{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T23:23:54Z","timestamp":1778196234229,"version":"3.51.4"},"reference-count":48,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,1,15]],"date-time":"2014-01-15T00:00:00Z","timestamp":1389744000000},"content-version":"unspecified","delay-in-days":6895,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Bull. symb. log."],"published-print":{"date-parts":[[1995,3]]},"abstract":"<jats:p>The best known and most widely discussed aspect of Kurt G\u00f6del's philosophy of mathematics is undoubtedly his robust realism or platonism about mathematical objects and mathematical knowledge. This has scandalized many philosophers but probably has done so less in recent years than earlier. Bertrand Russell's report in his autobiography of one or more encounters with G\u00f6del is well known:<\/jats:p><jats:p>G\u00f6del turned out to be an unadulterated Platonist, and apparently believed that an eternal \u201cnot\u201d was laid up in heaven, where virtuous logicians might hope to meet it hereafter.<\/jats:p><jats:p>On this G\u00f6del commented:<\/jats:p><jats:p>Concerning my \u201cunadulterated\u201d Platonism, it is no more unadulterated than Russell's own in 1921 when in the<jats:italic>Introduction to Mathematical Philosophy<\/jats:italic>\u2026 he said, \u201cLogic is concerned with the real world just as truly as zoology, though with its more abstract and general features.\u201d At that time evidently Russell had met the \u201cnot\u201d even in this world, but later on under the infuence of Wittgenstein he chose to overlook it.<\/jats:p><jats:p>One of the tasks I shall undertake here is to say something about what G\u00f6del's platonism is and why he held it.<\/jats:p><jats:p>A feature of G\u00f6del's view is the manner in which he connects it with a strong conception of mathematical intuition, strong in the sense that it appears to be a basic epistemological factor in knowledge of highly abstract mathematics, in particular higher set theory. Other defenders of intuition in the foundations of mathematics, such as Brouwer and the traditional intuitionists, have a much more modest conception of what mathematical intuition will accomplish.<\/jats:p>","DOI":"10.2307\/420946","type":"journal-article","created":{"date-parts":[[2006,4,18]],"date-time":"2006-04-18T16:43:38Z","timestamp":1145378618000},"page":"44-74","source":"Crossref","is-referenced-by-count":58,"title":["Platonism and Mathematical Intuition in Kurt G\u00f6del's Thought"],"prefix":"10.1017","volume":"1","author":[{"given":"Charles","family":"Parsons","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,1,15]]},"reference":[{"key":"S1079898600008295_ref028","doi-asserted-by":"crossref","unstructured":"Feferman Solomon , G\u00f6del's life and work, in CW I, pp. 1\u201336.","DOI":"10.1093\/oso\/9780195147209.003.0001"},{"key":"S1079898600008295_ref016","unstructured":"G\u00f6del [*1953\/9] Is mathematics syntax of language?, versions III and V, in CW III, pages 334\u2013356 and 356\u2013362."},{"key":"S1079898600008295_ref011","doi-asserted-by":"crossref","unstructured":"G\u00f6del [1946] Remarks before the Princeton bicentennial conference on problems in mathematics, in Davis [6], pp. 84\u201388, reprinted in CW II, pages 150\u2013153.","DOI":"10.1093\/oso\/9780195147216.003.0009"},{"key":"S1079898600008295_ref047","doi-asserted-by":"publisher","DOI":"10.1093\/philmat\/1.2.97"},{"key":"S1079898600008295_ref008","unstructured":"G\u00f6del [*1939b] Vortrag G\u00f6ttingen, lecture at G\u00f6ttingen, 1939, with a translation by Dawson John , revised by Dawson and Craig William , in CW III, pages 127\u2013155."},{"key":"S1079898600008295_ref039","volume-title":"Introduction to mathematicalphilosophy","author":"Russell","year":"1919"},{"key":"S1079898600008295_ref030","first-page":"127","volume-title":"Jour fixe der Vernunft","author":"K\u00f6hler","year":"1991"},{"key":"S1079898600008295_ref037","doi-asserted-by":"publisher","DOI":"10.2307\/3129858"},{"key":"S1079898600008295_ref021","unstructured":"G\u00f6del [1972a] Some remarks on the undecidability results, in CW II, pages 305\u2013306."