## Paradoxes in Göttingen

Citations: | 1 - 0 self |

### BibTeX

@MISC{Peckhaus_paradoxesin,

author = {Volker Peckhaus},

title = {Paradoxes in Göttingen},

year = {}

}

### OpenURL

### Abstract

In 1903 Russell’s paradox came over the mathematical world with a double stroke. Bertrand Russell himself published it under the heading “The Contradiction” in chapter 10 of his Principles of Mathematics (Russell 1903). Almost at the same time Gottlob Frege (1848–1925) referred to Russell’s

### Citations

51 |
Grundgesetze der Arithmetik, begriffschriftlich abgeleitet, volume I
- Frege
- 1962
(Show Context)
Citation Context ...es of Mathematics (Russell 1903 ). Almost at the same time Gottlob Frege (1848–1925) referred to Russell’s paradox in the postscript of the second and final volume of his Grundgesetze der Arithmetik (=-=Frege 1903-=- ), admitting that the foundational system of the Grundgesetze had proved to be inconsistent. Frege sent a copy of this volume to his Göttingen colleague David Hilbert (1862–1943), and received an ast... |

50 | From Frege to Gödel. A Source Book - Heijenoort - 1967 |

49 | Vorlesungen über die Algebra der Logik - Schröder - 1905 |

40 | Arithmetices principia, nova methodo exposita. Bocca, Turin, 1889. English translation in [18 - Peano |

24 |
Zermelo’s axiom of choice: Its origins, development, and influence
- Moore
- 1982
(Show Context)
Citation Context ...ngen über die Algebra der Logik (Schröder 1890 ). Schröder had criticized George Boole’s interpretation of the symbol 1 as the class of everything that 13On Zermelo’s activities in Göttingen cf. esp. =-=Moore 1982-=-, Peckhaus 1990a, Peckhaus 1990b, 76–122. 14Critical edition in Husserliana XXII (Husserl 1979, 399). English translation in Rang/Thomas 1981.8 Volker Peckhaus can be a subject of discourse (the univ... |

21 | Kritische Untersuchungen über die Grundlagen der Analysis (Velt - Weyl, Kontinuum |

15 | der Geometrie’, in Festschrift zur Feier der Enthüllung des Gauss-Weber Denkmals in Göttingen (Leipzig: Teubner). Trans. by Leo Unger (1971) asFoundations of geometry (La Salle: Open - Hilbert, ‘Grundlagen |

7 | 1990a “ ‘Ich habe mich wohl gehütet, alle Patronen auf einmal zu verschießen’. Ernst Zermelo - Peckhaus |

5 |
Ueber unendliche lineare Punktmannichfaltigkeiten
- Cantor
(Show Context)
Citation Context ...owing that the assumption of its existence contradicts his definition of a set as the comprehension of certain well distinguished objects of our intuition or our thinking in a whole (Cantor 1895, cf. =-=Cantor 1932-=-, 282). The totality of all cardinals (and of all ordinals) cannot be thought of as one such thing, contrary to actual infinite objects like transfinite sets. Hilbert’s letters to Cantor have not been... |

4 | Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse aus dem Jahre 1900 , 253–297; English translation Hilbert 1902b - der |

3 | Moore’s paradox - Moore - 1993 |

2 | Bemerkungen zu den Paradoxieen von Russell und Burali-Forti. Abhandlungen der Fries’schen Schule n. s - Grelling, Nelson - 1908 |

2 |
Review of Schröder 1890. Göttingische gelehrte Anzeigen, 243– 278; critical edition in [Husserl
- Husserl
- 1979
(Show Context)
Citation Context ...erpretation of the symbol 1 as the class of everything that 13On Zermelo’s activities in Göttingen cf. esp. Moore 1982, Peckhaus 1990a, Peckhaus 1990b, 76–122. 14Critical edition in Husserliana XXII (=-=Husserl 1979-=-, 399). English translation in Rang/Thomas 1981.8 Volker Peckhaus can be a subject of discourse (the universe of discourse, universal class). 15 Husserl had dismissed Schröder’s argumentation as soph... |

2 |
Ueber die Addition transfiniter Cardinalzahlen. Nachrichten von der Königl. Gesellschaft der Wissenschaften zu Göttingen. Mathematischphysikalische Klasse aus dem Jahre 1901
- Zermelo
- 1901
(Show Context)
Citation Context ...ests to set theory and foundations. He became Hilbert’s collaborator in the foundations of mathematics. His first set-theoretical publication on the addition of transfinite cardinals dates from 1901 (=-=Zermelo 1901-=- ), but as early as the winter term 1900/1901 he gave a lecture course on set theory in Göttingen. It is possible that he may have found the paradox while preparing this course. He referred to it in t... |

1 |
Lebensgeschichte,” in David Hilbert, Gesammelte Abhandlungen, vol
- Blumenthal
- 1935
(Show Context)
Citation Context ...ttingen as “Hilbert’s paradox”, the one he obviously referred to in his letter to Frege, and which Otto Blumenthal mentioned in his biographical note in the third volume of Hilbert’s Collected Works (=-=Blumenthal 1935-=- ). 6 Hilbert never published the paradox. He discussed it, however, in a lecture course on the “Logical Principles of Mathematical Thinking” he gave in Göttingen in the summer term of 1905. It is pre... |

1 | is autological, “long” heterological; “English” is autological, “German” heterological. Volker Peckhaus Boole, George 1854 An Investigation of the Laws of Thought on which are Founded the - “Short” - 1958 |

1 | Bertrand Russell and the - Dantan, Alejandro - 1992 |

1 |
Grundbegriffe der Mengenlehre. Zweiter Bericht über das Unendliche in der Mathematik,” Abhandlungen der Fries’schen Schule n
- Hessenberg
- 1906
(Show Context)
Citation Context ...ar Berlin, and by the physiologist Karl Kaiser (1861–c. 1933). Hessenberg was a known geometer, but he also gain recognition as a set theorist after having published the first textbook on set theory (=-=Hessenberg 1906-=- ). In June 1905 Nelson sent a letter to Hessenberg commenting on Hilbert’s lecture “ Über die Grundlagen der Arithmetik” (Hilbert 1905a), and he ex19 For more details on Nelson and his circle cf. Pec... |

1 | Georg Cantor, Leipzig (Biographien hervorragender Naturwissenschaftler, Techniker und Mediziner; 79 - Purkert, Joachim - 1985 |

1 | Plumpton 1926 “The Foundations of - Ramsey |

1 |
Der Lügner. Theorie, Geschichte und Auflösung
- Rüstow
- 1910
(Show Context)
Citation Context ...L 169, Rüstow.Paradoxes in Göttingen 13 thesis was published not before 1910, and it is also characteristic that in the title of the published version the reference to Russell’s paradox was omitted (=-=Rüstow 1910-=- ). It was during Grelling’s and Nelson’s struggle with Goesch’s “solution” that Grelling and Nelson compiled material for a joint paper which was finally published in 1908 (Grelling/Nelson 1908 ). Th... |

1 |
The Principles of Mathematics, The University Press, Cambridge [as “Vol
- Russell
- 1903
(Show Context)
Citation Context ...03 Russell’s paradox came over the mathematical world with a double stroke. Bertrand Russell himself published it under the heading “The Contradiction” in chapter 10 of his Principles of Mathematics (=-=Russell 1903-=- ). Almost at the same time Gottlob Frege (1848–1925) referred to Russell’s paradox in the postscript of the second and final volume of his Grundgesetze der Arithmetik (Frege 1903 ), admitting that th... |