%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% BibTeX-File for Bernays Project %%% %%% Version 3 (2/5/05) %%% %%% Compiled by Dirk Schlimm %%% %%% and contributions by %%% %%% Gerhard Heinzmann %%% %%% Charles Parsons %%% %%% Wilfried Sieg %%% %%% Richard Zach %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Keys for citation begin with "ar:" for articles, "re:" for reviews, % "bo:" for books, "ms:" for unpublished manuscripts, or "th:" for % theses. Then the author's name and the last % two digits of the year follow, and (to distinguish publications made in % the same year) a letter. % The field "annote" contains additional information that is not % intended to be published with the bibliography. %%% %%% Abbreviations %%% %%% % Journals @STRING{abhms = "Abhandlungen aus dem Mathematischen Seminar der Universit{\"a}t Hamburg"} @STRING{acarb = "Acad. Roy. Belg."} @STRING{amejm = "American Journal of Mathematics"} @string{ASI = "Actualit{\'e}s scientifiques et industrielles"} @STRING{annpa = "Annals of Pure and Applied Logic"} @STRING{arcml2 = "Archiv f{\"u}r Mathematische Logik und Grundlagenforschung"} @STRING{artii = "Artificial Intelligence"} @STRING{aspm = "Annales de la Soci\'et\'e Polonaise de Math\'ematique"} @STRING{bsl = "Bulletin of Symbolic Logic"} @STRING{bulapm = "Bull. Acad. Polon. Sci. S{\'e}r. Sci. Math. Astronom. Phys."} @STRING{bullams = "Bulletin of the American Mathematical Society"} @STRING{fundi3 = "Fund. Inform."} @STRING{fundm = "Fundamenta Mathematicae"} @STRING{jassc = "J.~Assoc. Comput. Mach."} @STRING{jdmv = "Jahres\-bericht der Deut\-schen Mathe\-matiker-Ver\-eini\-gung"} @string{JDMV = "Jahresbericht der Deutschen Mathematiker Vereinigung (JDMV)"} @STRING{jp = "Journal of Philosophy"} @STRING{jphil = "Journal of Philosophical Logic"} @STRING{jsyml = "Journal of Symbolic Logic"} @string{JSL = "Journal of Symbolic Logic"} @STRING{ma = "Mathe\-ma\-tische An\-nalen"} @string{MA = "Mathematische Annalen"} @STRING{mathj = "Math. Japon."} @STRING{mathz = "Mathe\-mati\-sche Zeit\-schrift"} @STRING{mitmg1 = "Mitt. Math. Ges. Hamburg"} @STRING{nat = "Die Naturwissenschaften"} @STRING{repml = "Rep. Math. Logic"} @STRING{rip = "Revue internationale de philosophie"} @STRING{thec5 = "Theoret. Comput. Sci."} @STRING{traam = "Transactions of the American Mathematical Society"} @STRING{zmatl2 = "Zeitschrift f{\"u}r Mathematische Logik und Grundlagen der Mathematik"} % Publishers @string{NH = "North--Holland, Amsterdam"} @string{OUP = "Oxford University Press, Oxford"} @string{PH = "Prentice Hall, Englewood Cliffs, NJ"} @string{SPR = "Springer Verlag, Berlin, Heidelberg, New York"} %%% %%% Entries %%% %%% @Article{ar:Bernays10a, author = "Paul Bernays", title = "{Das Moralprinzip bei Sidgwick und Kant}", journal = "Abhandlungen der Fries'schen Schule", year = 1910, OPTpages = {}, volume = "III", number = 3, annote = "Reference in Mancosu98a. \\ $\bullet$ No.~1 in \cite{bo:Mueller76a}"} @Article{ar:Bernays13a, author = "Paul Bernays", title = "{\"{U}ber den transzendentalen Idealismus}", journal = "Abhandlungen der Fries'schen Schule", year = 1913, pages = {367--94}, volume = "IV", number = 2, annote = "\\ $\bullet$ No.~4 in \cite{bo:Mueller76a}. In \cite{bo:Mancosu98a} the pages are referenced as: 365--94"} @Article{ar:Bernays13b, author = "Paul Bernays", title = "{\"{U}ber die Bedenklichkeiten der neueren Relativit\"{a}tstheorie}", journal = "Abhandlungen der Fries'schen Schule", year = 1913, pages = {459--82}, volume = "IV", number = 3, annote = "\\ $\bullet$ No.~5 in \cite{bo:Mueller76a}" } @Article{ar:Bernays13c, author = "Paul Bernays", title = "{Zur elementaren Theorie der Landauschen Funktion $\varphi(\alpha)$}", journal = "{Vierteljahresschrift der Naturforschenden Gesellschaft in Z\"{u}rich}", pages = {203--238}, year = 1913, volume = 58, note = "{Habilitations\-schrift Universit\"{a}t Z\"{u}rich.}", annote = "{\\ $\bullet$ No.~3 in \cite{bo:Mueller76a}. Page numbers from JFM. JFM has ``Funktionen'' and also lists separately: {Zur elementaren Theorie der Landauschen Funktion $\varphi (\alpha)$.} {Habilitationsschrift Z\"urich. 38 S. (1913).}}" } @Article{ar:Bernays18a, author = "Paul Bernays", title = "{Zum Beweise der Legendreschen Bedingung in der Variationsrechnung}", journal = "Archiv der Mathematik und Physik", volume = "III. Reihe XXVII", pages = {177--180}, year = 1918, annote = "\\ $\bullet$ No.~6 in \cite{bo:Mueller76a}, Page numbers from JFM" } @Article{ar:Bernays22a, author = "Paul Bernays", title = "{\"{U}ber Hilbert's Gedanken zur Grundlegung der Arithmetik}", key = "1922a", journal = JDMV, number = "1.~Abteilung, Heft 1/4", year = "1922", volume = 31, pages = "10--19", note = "Lecture delivered at the Mathematikertagung in Jena, September 1921. Received October 13, 1921. English translation: On Hilbert's Thoughts Concerning the Grounding of Arithmetic, by Paolo Mancosu in \cite{bo:Mancosu98a}, pp.~215--222.", annote = "\mueller{No.~7.}" } @Article{ar:Bernays22b, author = "Paul Bernays", title = "{Die Bedeutung Hilberts f\"{u}r die Philosophie der Mathematik}", key = "1922b", journal = "Die Naturwissenschaften", year = "1922", volume = 10, pages = "93-99", note = "English translation: Hilbert's Significance for the Philosophy of Mathematics, by Paolo Mancosu in \cite{bo:Mancosu98a}, pp.