a reconstruction and defence. Journal of Philosophy, 95(12), 599\u2013634. \n                              https:\/\/doi.org\/10.2307\/2564641\n                              \n                           .","journal-title":"Journal of Philosophy"},{"issue":"2","key":"9490_CR7","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1007\/s11225-013-9479-2","volume":"101","author":"E Gr\u00e4del","year":"2013","unstructured":"Gr\u00e4del, E., & V\u00e4\u00e4n\u00e4nen, J. (2013). Dependence and independence. Studia Logica, 101(2), 399\u2013410. \n                              https:\/\/doi.org\/10.1007\/s11225-013-9479-2\n                              \n                           .","journal-title":"Studia Logica"},{"issue":"2","key":"9490_CR8","doi-asserted-by":"publisher","first-page":"174","DOI":"10.1093\/philmat\/nki021","volume":"13","author":"V Halbach","year":"2005","unstructured":"Halbach, V., & Horsten, L. (2005). Computational structuralism. Philosophia Mathematica, 13(2), 174\u2013186. \n                              https:\/\/doi.org\/10.1093\/philmat\/nki021\n                              \n                           .","journal-title":"Philosophia Mathematica"},{"issue":"3","key":"9490_CR9","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1007\/s11225-010-9243-9","volume":"94","author":"J Heylen","year":"2010","unstructured":"Heylen, J. (2010). Carnap\u2019s theory of descriptions and its problems. Studia Logica, 94(3), 355\u2013380. \n                              https:\/\/doi.org\/10.1007\/s11225-010-9243-9\n                              \n                           .","journal-title":"Studia Logica"},{"key":"9490_CR10","doi-asserted-by":"publisher","unstructured":"Hintikka, J., & Sandu, G. (1989). Informational dependence as a semantical phenomenon. In J.E. Fenstad, I.T. Frolov, R. Hilpinen (Eds.) Logic, methodology, and philosophy of science VIII, Studies in logic and the foundations of mathematics 126 (pp. 571\u2013589). North-Holland Publishing Company. \n                              https:\/\/doi.org\/10.1016\/S0049-237X(08)70066-1\n                              \n                           .","DOI":"10.1016\/S0049-237X(08)70066-1"},{"key":"9490_CR11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511624919","volume-title":"The principles of mathematics revisited","author":"J Hintikka","year":"1996","unstructured":"Hintikka, J. (1996). The principles of mathematics revisited. Cambridge: Cambridge University Press. \n                              https:\/\/doi.org\/10.1017\/CBO9780511624919\n                              \n                           ."},{"issue":"3","key":"9490_CR12","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1093\/philmat\/nkr039","volume":"20","author":"L Horsten","year":"2012","unstructured":"Horsten, L. (2012). Vom Z\u00e4hlen zu den Zahlen: on the relation between computation and arithmetical structuralism. Philosophia Mathematica, 20(3), 275\u2013288. \n                              https:\/\/doi.org\/10.1093\/philmat\/nkr039\n                              \n                           .","journal-title":"Philosophia Mathematica"},{"key":"9490_CR13","doi-asserted-by":"publisher","unstructured":"Horsten, L. (2018). Generic structures. Philosophia Mathematica. Published online. \n                              https:\/\/doi.org\/10.1093\/philmat\/nky015\n                              \n                           .","DOI":"10.1093\/philmat\/nky015"},{"issue":"2","key":"9490_CR14","first-page":"70","volume":"66","author":"SA Kripke","year":"1992","unstructured":"Kripke, S.A. (1992). Individual concepts: their logic, philosophy, and some of their uses. Proceedings and Addresses of the American Philosophical Association, 66 (2), 70\u201373.","journal-title":"Proceedings and Addresses of the American Philosophical Association"},{"issue":"1","key":"9490_CR15","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1017\/S1755020311000281","volume":"5","author":"J Ladyman","year":"2012","unstructured":"Ladyman, J., Linnebo, \u00d8., Pettigrew, R. (2012). Identity and discernibility in philosophy and logic. Review of Symbolic Logic, 5(1), 162\u2013186. \n                              https:\/\/doi.org\/10.1017\/S1755020311000281\n                              \n                           .","journal-title":"Review of Symbolic Logic"},{"key":"9490_CR16","doi-asserted-by":"publisher","DOI":"10.1093\/0195139305.001.0001","volume-title":"Philosophy of mathematics: structure and ontology","author":"S Shapiro","year":"1997","unstructured":"Shapiro, S. (1997). Philosophy of mathematics: structure and ontology. Oxford: Oxford University Press. \n                              https:\/\/doi.org\/10.1093\/0195139305.001.0001\n                              \n                           ."},{"key":"9490_CR17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31933-4","volume-title":"Turing computability: theory and applications","author":"RI Soare","year":"2016","unstructured":"Soare, R.I. (2016). Turing computability: theory and applications. Berlin: Springer. \n                              https:\/\/doi.org\/10.1007\/978-3-642-31933-4\n                              \n                           ."},{"issue":"5\u20136","key":"9490_CR18","doi-asserted-by":"publisher","first-page":"507","DOI":"10.1007\/s00153-013-0328-9","volume":"52","author":"SO Speranski","year":"2013","unstructured":"Speranski, S.O. (2013). A note on definability in fragments of arithmetic with free unary predicates. Archive for Mathematical Logic, 52(5\u20136), 507\u2013516. \n                              https:\/\/doi.org\/10.1007\/s00153-013-0328-9\n                              \n                           .","journal-title":"Archive for Mathematical Logic"},{"key":"9490_CR19","doi-asserted-by":"publisher","DOI":"10.1093\/acprof:oso\/9780199552078.001.0001","volume-title":"Modal logic as metaphysics","author":"T Williamson","year":"2013","unstructured":"Williamson, T. (2013). Modal logic as metaphysics. Oxford: Oxford University Press. \n                              https:\/\/doi.org\/10.1093\/acprof:oso\/9780199552078.001.0001\n                              \n                           ."}],"container-title":["Journal of Philosophical Logic"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10992-018-9490-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-018-9490-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-018-9490-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T16:16:01Z","timestamp":1572020161000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10992-018-9490-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,25]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,8]]}},"alternative-id":["9490"],"URL":"https:\/\/doi.org\/10.1007\/s10992-018-9490-1","relation":{},"ISSN":["0022-3611","1573-0433"],"issn-type":[{"value":"0022-3611","type":"print"},{"value":"1573-0433","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,25]]},"assertion":[{"value":"15 May 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 October 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 October 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}