{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T16:01:05Z","timestamp":1775318465721,"version":"3.50.1"},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":6803,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[1995,6]]},"abstract":"<jats:p><jats:italic>Dedicated to Dana Scott on his sixtieth birthday<\/jats:italic>.<\/jats:p><jats:p>It is common knowledge that for a short while Hermann Weyl joined Brouwer in his pursuit of a revision of mathematics according to intuitionistic principles. There is, however, little in the literature that sheds light on Weyl's role and in particular on Brouwer's reaction to Weyl's allegiance to the cause of intuitionism. This short episode certainly raises a number of questions: what made Weyl give up his own program, spelled out in \u201c<jats:italic>Das Kontinuum<\/jats:italic>\u201d, how did Weyl come to be so well-informed about Brouwer's new intuitionism, in what respect did Weyl's intuitionism differ from Brouwer's intuitionism, what did Brouwer think of Weyl's views,\u2026? To some of these questions at least partial answers can be put forward on the basis of some of the available correspondence and notes. The present paper will concentrate mostly on the historical issues of the intuitionistic episode in Weyl's career.<\/jats:p><jats:p>Weyl entered the foundational controversy with a bang in 1920 with his sensational paper \u201cOn the new foundational crisis in mathematics\u201d. He had already made a name for himself in the foundations of mathematics in 1918 with his monograph \u201cThe Continuum\u201d [18]; this contained in addition to a technical logical-mathematical construction of the continuum, a fairly extensive discussion of the shortcomings of the traditional construction of the continuum on the basis of arbitrary\u2014and hence also impredicative\u2014Dedekind cuts.<\/jats:p>","DOI":"10.2307\/421038","type":"journal-article","created":{"date-parts":[[2006,5,7]],"date-time":"2006-05-07T07:07:50Z","timestamp":1146985670000},"page":"145-169","source":"Crossref","is-referenced-by-count":36,"title":["Hermann Weyl's Intuitionistic Mathematics"],"prefix":"10.1017","volume":"1","author":[{"given":"Dirk","family":"van Dalen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600008209_ref024","volume-title":"Selecta Hermann Weyl","author":"Weyl","year":"1956"},{"key":"S1079898600008209_ref023","doi-asserted-by":"publisher","DOI":"10.2307\/2306078"},{"key":"S1079898600008209_ref021","first-page":"1","article-title":"Die heutige Erkenntnislage in der Mathematik","volume":"1","author":"Weyl","year":"1925","journal-title":"Symposion"},{"key":"S1079898600008209_ref020","doi-asserted-by":"publisher","DOI":"10.1007\/BF01188076"},{"key":"S1079898600008209_ref015","first-page":"163","volume-title":"Intuitionism and Proof Theory","author":"Van Dalen","year":"1970"},{"key":"S1079898600008209_ref018","doi-asserted-by":"crossref","DOI":"10.1515\/9783112451144","volume-title":"Das Kontinuum. Kritische Untersuchungen \u00fcber die Grundlagen der Analysis","author":"Weyl","year":"1918"},{"key":"S1079898600008209_ref022","doi-asserted-by":"publisher","DOI":"10.1007\/BF02940603"},{"key":"S1079898600008209_ref001","unstructured":"Brouwer L. E. J. , Intuitionisme en Formalisme, Noordhoff, Groningen, 1912, 32 pp."},{"key":"S1079898600008209_ref009","volume-title":"Die Grundlagen der Mathematik, I","author":"Hilbert","year":"1934"},{"key":"S1079898600008209_ref017","first-page":"660","volume-title":"From Frege to G\u00f6del. a source book in mathematical logic, 1879\u20131931","author":"Heijenoort","year":"1967"},{"key":"S1079898600008209_ref014","volume-title":"Constructivism in Mathematics","volume":"II","author":"Troelstra","year":"1988"},{"key":"S1079898600008209_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1913-02440-6"},{"key":"S1079898600008209_ref003","first-page":"43","article-title":"Begr\u00fcndung der Mengenlehre unabh\u00e4ngig vom logischen Satz vom ausgeschlossenen Dritten. Erster Teil. Allgemeine Mengenlehre","volume":"12","author":"Brouwer","year":"1918","journal-title":"Koninklijke Nederlandse Akademie van Wetenschappen\u2013Verhandelingen"},{"key":"S1079898600008209_ref007","first-page":"73","volume-title":"Mathematische Grundlagenforschung. Beweistheorie","author":"Heyting","year":"1934"},{"key":"S1079898600008209_ref006","volume-title":"Hermann Weyl und die Mathematik an der ETH Z\u00fcrich","author":"Frey","year":"1913"},{"key":"S1079898600008209_ref016","unstructured":"Hoeven G. van der , Projections of lawless sequences, (diss.) Mathematical Centre Tracts, Amsterdam, 1982."},{"key":"S1079898600008209_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/BF02102305"},{"key":"S1079898600008209_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02940602"},{"key":"S1079898600008209_ref011","doi-asserted-by":"publisher","DOI":"10.1007\/BF01186549"},{"key":"S1079898600008209_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066772"},{"key":"S1079898600008209_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-01539-1"},{"key":"S1079898600008209_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01447860"},{"key":"S1079898600008209_ref012","doi-asserted-by":"publisher","DOI":"10.2307\/2964012"},{"key":"S1079898600008209_ref005","volume-title":"Termi e prospettive della logica e della filosofia della scienza contemporanee","volume":"I","author":"Feferman","year":"1988"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600008209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,7]],"date-time":"2023-05-07T10:15:53Z","timestamp":1683454553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600008209\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,6]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,6]]}},"alternative-id":["S1079898600008209"],"URL":"https:\/\/doi.org\/10.2307\/421038","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,6]]}}}