{"title":"布劳威尔与豪斯多夫:关于重新评估基础危机","authors":"David E. Rowe","doi":"10.1017/s0269889724000103","DOIUrl":null,"url":null,"abstract":"<p>Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this “foundations crisis” was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went a step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal <span>Mathematische Annalen.</span></p>","PeriodicalId":49562,"journal":{"name":"Science in Context","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Brouwer and Hausdorff: On reassessing the foundations crisis\",\"authors\":\"David E. Rowe\",\"doi\":\"10.1017/s0269889724000103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this “foundations crisis” was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went a step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal <span>Mathematische Annalen.</span></p>\",\"PeriodicalId\":49562,\"journal\":{\"name\":\"Science in Context\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2024-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Science in Context\",\"FirstCategoryId\":\"98\",\"ListUrlMain\":\"https://doi.org/10.1017/s0269889724000103\",\"RegionNum\":4,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Science in Context","FirstCategoryId":"98","ListUrlMain":"https://doi.org/10.1017/s0269889724000103","RegionNum":4,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Arts and Humanities","Score":null,"Total":0}
Brouwer and Hausdorff: On reassessing the foundations crisis
Epistemological issues associated with Cantorian set theory were at the center of the foundational debates from 1900 onward. Hermann Weyl, as a central actor, saw this as a smoldering crisis that burst into flames after World War I. The historian Herbert Mehrtens argued that this “foundations crisis” was part of a larger conflict that pitted moderns, led by David Hilbert, against various counter-moderns, who opposed the promotion of set theory and trends toward abstract theories. Among counter-moderns, L.E.J. Brouwer went a step further by proposing new foundational principles based on his philosophy of intuitionism. Meanwhile, Felix Hausdorff emerged as a leading proponent of the new modern style. In this essay, I offer a reassessment of the foundations crisis that stresses the marginal importance of the various intellectual issues involved. Instead, I offer an interpretation that focuses on tensions within the German mathematical community that led to a dramatic power struggle for control of the journal Mathematische Annalen.
期刊介绍:
Science in Context is an international journal edited at The Cohn Institute for the History and Philosophy of Science and Ideas, Tel Aviv University, with the support of the Van Leer Jerusalem Institute. It is devoted to the study of the sciences from the points of view of comparative epistemology and historical sociology of scientific knowledge. The journal is committed to an interdisciplinary approach to the study of science and its cultural development - it does not segregate considerations drawn from history, philosophy and sociology. Controversies within scientific knowledge and debates about methodology are presented in their contexts.