{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T08:10:16Z","timestamp":1707034216779},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":6711,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[1995,9]]},"abstract":"<jats:p>In 1934 Alonzo Church, Kurt G\u00f6dei, S. C. Kleene, and J. B. Rosser were all to be found in Princeton, New Jersey. In 1936 Church founded The Journal of Symbolic Logic. Shortly thereafter Alan Turing arrived for a two year visit. The United States had become a world center for cutting-edge research in mathematical logic. In this brief survey<jats:sup>1<\/jats:sup>we shall examine some of the writings of American logicians during the 1920s, a period of important beginnings and remarkable insights as well as of confused gropings.<\/jats:p><jats:p>The publication of Whitehead and Russell's monumental<jats:italic>Principia Mathematica<\/jats:italic>[18] during the years 1910-1913 provided the basis for much of the research that was to follow. It also provided the basis for confusion that remained a factor during the period we are discussing. In 1908, Henri Poincar\u00e9, a famous skeptic where mathematical logic was concerned, wrote pointedly ([13]):<\/jats:p><jats:p>It is difficult to admit that the word<jats:italic>if<\/jats:italic>acquires, when written \u2283, a virtue it did not possess when written<jats:italic>if<\/jats:italic>.<\/jats:p><jats:p><jats:italic>Principia<\/jats:italic>provided no very convincing answer to Poincar\u00e9. Indeed the fact that the authors of<jats:italic>Principia<\/jats:italic>saw fit to place their first two \u201cprimitive propositions\u201d<\/jats:p><jats:p>*1.1: Anything implied by a true proposition is true.<\/jats:p><jats:p>*1.2: \u22a2<jats:italic>p<\/jats:italic>\u22c1<jats:italic>p<\/jats:italic>\u2283<jats:italic>p<\/jats:italic><\/jats:p><jats:p>under one and the same heading suggest that they had thought of what they were doing as just such a translation as Poincare had derided.<\/jats:p>","DOI":"10.2307\/421156","type":"journal-article","created":{"date-parts":[[2006,5,7]],"date-time":"2006-05-07T07:08:06Z","timestamp":1146985686000},"page":"273-278","source":"Crossref","is-referenced-by-count":4,"title":["American Logic in the 1920s"],"prefix":"10.1017","volume":"1","author":[{"given":"Martin","family":"Davis","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S107989860000809X_ref018","volume-title":"Principia mathematica","volume":"1","author":"Whitehead","year":"1910"},{"key":"S107989860000809X_ref016","volume-title":"Solvability, provability, definability: The collected works of Emil L. Post","author":"Post","year":"1994"},{"key":"S107989860000809X_ref006","first-page":"xi","volume-title":"Solvability, Provability, Definability: The Collected Works of Emil L. Post","author":"Davis"},{"key":"S107989860000809X_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1928-04516-0"},{"key":"S107989860000809X_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1928-04625-6"},{"key":"S107989860000809X_ref008","doi-asserted-by":"publisher","DOI":"10.2307\/1968352"},{"key":"S107989860000809X_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01283841"},{"key":"S107989860000809X_ref017","volume-title":"From Frege to G\u00f6del","author":"van Heijenoort","year":"1967"},{"key":"S107989860000809X_ref015","first-page":"249","volume-title":"The two-valued iterative systems of mathematical logic","author":"Post","year":"1941"},{"key":"S107989860000809X_ref002","first-page":"178","article-title":"Alternatives to Zermelo's assumption","volume":"29","author":"Church","year":"1926","journal-title":"Transactions of the American Mathematical Society"},{"key":"S107989860000809X_ref012","doi-asserted-by":"crossref","DOI":"10.1525\/9780520398252","volume-title":"A survey of symbolic logic","author":"Lewis","year":"1918"},{"key":"S107989860000809X_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(82)91226-8"},{"key":"S107989860000809X_ref007","volume-title":"Grundz\u00fcge der theoretischen Logik","author":"Hilbert","year":"1928"},{"key":"S107989860000809X_ref004","doi-asserted-by":"publisher","DOI":"10.2307\/2370728"},{"key":"S107989860000809X_ref014","doi-asserted-by":"publisher","DOI":"10.2307\/2370324"},{"key":"S107989860000809X_ref013","volume-title":"Science and method","author":"Poincar\u00e9","year":"1952"},{"key":"S107989860000809X_ref009","doi-asserted-by":"publisher","DOI":"10.2307\/1968390"},{"key":"S107989860000809X_ref011","article-title":"Review of","volume":"36","author":"Langford","year":"1930","journal-title":"Bulletin of the American Mathematical Society"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S107989860000809X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T07:35:41Z","timestamp":1707032141000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S107989860000809X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,9]]},"references-count":18,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["S107989860000809X"],"URL":"https:\/\/doi.org\/10.2307\/421156","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,9]]}}}