~189--197.", annote = "\mueller{No.~9.}" } @Article{ar:Bernays22c, author = "Paul Bernays", title = "{Zur mathematischen Grundlegung der kinetischen Gastheorie}", journal = MA, year = 1922, volume = 85, pages = "242--255", annote = "\\ $\bullet$ No.~8 in \cite{bo:Mueller76a}" } @Article{ar:Bernays23b, author = "Paul Bernays", title = "{Erwiederung auf die Note von Herrn Aloys M\"{u}ller: `\"{U}ber Zahlen als Zeichen'}", journal = MA, year = 1923, volume = 90, pages = "159--63", note = "{\\Received April 7, 1923. Reprinted in {\em Annalen der Philosophie und philosophischen Kritik}, vol.~4, pp.~492--497, 1924. English translation: Reply to the Note of Aloys M\"{u}ller, `On Numbers as Signs', by Paolo Mancosu in \cite{bo:Mancosu98a}, pp.~223--226}.", annote = "\\ $\bullet$ No.~10 in \cite{bo:Mueller76a}" } @Article{ar:Bernays26a, author = "Paul Bernays", title = "{Axiomatische Untersuchungen des Aussagen-Kalk\"{u}ls der `Principia Mathematica'}", journal = "Mathematische Zeitschrift", year = 1926, volume = 25, pages = "305-20", note = "Abridged version of \cite{th:Bernays18b}.", annote ="\\ $\bullet$ No.~11 in \cite{bo:Mueller76a}" } @Article{ar:Bernays27a, author = "Paul Bernays", title = "{Probleme der theoretischen Logik}", journal = "{Unterrichtsbl\"{a}tter f\"{u}r Ma\-the\-matik und Naturwissenschaften}", year = 1927, volume = 33, pages = "369--377", annote = "\\ $\bullet$ No.~12 in \cite{bo:Mueller76a}" } @Article{ar:Bernays27b, author = "Paul Bernays", title = "{Zusatz zu Hilberts Vortrag \"{u}ber `Die Grundlagen der Mathematik'}", journal = "{Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universit\"{a}t}", year = 1928, volume = 6, pages = "89--92", note = "{Reprinted in \cite{bo:Hilbert28a}, pp.~25--28. English translation: Appendix to Hilbert's lecture `The foundations of mathematics', by Stefan Bauer-Mengelberg and Dagfinn Follesdal in \cite{bo:vanHeijenoort67a}, pp.~485--489.}", annote = "{\\ $\bullet$ \cite{bo:vanHeijenoort67a}, pp.~631, not listed by M\"{u}ller. JFM has: 1928}" } @Article{ar:Bernays28a, author = "Paul Bernays", title = "{\"{U}ber Nelsons Stellungnahme in der Philosophie der Mathematik}", journal = "Die Naturwissenschaften", year = 1928, pages = {142--145}, volume = 16, number = 9, annote = "\\ $\bullet$ No.~14 in \cite{bo:Mueller76a}. Page numbers from JFM" } @Article{ar:Bernays28b, author = "Paul Bernays", title = "{Die Grundbegriffe der reinen Geometrie in ihrem Verh\"{a}ltnis zur Anschauung}", journal = "Die Naturwissenschaften", year = 1928, volume = 16, number = 12, pages = "197--203", annote = "\\ Criticism of a book with the same title by R.~Strohal.\\ $\bullet$ No.~15 in \cite{bo:Mueller76a}" } @Article{ar:Bernays30a, author = "Paul Bernays", title = "{Die Grundgedanken der Friesschen Philosophie in ihrem Verh\"{a}ltnis zum heutigen Stand der Wissenschaft}", journal = "{Abhandlungen der Fries'schen Schule}", year = 1930, volume = "neue Folge, V", number = 2, pages = "99--113", annote = "\\ $\bullet$ No.~16 in \cite{bo:Mueller76a}" } @Article{ar:Bernays30b, author = "Paul Bernays", title = "{Die Philosophie der Mathematik und die Hilbertsche Beweistheorie}", journal = "{Bl\"{a}tter f\"{u}r deutsche Philosophie}", year = 1930, volume = 4, pages = "326--367", annote = "\\ $\bullet$ No.~17 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays32a, author = "Paul Bernays", title = "{Methoden des Nachweises von Widerspruchsfreiheit und ihre Grenzen}", booktitle = "{Verhandlungen des Internationalen Mathematiker-Kongresses Z\"{u}rich}", volume = 2, publisher = "{Orell F\"{u}ssli Verlag}", year = 1933, pages = "342-343", address = "{Z\"{u}rich--Leipzig}", annote = "\\ $\bullet$ No.~18 in \cite{bo:Mueller76a} Parsons: I checked this one for the Goedel edition. The proceedings volume has no date, but it seems certain that it appeared in 1933, since the Congress took place in September 1932" } @InCollection{ar:Bernays35a, author = "Paul Bernays", title = "{Hilberts Untersuchungen \"{u}ber die Grundlagen der Arithmetik}", booktitle = "David Hilbert -- Gesammelte Abhandlungen", publisher = SPR, year = 1935, volume = 3, pages = "196--216", annote = "\\ $\bullet$ No.~20 in \cite{bo:Mueller76a}" } @Article{ar:Bernays35b, author = "Paul Bernays", title = "{Sur le platonisme dans les math\'{e}matiques}", journal = "{L'Enseignement Math\'{e}matique}", year = 1935, volume = 34, pages = "52--69", note = "{\\ Lecture delivered June 18, 1934, in the cycle of {\em Conf\'{e}rences internationales des Sciences math\'{e}matiques} organized by the University of Geneva, in the series on Mathematical Logic. \\ English translation: On platonism in mathematics, by Charles D.~Parsons in \cite{bo:BenacerrafPutnam64a}, pp.~274--286.\\German translation in \cite{bo:Bernays76a}.}", annote="{\\ $\bullet$ No.~21 in \cite{bo:Mueller76a}}" } @Article{ar:Bernays35c, author = "Paul Bernays", title = "{Quelques points essentiels de la m\'{e}tamath\'{e}matique}", journal = "{L'Enseignement Math\'{e}matique}", year = 1935, volume = 34, pages = "70--95", annote = "\\ $\bullet$ No.