{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,14]],"date-time":"2024-07-14T10:11:31Z","timestamp":1720951891539},"reference-count":6,"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":12611,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,9]]},"abstract":"<jats:p>With PC understood to be the propositional calculus of [3], call a binary function <jats:italic>Pr<\/jats:italic> from the wffs of PC to the reals a <jats:italic>Carnap (probability) function<\/jats:italic> if it meets requirements A1\u2014A5 in Table I (with \u2018\u22a2\u2026\u2019 short in A3\u2014A4 for \u2018\u2026 is a tautology\u2019), and call the function a <jats:italic>Popper (probability) function<\/jats:italic> if it meets requirements Bl\u2014B6 there:<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200048283_eqnU1\" \/><\/jats:disp-formula><\/jats:p><jats:p>Leblanc established in [3] that <jats:italic>every Carnap function is a Popper one<\/jats:italic>, and he tendered proof of the converse. As reported by Stalnaker in [5], the proof unfortunately was incomplete, a mishap due to Leblanc's abbreviating \u2018<jats:italic>Pr(A, \u223c A)<\/jats:italic> = 1\u2019 as \u2018\u22a2 <jats:italic>A<\/jats:italic>\u2019 when <jats:italic>Pr<\/jats:italic> is a Popper function. Borrowing from [4], Leblanc <jats:italic>did<\/jats:italic> show, as Harper notes in [2, footnote 17], that<\/jats:p><jats:p>(1) <jats:italic>If Pr is a Popper function and A is a tautology, then Pr(A, \u223c A) = 1<\/jats:italic>. He did <jats:italic>not<\/jats:italic>, however, show that<\/jats:p><jats:p>(2) <jats:italic>If Pr is a Popper function and Pr(A, \u223c A) = 1, then A is a tautology<\/jats:italic>.<\/jats:p><jats:p>Nor could he have done so: (2) is false, as the simplest of counterexamples shows. Denied (2), Leblanc had no hope of proving that <jats:italic>every Popper function is a Carnap one<\/jats:italic>: of a Popper function <jats:italic>Pr<\/jats:italic> it is easily ascertained that <jats:italic>Pr<\/jats:italic> meets requirement A4 if and only if <jats:italic>Pr(A, \u223c A)<\/jats:italic> = 1 just in case <jats:italic>A<\/jats:italic> is a tautology.<\/jats:p>","DOI":"10.2307\/2273129","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:50:56Z","timestamp":1146952256000},"page":"369-373","source":"Crossref","is-referenced-by-count":10,"title":["On carnap and popper probability functions"],"prefix":"10.1017","volume":"44","author":[{"given":"Hugues","family":"Leblanc","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bas C.","family":"van Fraassen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048283_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF00649400"},{"key":"S0022481200048283_ref001","volume-title":"Logical foundations of probability","author":"Carnap","year":"1950"},{"key":"S0022481200048283_ref005","doi-asserted-by":"publisher","DOI":"10.1086\/288280"},{"key":"S0022481200048283_ref003","first-page":"238","volume":"25","author":"Leblanc","year":"1960","journal-title":"On requirements for conditional probability functions"},{"key":"S0022481200048283_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-1853-1_5"},{"key":"S0022481200048283_ref004","volume-title":"The logic of scientific discovery","author":"Popper","year":"1959"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048283","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T20:53:11Z","timestamp":1558903991000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048283\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,9]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1979,9]]}},"alternative-id":["S0022481200048283"],"URL":"https:\/\/doi.org\/10.2307\/2273129","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,9]]}}}