},{"key":"S1079898600008295_ref042","volume-title":"Albert Einstein: Philosopher-scientist","author":"Schilpp","year":"1949"},{"key":"S1079898600008295_ref001","volume-title":"Collected Works, Volume I: Publications 1929-1936","author":"G\u00f6del","year":"1986"},{"key":"S1079898600008295_ref048","doi-asserted-by":"publisher","DOI":"10.2307\/2107966"},{"key":"S1079898600008295_ref029","first-page":"61","volume-title":"Science and subjectivity","author":"Goldfarb","year":"1992"},{"key":"S1079898600008295_ref018","unstructured":"G\u00f6del [*1961\/?] The modern development of the foundations of mathematics in the light of philosophy, transcription of German shorthand draft, with translation by K\u00f6hler Eckehart and Wang Hao , revised by Dawson John , Parsons Charles , and Craig William , in CW III, pages 374\u2013377."},{"key":"S1079898600008295_ref038","volume-title":"Political liberalism","author":"Rawls","year":"1993"},{"key":"S1079898600008295_ref025","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-25375-5"},{"key":"S1079898600008295_ref010","unstructured":"G\u00f6del [1944] Russell's mathematical logic, in Schilpp [20], pp. 125-153, reprinted in CW II, pages 119\u2013141."},{"key":"S1079898600008295_ref027","volume-title":"The undecidable","author":"Davis","year":"1965"},{"key":"S1079898600008295_ref002","volume-title":"Collected works, Volume II: Publications 1938-1974","author":"G\u00f6del","year":"1990"},{"key":"S1079898600008295_ref007","unstructured":"G\u00f6del [*193?][Undecidable diophantinepropositions], untitled text for (apparently) undelivered lecture, in CW III, pages 164\u2013175."},{"key":"S1079898600008295_ref019","unstructured":"G\u00f6del [1964] What is Cantor's continuum problem?, revised and expanded version of 1947, in Benacerraf and Putnam [1], pp. 258\u2013273, reprinted in CW II, pages 254\u2013270."},{"key":"S1079898600008295_ref004","unstructured":"G\u00f6del [*1933o] The present situation in the foundations of mathematics, lecture to the Mathematical Association of America, 1933, in CW III, pages 45\u201353."},{"key":"S1079898600008295_ref036","doi-asserted-by":"crossref","DOI":"10.4159\/9780674042605","volume-title":"A theory of justice","author":"Rawls","year":"1971"},{"key":"S1079898600008295_ref031","first-page":"241","article-title":"On the interpretation of non-finitist proofs, part I","volume":"16","author":"Kreisel","year":"1951","journal-title":"The Journal of Symbolic Logic"},{"key":"S1079898600008295_ref023","first-page":"52","volume":"34","author":"Bernays","year":"1935","journal-title":"Sur le platonisme dans les 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W. Leibniz","volume":"IV","author":"Leibniz","year":"1684"},{"key":"S1079898600008295_ref009","first-page":"33","volume-title":"[1940] The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory","volume":"3","author":"G\u00f6del","year":"1940"},{"key":"S1079898600008295_ref003","volume-title":"Collected works, Volume III: Unpublished essays and lectures","author":"G\u00f6del","year":"1995"},{"key":"S1079898600008295_ref026","volume-title":"Logical syntax of language","author":"Carnap","year":"1937"},{"key":"S1079898600008295_ref020","doi-asserted-by":"crossref","unstructured":"G\u00f6del [1972] On an extension of finitary mathematics which has not yet been used, revised and expanded version of 1958, based on a draft translation by Boron Leo F. , in CW II, pages 271\u2013280.","DOI":"10.1093\/oso\/9780195147216.003.0022"},{"key":"S1079898600008295_ref014","doi-asserted-by":"crossref","unstructured":"G\u00f6del [1949a] A remark about the relationship between relativity theory and idealistic philosophy, in Schilpp [21], pp. 555\u2013562, reprinted in CW II, pages 202\u2013207.","DOI":"10.1093\/oso\/9780195147216.003.0015"},{"key":"S1079898600008295_ref033","doi-asserted-by":"publisher","DOI":"10.1017\/S0022481200041037"}],"container-title":["Bulletin of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1079898600008295","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,3]],"date-time":"2024-02-03T20:09:02Z","timestamp":1706990942000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1079898600008295\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,3]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1995,3]]}},"alternative-id":["S1079898600008295"],"URL":"https:\/\/doi.org\/10.2307\/420946","relation":{},"ISSN":["1079-8986","1943-5894"],"issn-type":[{"value":"1079-8986","type":"print"},{"value":"1943-5894","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,3]]}}}