~22 in \cite{bo:Mueller76a}" } @Misc{ar:Bernays35d, author = "Paul Bernays", title = "Logical calculus", howpublished = "Mimeographed lecture notes 1935/6, 125 pages, Institute for Advanced Study, Princeton, New Jersey", year = 1935, annote = "\\ $\bullet$ No.~23 in \cite{bo:Mueller76a}" } @Article{ar:Bernays37a, author = "Paul Bernays", title = "{Grunds\"{a}tzliche Betrachtungen zur Erkenntnistheorie}", journal = "{Abhandlungen der Fries'schen Schule}", year = 1937, volume = "neue Folge, 6", number = {3/4}, pages = "279--290", annote = "\\ $\bullet$ No.~24 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays37b, author = "Paul Bernays", title = "{Thesen und Bemerkungen zu den philosophischen Fragen und zur Situation der logisch-mathematischen Grundlagenforschung}", pages = "104--110", booktitle = "{Travaux du IX$^e$ Congr\'{e}s international de Philosophie}", year = 1937, publisher = "Hermann et Cie", address = "Paris", annote = "\\ $\bullet$ No.~25 in \cite{bo:Mueller76a}" } @Article{ar:Bernays37c, author = "Paul Bernays", title = "A system of axiomatic set theory, {Part I}", journal = JSL, year = 1937, volume = 2, pages = "65-77", annote = "\\ $\bullet$ No.~26 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays39a, author = "Paul Bernays", title = "{Bemerkungen zur Grundlagenfrage}", booktitle = "{Philosophie Math\'{e}matique}", publisher = "{Actualit\'{e}s Scientifique et Industrielles}", year = 1939, editor = "Ferdinand Gonseth", pages = "83--87", address = "Paris", annote = "\\ $\bullet$ No.~28a added in \cite{ar:Mueller81a}" } @Article{ar:Bernays39c, author = "Paul Bernays", title = "{Zur Frage der Vereinheitlichung der logischen Symbolik}", journal = "Erkenntnis", year = 1939, volume = 7, number = "5/6", pages = "388--9", OPTmonth = "", annote = "{\\ $\bullet$ not listed by M\"{u}ller, reference in JSL 4(2) 1939. p.~172}" } @InProceedings{ar:Bernays41a, author = "Paul Bernays", title = "{Sur les questions m\'{e}thodologiques actuelles de la th\'{e}orie Hilbertienne de la d\'{e}monstration}", pages = "144--152", editor = "Ferdinand Gonseth", booktitle = "{Les entretiens de Z\"{u}rich sur le fondements et la m\'{e}thode des sciences math\'{e}matiques, 6--9 d\'{e}cembre 1938}", year = 1941, publisher = "Leemann \& Co.", address = "{Z\"{u}rich}", note = "Discussion pp.~153--161.", annote ="\\ $\bullet$ No.~29 in \cite{bo:Mueller76a}, additional information in \cite{bo:vanHeijenoort67a}" } @Article{ar:Bernays41b, author = "Paul Bernays", title = "A system of axiomatic set theory, {Part II}", journal = JSL, year = 1941, volume = 6, pages = "1--17", annote = "\\ $\bullet$ No.~30 in \cite{bo:Mueller76a}" } @Article{ar:Bernays42a, author = "Paul Bernays", title = "A system of axiomatic set theory, {Part III}", journal = JSL, year = 1941, volume = 7, pages = "65--89", annote = "\\ $\bullet$ No.~31 in \cite{bo:Mueller76a}" } @Article{ar:Bernays42b, author = "Paul Bernays", title = "A system of axiomatic set theory, {Part IV}", journal = JSL, year = 1941, volume = 6, pages = "133--145", annote = "\\ $\bullet$ No.~32 in \cite{bo:Mueller76a}" } @Article{ar:Bernays43a, author = "Paul Bernays", title = "A system of axiomatic set theory, {Part V}", journal = JSL, year = 1943, volume = 6, pages = "89--106", annote = "\\ $\bullet$ No.~33 in \cite{bo:Mueller76a}" } @Article{ar:Bernays46a, author = "Paul Bernays", title = "{Zum Begriff der Dialektik}", journal = "Dialectica", year = 1947, volume = 1, pages = "172--175", annote = "\\ $\bullet$ No.~27 in \cite{bo:Mueller76a}\\ NOTE: Year might be incorrect!" } @Article{ar:Bernays46b, author = "Paul Bernays", title = "{Quelques points de vue concernant le probl\`{e}me de l'\'{e}vidence}", journal = "Synthese", year = 1946, volume = "V", pages = "321--326", annote = "\\ $\bullet$ No.~34 in \cite{bo:Mueller76a}" } @Article{ar:Bernays47a, author = {Paul Bernays}, title = {Contradiction et non-contradiction. {Zu einem Brief an Dialectica}}, journal = {Dialectica}, year = {1947}, OPTkey = {}, volume = {1}, OPTnumber = {}, pages = {305--309}, OPTmonth = {}, OPTnote = {}, annote = {Not listed by Mueller. From: Parsons 8/11/03.} } @Article{ar:Bernays48a, author = "Paul Bernays", title = "{Grunds\"{a}tzliches zur `philosophie ouverte'}", journal = "Dialectica", year = 1948, pages = {273--279}, volume = 2, note = "{Les deuxi\'{e}mes Entretiens de Z\"{u}rich.}", annote ="{\\ $\bullet$ No.~35 in \cite{bo:Mueller76a}}" } @InProceedings{ar:Bernays48b, author = "Paul Bernays", title = "{Die Erneuerung der rationalen Aufgabe}", pages = "42--50", booktitle = "Proceedings of the Xth international congress of philosophy", year = 1948, address = "Amsterdam", annote = "\\ $\bullet$ No.~36 in \cite{bo:Mueller76a}" } @Article{ar:Bernays48c, author = "Paul Bernays", title = "{\"{U}ber die Ausdehnung des Begriffes der Komplementarit\"{a}t auf die Philosophie}", journal = "Synthese", year = "1948", volume = "VII", pages = "66--70", annote = "\\ $\bullet$ No.~37 in \cite{bo:Mueller76a}" } @Article{ar:Bernays48d, author = "Paul Bernays", title = "A system of axiomatic set theory, {Part VI}", journal = JSL, year = 1943, volume = 13, pages = "65--79", annote = "\\ $\bullet$ No.