{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T15:40:04Z","timestamp":1762270804108},"reference-count":23,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":3114,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2005,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we devise some technical tools for dealing with problems connected with the philosophical view usually called mathematical instrumentalism. These tools are interesting in their own right, independently of their philosophical consequences. For example, we show that even though the fragment of Peanos Arithmetic known as <jats:italic>I<\/jats:italic>\u03a3<jats:sub>1<\/jats:sub> is a conservative extension of the equational theory of Primitive Recursive Arithmetic (<jats:italic>PRA<\/jats:italic>). <jats:italic>I<\/jats:italic>\u03a3<jats:sub>1<\/jats:sub> has a super-exponential speed-up over <jats:italic>PRA<\/jats:italic>. On the other hand, theories studied in the Program of Reverse Mathematics that formalize powerful mathematical principles have only polynomial speed-up over <jats:italic>I<\/jats:italic>\u03a3<jats:sub>1<\/jats:sub>.<\/jats:p>","DOI":"10.2178\/jsl\/1122038914","type":"journal-article","created":{"date-parts":[[2005,7,22]],"date-time":"2005-07-22T18:44:56Z","timestamp":1122057896000},"page":"778-794","source":"Crossref","is-referenced-by-count":12,"title":["On mathematical instrumentalism"],"prefix":"10.1017","volume":"70","author":[{"given":"Patrick","family":"Caldon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aleksandar","family":"Ignjatovi\u0107","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200006794_ref023","first-page":"281","volume":"37","author":"Wainer","year":"1972","journal-title":"Ordinal recursion, and a refinement of the extended Grzegorczyk hierarchy"},{"key":"S0022481200006794_ref021","doi-asserted-by":"publisher","DOI":"10.2307\/2026089"},{"key":"S0022481200006794_ref019","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(86)90074-6"},{"key":"S0022481200006794_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(85)90030-2"},{"key":"S0022481200006794_ref017","first-page":"349","volume":"53","author":"Simpson","year":"1988","journal-title":"Partial realization of Hilbert'sprogram"},{"key":"S0022481200006794_ref014","first-page":"423","volume":"50","author":"Pudl\u00e1k","year":"1985","journal-title":"Cuts, consistency statements and interpretations"},{"key":"S0022481200006794_ref013","first-page":"564","volume":"48","author":"Paris","year":"1983","journal-title":"A note on undefinability of cuts"},{"key":"S0022481200006794_ref010","first-page":"322","volume":"59","author":"Ignjatovi\u0107","year":"1994","journal-title":"Hilbert's program and the \u03c9-rule"},{"key":"S0022481200006794_ref007","first-page":"185","volume-title":"Arithmetic, Proof Theory, and Computational Complexity","author":"H\u00e1jek","year":"1993"},{"key":"S0022481200006794_ref020","unstructured":"Solovay R. , Letter to P. H\u00e1jek, see also [6] and [13]."},{"key":"S0022481200006794_ref003","volume-title":"Bounded Arithmetic","author":"Buss","year":"1986"},{"key":"S0022481200006794_ref005","first-page":"1","volume":"29","author":"Feferman","year":"1964","journal-title":"Systems of predicative analysis"},{"key":"S0022481200006794_ref012","first-page":"273","volume-title":"Bertrand Russell: Philosopher of the Century","author":"Kreisel","year":"1967"},{"key":"S0022481200006794_ref004","volume-title":"A Mathematical Introduction to Logic","author":"Enderton","year":"1972"},{"key":"S0022481200006794_ref018","volume-title":"Subsystems of second order arithmetic","author":"Simpson","year":"1998"},{"key":"S0022481200006794_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-86894-8"},{"key":"S0022481200006794_ref022","volume-title":"Proof Theory","author":"Takeuti","year":"1987"},{"key":"S0022481200006794_ref006","first-page":"667","article-title":"On interpretability of theories containing arithmetic, II","volume":"22","author":"H\u00e1jek","year":"1981","journal-title":"Commentationes Mathematical Universitatis Carolinae"},{"key":"S0022481200006794_ref009","unstructured":"Ignjatovi\u0107 A. , Fragments of first- and second-order arithmetic and length of proofs, Ph.D. thesis, University of California at Berkeley, Berkeley, California, 1990."},{"key":"S0022481200006794_ref015","volume-title":"Logic Colloquium '84","author":"Pudl\u00e1k","year":"1986"},{"key":"S0022481200006794_ref002","unstructured":"Brown D. K. , Subsystems of second order arithmetic, Ph.D. thesis, Pennsylvania State University, 1987."},{"key":"S0022481200006794_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(96)00003-6"},{"key":"S0022481200006794_ref011","volume-title":"Logic Colloquium '85","author":"Isaacson","year":"1987"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200006794","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T20:14:49Z","timestamp":1556914489000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200006794\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,9]]},"references-count":23,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2005,9]]}},"alternative-id":["S0022481200006794"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1122038914","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,9]]}}}