~38 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays48e, author = "Paul Bernays", title = "{Bemerkungen zu den Grundlagen der Geometrie}", booktitle = "Courant Anniversary Volume", year = 1948, pages = "29-44", annote = "\\ $\bullet$ No.~39 in \cite{bo:Mueller76a}\\ NOTE: incomplete bibliographical information" } @Article{ar:Bernays48f, author = {Paul Bernays}, title = {{Bemerkungen zum Problem der Aesthetik}}, journal = {Dialectica}, year = {1948}, OPTkey = {}, volume = {2}, OPTnumber = {}, pages = {211}, OPTmonth = {}, OPTnote = {}, annote = {Not listed by Mueller. From: Parsons 8/11/03.} } @InProceedings{ar:Bernays50a, author = "Paul Bernays", title = "{Logique and science}", pages = "1--5", booktitle = "{XVI$^e$ Congr\'{e}s Internationale de Philosophie de science, Paris, 1949}", year = 1950, publisher = "Hermann \& Cie.", address = "Paris", annote = "\\ $\bullet$ No.~40 in \cite{bo:Mueller76a} Parsons 8/11/03: There is a reply to this, by Perelman, ``R{\'e}ponse {\`a} M. Bernay{\ss}'', Dialectica 6 (1952), 92-95." } @InCollection{ar:Bernays50b, author = "Paul Bernays", title = "{Mathematische Existenz und Widerspruchsfreiheit}", booktitle = "{Etudes de Philosophie des sciences en hommage \`{a} Ferdinand Gonseth}", publisher = "Editions du Griffon", year = 1950, pages = "11--25", address = "Neuchatel", annote = "\\ $\bullet$ No.~41 in \cite{bo:Mueller76a}" } @Article{ar:Bernays50c, author = "Paul Bernays", title = "{Zur Methodischen Diskussion -- Bemerkungen zu Herrn Perelmans Er\"{o}rterung `Philosophies Premi\`{e}res et Philosophie R\'{e}gressive}", journal = "Dialectica", year = 1950, volume = 4, pages = "43--45", annote = "\\ $\bullet$ No.~59a added in \cite{ar:Mueller81a}" } @InCollection{ar:Bernays51a, author = "Paul Bernays", title = "{\"{U}ber das Induktionsschema in der rekursiven Zahlentheorie}", booktitle = "{Kontrolliertes Denken, Festschrift f\"{u}r Wilhelm Britzelmayr}", year = 1951, editor = "A.~Menne, A.~Wilhelmy, H.~Angstl", pages = "10--17", address = "{Freiburg (Breisgau) -- M\"{u}nchen}", annote = "{\\ $\bullet$ No.~42 in \cite{bo:Mueller76a}. \cite{bo:Peter67a} pp.~293 writes: Kontrolliertes Denken, Untersuchungen zum Logikkalk\"{u}l und zur Logik der Einzelwissenschaften. Kommissions-Verlag K.~Alber, M\"{u}nchen}" } @Article{ar:Bernays52a, author = "Paul Bernays", title = "{Dritte Gespr\"{a}che von Z\"{u}rich}", journal = "Dialectica", year = 1952, volume = 6, pages = "130--136", annote = "\\ $\bullet$ No.~59b added in \cite{ar:Mueller81a}" } @Article{ar:Bernays52b, author = "Paul Bernays", title = "{Gesichtspunkte der Erkenntnistheorie (insbesondere zur Auseinandersetzung mit der kantischen Erkenntnistheorie). Thesen zu den ``Dritten Gespr{\"a}chen von Z{\"u}rich''}", journal = "Dialectica", year = 1952, volume = 6, pages = "137--140", annote = "\\ $\bullet$ No.~59c added in \cite{ar:Mueller81a}" } @Article{ar:Bernays52c, author = {Paul Bernays}, title = {{Zu der Arbeit von E.~Harris}}, journal = {Dialectica}, year = {1952}, OPTkey = {}, volume = {6}, OPTnumber = {}, pages = {166}, OPTmonth = {}, OPTnote = {}, annote = {Not listed by Mueller. From: Parsons 8/11/03. The 'Arbeit' is Errol E. Harris, Some recent criticisms of Berkeley, ibid. 167-185.} } @Article{ar:Bernays52d, author = {Paul Bernays}, title = {Discussion Pr{\'e}liminaire}, journal = {Dialectica}, year = 1952, volume = 6, pages = {145--165}, annote = {Not listed by Mueller. From: Parsons 8/11/03. This consists of remarks by a succession of people, beginning with Gonseth. Bernays' interventions are on pp. 153-156 and 164-165.} } @Article{ar:Bernays53a, author = "Paul Bernays", title = "{\"{U}ber die Verwendung der Polygoninhalte an Stelle eines Spiegelungsaxioms in der Axiomatik der Planimetrei}", journal = "Elemente der Mathematik", year = 1953, volume = "VIII", number = 5, pages = "102-107", annote = "\\ $\bullet$ No.~43 in \cite{bo:Mueller76a}\\ NOTE: Title may be wrong (cf.~comment by W.~Sieg)" } @InCollection{ar:Bernays53b, author = "Paul Bernays", title = "{\"{U}ber die Friessche Annahme einer Wiederbeobachtung der unmittelbaren Erkenntnis}", booktitle = "{Leonard Nelson zum Ged\"{a}chtnis}", publisher = "{Verlag \"{o}ffentliches Leben}", year = 1953, pages = "113--131", address = "{Frankfurt/M.--G\"{o}ttingen}", annote = "\\ $\bullet$ No.~44 in \cite{bo:Mueller76a}" } @Article{ar:Bernays53c, author = {Paul Bernays}, title = {Existence et non-contradiction en math{\'e}matiques}, journal = {Revue philosophique de la France et de l'{\'e}tranger}, year = 1953, volume = 143, pages = {85--87}, note = {With a note by G.~Bouligand.}, annote = {Not in Mueller, from: Parsons 8/12/03. Van Heijenoort writes in his review of [1950b] (JSL 22 (1957), 210-211) that this consists of a letter to Bouligand and is a ``limpid summary'' of that paper.} } @Article{ar:Bernays53d, author = {Paul Bernays}, title = {{Einleitendes Referat}}, journal = {Dialectica}, year = 1953, volume = 7, pages = {318--321}, annote = {Not in Mueller, from Heinzmann 8/28/03.} } @Article{ar:Bernays54a, author = "Paul Bernays", title = "{A system of axiomatic set theory, Part VII}", journal = JSL, year = 1954, volume = 19, pages = "81-96", annote = "\\ $\bullet$ No.~45 in \cite{bo:Mueller76a}" } @Article{ar:Bernays54b, author = "Paul Bernays", title = "{Die Mathematik als ein zugleich Vertrautes und Unbekanntes -- Vortrag zur Ged\"{a}chtnisfeier f\"{u}r B.~Nieuwentijt in Purmerend}", journal = "Synthese", year = 1954, volume = "IX", pages = "465--471", annote = "\\ $\bullet$ No.~46 in \cite{bo:Mueller76a}" } @Article{ar:Bernays54c, author = "Paul Bernays", title = "{Zur Beurteilung der Situation in der beweistheoretischen Forschung}", journal = "Revue Internationale de Philosophie", year = 1954, volume = "27/28", pages = "1--5", note = {{\bf Note:} This should surely be checked. I have a copy of the paper, which gives the pages as 1-5. At the bottom it says it is from nos. 27-28, so the volume number is different and very probably smaller. Extapolating back from what we have in our department library, it should be vol. 8 (Parsons, 8/11/03).}, annote = "\\ $\bullet$ No.~47 in \cite{bo:Mueller76a}. \cite{bo:vanHeijenoort67a} writes: vol.~8, pp.~9--13, Discussion pp.~15--21." } @InProceedings{ar:Bernays54d, author = "Paul Bernays", title = "{\"{U}ber den Zusammenhang des Herbrand'schen Satzes mit den neueren Ergebnissen von Sch\"{u}tte und Stenius}", booktitle = "Proceedings of the International Congress of Mathematicians 1954", publisher = {Noordhoff and North-Holland}, address = {Groningen and Amsterdam}, year = 1957, annote = "\\ $\bullet$ No.~48 in \cite{bo:Mueller76a}" } @Article{ar:Bernays54e, author = "Paul Bernays", title = "{Bemerkungen zu der Betrachtung von Alexander Wittenberg: \"{u}ber ad\"{a}quate Problemstellung in der mathematischen Grundlagenforschung}", journal = "Dialectica", year = 1954, volume = 8, pages = "147--151", annote = "\\ $\bullet$ No.~49 in \cite{bo:Mueller76a}" } @Article{ar:Bernays55a, author = "Paul Bernays", title = "{Betrachtungen \"{u}ber das Vollst\"{a}ndigkeitsaxiom und verwandte Axiome}", journal = "Mathematische Zeitschrift", year = 1955, volume = 63, pages = "219--229", annote = "\\ $\bullet$ No.~50 in \cite{bo:Mueller76a}" } @Misc{ar:Bernays56a, author = "Paul Bernays", title = "{Vereinfachte Begr\"{u}ndung der Proportionenlehre}", howpublished = "{Supplement II to the 8$^{th}$ edition of David Hilbert: {\em Grundlagen der Geometrie}, pages 241--245, Stuttgart}", year = 1956, annote = "\\ $\bullet$ No.~51 in \cite{bo:Mueller76a}" } @Article{ar:Bernays56b, author = "Paul Bernays", title = "{Zur Diskussion des Themas ``Der platonische Standpunkt in der Mathematik''}", journal = "Dialectica", year = 1956, volume = 10, pages = "262--266", annote = "\\ $\bullet$ No.~59d added in \cite{ar:Mueller81a} Parsons (8/22/03): This is a comment on a paper with that title by Paul Finsler." } @InProceedings{ar:Bernays57a, author = "Paul Bernays", title = "{Betrachtungen zum Paradoxen von Thoralf Skolem}", pages = "3--9", booktitle = "Avandlinger utgitt av Det Norske Videnskaps-Akademi i Oslo", year = 1957, publisher = "Aschehoug", address = "Oslo", annote = "\\ $\bullet$ No.~53 in \cite{bo:Mueller76a}" } @Article{ar:Bernays57b, author = "Paul Bernays", title = "{Von der Syntax der Sprache zur Philosophie der Wissenschaften}", journal = "Dialectica", year = 1957, volume = 11, pages = "233--246", annote = "\\ $\bullet$ No.~54 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays58a, author = "Paul Bernays", title = "{Remarques sur le probl\`{e}me de la d\'{e}cision en logique \'{e}l\'{e}lementaire}", booktitle = "{Le Raisonnment en math\'{e}matique et en sciences exp\'{e}rimentales}", year = 1958, series = "{Editions du Centre National de la Recherche Scientifique}", pages = "39--43", address = "Paris", annote = "\\ $\bullet$ No.~55 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays59a, author = "Paul Bernays", title = "{\"{U}ber eine nat\"{u}rliche Erweiterung des Relationenkalk\"{u}ls}", editor = "Arend Heyting", pages = "1--14", booktitle = "Constructivity in Mathematics. Proceedings of the Colloquium held at Amsterdam, 1957", year = 1959, publisher = NH, annote = "\\ $\bullet$ No.~57 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays59b, author = "Paul Bernays", title = "{Die Mannigfaltigkeit der Direktiven f\"{u}r die Gestaltung geometrischer Axiomensysteme}", editor = "L.~Henkin and P.~Suppes and A.~Tarski", series = "Proceedings of an international symposium held at Berkeley 1957--58", pages = "1--15", booktitle = "The Axiomatic Method", year = 1959, publisher = NH, OPTannote = "\\ $\bullet$ No.~58 in \cite{bo:Mueller76a}" } @Article{ar:Bernays59c, author = "Paul Bernays", title = "{Betrachtungen zu Ludwig Wittgensteins `Bemerkungen \"{u}ber die Grundlagen der Mathematik'}", journal = "Ratio", year = 1959, volume = 1, number = "1--18", annote = "\\ $\bullet$ No.~59 in \cite{bo:Mueller76a}" } @Article{ar:Bernays60a, author = "Paul Bernays", title = "{Charakterz\"{u}ge der Philosophie Gonseths}", journal = "Dialectica", year = 1960, volume = 14, pages = "151--156", annote = "\\ $\bullet$ No.~60 in \cite{bo:Mueller76a}" } @Article{ar:Bernays61a, author = "Paul Bernays", title = "{Zur Rolle der Sprache in erkenntnistheoretischer Hinsicht}", journal = "Synthese", year = 1961, volume = "XIII", pages = "185--200", annote = "\\ $\bullet$ No.~61 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays61b, author = "Paul Bernays", title = "{Die hohen Unendlichkeiten und die Axiomatik der Mengenlehre}", pages = "11-20", booktitle = "Infinitistic Methods", year = 1961, organization = "Proceedings of the Symposium on Foundations of Mathematics, Warsaw, 2--9 September 1959", publisher = "Pergamon Press", address = "Oxford", annote = "\\ $\bullet$ No.~62 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays61c, author = "Paul Bernays", title = "{Zur Frage der Unendlichkeitsschemata in der axiomatischen Mengenlehre}", booktitle = "Essays on the foundations of mathematics -- dedicated to Prof.~A.~A.~Fraenkel", publisher = "Magnes Press", year = 1961, pages = "3--49", address = "Jerusalem", annote = "\\ $\bullet$ No.~63 in \cite{bo:Mueller76a}, \cite{bo:vanHeijenoort67a} omits `Prof.' and adds `on his seventieth anniversary' in the title" } @InProceedings{ar:Bernays62a, author = "Paul Bernays", title = "Remarks about formalization and models", editor = "E.~Nagel and P.~Suppes and A.~Tarski", booktitle = "Logic, Methodology, and Philosophy of Science", year = 1962, organization = "Proceedings of the 1960 international Congress", publisher = "Stanford University Press, Stanford, Calif.", annote = "\\ $\bullet$ No.~64 in \cite{bo:Mueller76a}" } @Misc{ar:Bernays62b, author = "Paul Bernays", title = "{Supplements to the 9$^{th}$ edition of David Hilbert: {\em Grundlagen der Geometrie}}", howpublished = "Teubner Verlag, Stuttgart", year = 1962, annote = "\\ $\bullet$ No.~65 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays62c, author = "Paul Bernays", title = "{\"{U}ber den Unterschied zwischen realistischer und konservativer Tendenz in der heutigen theoretischen Physik}", pages = "17--21", booktitle = "{Coll. de l'Acad\'{e}mie internat. de philosophie des Sciences, Paris, 1961}", year = 1962, organization = "Office internat. de Librairie", annote = "\\ $\bullet$ No.~66 in \cite{bo:Mueller76a}" } @Article{ar:Bernays63a, author = "Paul Bernays", title = "Remarks to `The End of a Phase'", journal = "Dialectica", year = 1963, volume = 16, pages = "49--50", note = "Remarks to an article by Errol E.~Harris.", annote = "\\ $\bullet$ No.~67 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays64a, author = "Paul Bernays", title = "{Reflections on Karl Popper's Epistemology}", booktitle = "The Critical Approach: in Honor of Karl R.~Popper's $60^{th}$ Birthday", publisher = "The Free Press, Glencoe", year = 1964, editor = "M.~Bunge", pages = "32--44", annote = "\\ $\bullet$ No.~68 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays65a, author = "Paul Bernays", title = "{Betrachtungen zum Sequenzen-Kalk\"{u}l}", booktitle = "Contributions to Logic and Methodology, in Honor of J.~M.~Bochenski", publisher = NH, year = 1965, editor = "Anna-Teresa Tymieniecka", pages = "1--44", annote = "\\ $\bullet$ No.~69 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays65b, author = "Paul Bernays", title = "{Some Empirical Aspects of Mathematics}", editor = "S.~Dockx and P.~Bernays", pages = "123--128", booktitle = "Information and Prediction in Science", year = 1965, organization = "Proceedings of a Symposium, Brussels, 1962", publisher = "Academic Press, New York, London", annote = "\\ $\bullet$ No.~70 in \cite{bo:Mueller76a}" } @Article{ar:Bernays66a, author = "Paul Bernays", title = "{Gedanken zu dem Buch `Bildung und Mathematik (Mathematik als exemplarisches Gymnasialfach)' von Alexander Israel Wittenberg}", journal = "Dialectica", year = 1966, volume = 20, pages = "27--41", annote = "\\ $\bullet$ No.~71 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays67a, author = "Paul Bernays", title = "{Scope and Limits of Axiomatics}", booktitle = "Delaware Seminar in the Foundations of Physics", publisher = SPR, year = 1967, series = "Studies in the Foundations Methodology and Philosophy of Science", volume = 1, chapter = 11, editor = "Mario Bunge", pages = "188--201", annote = "\mueller{No.~72.}" } @InProceedings{ar:Bernays67b, author = "Paul Bernays", title = "{David Hilbert}", editor = "P.~Edwards", volume = 3, pages = "496--504", booktitle = "Encyclopedia of Philosophy", year = 1967, publisher = "Macmillan Publishing Company, New York", comment = {Copy}, annote = "\\ $\bullet$ No.~73 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays67c, author = "Paul Bernays", title = "{What do some recent results in Set Theory suggest?}", pages = "109--117", booktitle = "Problems in the Philosophy of Mathematics", year = 1967, organization = "Lecture with discussion at the International Conference in the Philosophy of Science in London, 1965", publisher = NH, annote = "\\ $\bullet$ No.~74 in \cite{bo:Mueller76a}" } @Article{ar:Bernays68a, author = "Paul Bernays", title = "{Remarks to the paper by Dr.~Sandra Rosenthal: `The Cognitive Status of Theoretical Terms'}", journal = "Dialectica", year = 1968, volume = 22, annote = "\\ $\bullet$ No.~76 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays69a, author = "Paul Bernays", title = "{Bemerkungen zur Philosophie der Mathematik}", volume = "VI", pages = "192--198", booktitle = "{Akten des XIV. Internationalen Kongresses f\"{u}r Philosophie, Wien, Sept. 1968}", year = 1969, publisher = "Herder, Wien", annote = "\\ $\bullet$ No.~77 in \cite{bo:Mueller76a}" } @Article{ar:Bernays70a, author = "Paul Bernays", title = "{Die schematische Korrespondenz und die idealisierten Strukturen}", journal = "Dialectica", year = 1970, volume = 24, pages = "53-66", note = "Reprinted in \cite{bo:Bernays76a}, pages 176--188.", annote = "\\ $\bullet$ No.~78 in \cite{bo:Mueller76a}" } @Misc{ar:Bernays70b, author = "Paul Bernays", title = "{Zum Geleit}", howpublished = "{Introductory remarks to {\em Leonard Nelson. Gesammelte Schriften in neun B\"{a}nden}, vol.~I, pp.~IX--XI}", year = 1970, annote = "\\ $\bullet$ Part 1 of No.~79 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays70c, author = "Paul Bernays", title = "{On the original Gentzen consistency proof for number theory}", editor = "J.~Myhill and A.~Kino and R.~E.~Vesley", pages = "409--417", booktitle = "Intuitionism and Proof Theory, Proceedings of the Summer Conference on Intuitionism and Proof Theory, Buffalo, N.Y., August 1968", year = 1970, publisher = NH, annote = "\\ $\bullet$ No.~75 in \cite{bo:Mueller76a}, but 1968 instead of 1970" } @InCollection{ar:Bernays71a, author = "Paul Bernays", title = "{Causality, Determinism and Probability}", booktitle = "{Perspectives in Quantum Theory -- Essays in Honor of Alfred Land\'{e}}", publisher = "MIT Press, Cambridge, Mas.", year = 1971, editor = "Wolfgang Yourgrau and Alwyn van der Merwe", pages = "260--269", annote = "\\ $\bullet$ No.~80 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays71b, author = "Paul Bernays", title = "{Bemerkungen zur Rolle der Methode in den Wissenschaften}", volume = 34, series = "Archives de Philosophie", pages = "575--580", booktitle = "{Colloque `Probl\`{e}mes de M\'{e}thodologie, Lausanne, 1969}", year = 1971, annote = "\\ $\bullet$ No.~81 in \cite{bo:Mueller76a}" } @Article{ar:Bernays71c, author = "Paul Bernays", title = "{Zum Symposium \"{u}ber die Grundlagen der Mathematik}", journal = "Dialectica", year = 1971, volume = 25, pages = "171--195", annote = "\\ $\bullet$ No.~82 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays72a, author = "Paul Bernays", title = "{Bemerkungen \"{u}ber eine Ordnung der zahlentheoretischen Funktionen mittels eines additiven 0--1-Masses f\"{u}r die Mengen nat\"{u}rlicher Zahlen}", booktitle = "Theory of sets and topology, in Honor of Felix Haussdorff (1868--1942)", publisher = "VEB Deutscher Verlag der Wissenschaften, Berlin", year = 1972, editor = "G.~Asser and J.~Flachsmeyer and W.~Rinow", pages = "39--43", annote = "\\ $\bullet$ No.~83 in \cite{bo:Mueller76a}" } @Article{ar:Bernays73a, author = "Paul Bernays", title = "{\"{U}ber die Auffassung formaler Systeme als Sprachen}", journal = "Dialectica", year = 1973, volume = 27, pages = "359--362", annote = "\\ $\bullet$ No.~91a added in \cite{ar:Mueller81a}" } @InCollection{ar:Bernays74a, author = "Paul Bernays", title = "Concerning rationality", editor = "Paul A.~Schilpp", booktitle = "{The Philosophy of Karl Popper, Vol.~I}", publisher = "Open Court, La Salle, Ill.", year = 1974, volume = "XIV", series = "{The Library of Living Philosophers}", pages = "597--605", annote = "\\ $\bullet$ No.~84 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays74b, author = "Paul Bernays", title = "{Zu den Maximalprinzipien der Mengenlehre}", pages = "289--296", booktitle = "Proceedings of the Tarski-Symposium, June 1971", year = 1974, publisher = "American Mathematical Society, Providence, R.I.", annote = "\\ $\bullet$ No.~85 in \cite{bo:Mueller76a}" } @Misc{ar:Bernays74c, author = "Paul Bernays", title = "{Introduction to `Bemerkungen \"{u}ber die nichteuklidische Geometrie und den Ursprung der mathematischen Gewissheit'}", howpublished = "{In: {\em Leonard Nelson. Gesammelte Schriften in neun B\"{a}nden}, vol.~III, pp.~4--6}", year = 1974, annote = "\\ $\bullet$ Part 2 of No.~79 in \cite{bo:Mueller76a}" } @Misc{ar:Bernays74d, author = "Paul Bernays", title = "{Introduction to `Bemerkungen zu den Paradoxien von Russell und Burali-Forti'}", howpublished = "{In: {\em Leonard Nelson. Gesammelte Schriften in neun B\"{a}nden}, vol.~III, pp.~96--97}", year = 1974, note = "Critical remarks in the footnotes to this paper.", annote = "\\ $\bullet$ Part 3 of No.~79 in \cite{bo:Mueller76a}" } @Article{ar:Bernays75a, author = "Paul Bernays", title = "{Zu der Abhandlung von Raymond L.~Weiss `Historicism and Science: Thoughts on Quine'}", journal = "Dialectica", year = 1975, volume = 29, pages = "167--172", annote = "\\ $\bullet$ No.~86 in \cite{bo:Mueller76a}" } @InProceedings{ar:Bernays75b, author = "Paul Bernays", title = "Mathematics as a domain of theoretical science and of mental experience", editor = "H.~E.~Rose and J.~C.~Shepherdson", pages = "1--4", booktitle = "Logic Colloquium '73", year = 1975, organization = "Proceedings of the Logic Colloquium, Bristol, July 1973", publisher = NH, annote = "\\ $\bullet$ No.~87 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays76b, author = "Paul Bernays", title = "A system of axiomatic set theory", booktitle = "\cite{bo:Mueller76a}", year = 1976, pages = "1--120", note = "Slightly revised version of \cite{ar:Bernays37c,ar:Bernays41b,ar:Bernays42a,ar:Bernays42b,ar:Bernays43a,ar:Bernays48a,ar:Bernays54a}.", annote = "\\ $\bullet$ No.~89 in \cite{bo:Mueller76a}" } @InCollection{ar:Bernays76c, author = "Paul Bernays", title = "On the problem of schemata of infinity in axiomatic set theory", booktitle = "\cite{bo:Mueller76a}", year = 1976, pages = "121--172", note = "{Partially revised version of \cite{ar:Bernays61c}. Translated into English by J.~Bell and M.~Pl\"{a}nitz.}", annote = "{\\ $\bullet$ No.~90 in \cite{bo:Mueller76a}}" } @Misc{ar:Bernays76d, author = "Paul Bernays", title = "{Diskussion \"{u}ber die Grundlagen der Mathematik}", howpublished = "{Typoscript of a talk presented on Nov 17, 1976 at `Wissenschaftshistorisches Kolloquium', Z\"{u}rich, Winter semester 1976/77}", year = 1976, annote = "\\ $\bullet$ Reference in: Bernd Buldt, {\em Philosophische Implikationen der G\"{o}delschen S\"{a}tze? Ein Bericht}." } @Article{ar:Bernays77a, author = "Paul Bernays", title = "{\"{U}berlegungen zu F.~Gonseth's Philosophie}", journal = "Dialectica", year = 1977, volume = 31, pages = "119--128", annote = "\\ $\bullet$ No.~91b added in \cite{ar:Mueller81a}" } @Article{ar:Bernays77b, author = "Paul Bernays", title = "{Sprache und Wirklichkeit: Im Vorfeld der Fragestellungen}", journal = "Dialectica", year = 1977, volume = 31, pages = "217--223", annote = "\\ $\bullet$ No.~91c added in \cite{ar:Mueller81a}" } @InCollection{ar:Bernays78a, author = "Paul Bernays", title = "{Bemerkungen zu Lorenzen's Stellungnahme in der Philosophie der Mathematik}", booktitle = "Konstruktionen versus Positionen. Beitr{\"a}ge zur Diskussion um die konstruktive Wissenschaftstheorie. Band I: Spezielle Wissenschaftstheorie", publisher = "Walter de Gruyter, Berlin", year = 1978, editor = "K.~Lorenz", annote = "\\ $\bullet$ No.~91 in \cite{bo:Mueller76a} Parsons 8/11/03: Festschrift for Paul Lorenzen" } @Article{ar:BernaysSchoenfinkel28a, author = {Paul Bernays and Moses Sch\"{o}nfinkel}, title = "{Zum Entscheidungsproblem der mathematischen Logik}", journal = MA, year = 1928, volume = 99, pages = "342--372", annote = "\\ $\bullet$ No.~13 in \cite{bo:Mueller76a}"} @Article{ar:Esfeld01a, author = {Michael Esfeld}, title = {{Gonseth and Quine}}, journal = {Dialectica}, year = 2001, volume = 55, pages = {199--219} } @Article{ar:Gentzen36a, author = {Gerhard Gentzen}, title = {Die {W}iderspruchsfreiheit der reinen {Z}ahlentheorie}, journal = MA, year = 1936, volume = 112, pages = {493--565} } @Article{ar:Gonseth48a, author = {Ferdinand Gonseth}, title = {A propos des expos{\'e}s de {MM.~Ph.~Devaux et E.W.~Beth}}, journal = {Dialectica}, year = 1948, volume = 1, pages = {120--125} } @Article{ar:Gonseth75a, author = {Ferdinand Gonseth}, title = {Les math{\'e}matiques et la r{\'e}alit{\'e}}, journal = {Dialectica}, year = 1975, volume = 29, pages = {25--38} } @InCollection{ar:Gonseth85a, author = {Ferdinand Gonseth}, title = {Notes Autobiographiques}, booktitle = {Ferdinand Gonseth. Pour une philosophie dialectique ouverte {\`a} l'exp{\'e}rience,}, pages = {13--18}, publisher = {L'Age d'Homme}, year = 1985, editor = {Eric Emery}, address = {Lausanne} } @InCollection{ar:GonsethMueller50a, author = {Ferdinand Gonseth and Gert-Heinz M{\"u}ller}, title = {Philosophie Math{\'e}matique}, booktitle = {Philosophie, chronique actuelle}, pages = {33-127}, publisher = {Hermann}, year = 1950, series = ASI, number = 1105, address = {Paris} } @InCollection{ar:Specker78a, author = {Ernst Specker}, title = {Paul Bernays}, booktitle = {Logic Colloquium 78}, pages = {381--389}, publisher = {North-Holland}, year = 1978, editor = {M.~Boffa and D.~{van Dalen} and K.~McAloon}, address = {Amsterdam/London} } @Book{bo:BenacerrafPutnam64a, title = {Philosophy of Mathematics -- Selected readings}, publisher = {Prentice-Hall}, address = {Englewood Cliffs, NJ}, year = {1964}, editor = {Paul Benacerraf and Hilary Putnam} } @Book{bo:BenacerrafPutnam83a, title = {Philosophy of Mathematics -- Selected readings}, publisher = {Prentice-Hall}, address = {Englewood Cliffs, NJ}, edition = "2", year = {1983}, editor = {Paul Benacerraf and Hilary Putnam} } @Book{bo:Bernays58b, author = "Paul Bernays", title = "Axiomatic set theory", publisher = NH, year = 1958, note = "With a historical introduction by Abraham Fraenkel.", annote = "\\ $\bullet$ No.~56 in \cite{bo:Mueller76a}" } @Book{bo:Bernays76a, author = "Paul Bernays", title = "{Abhandlungen zur Philosophie der Mathematik}", publisher = "Wiss. Buchgesellschaft, Darmstadt", year = 1976, OPTnote = "{Containing the papers \cite{ar:Bernays27a,ar:Bernays30b,ar:Bernays37b,ar:Bernays50b,ar:Bernays54b,ar:Bernays57a,ar:Bernays59b,ar:Bernays59c,ar:Bernays61a,ar:Bernays69a,ar:Bernays70a,ar:Bernays71c}, and German translations of \cite{ar:Bernays35b,ar:Bernays46b}.\\ $\bullet$ No.~88 in \cite{bo:Mueller76a}}" } @Proceedings{bo:DockxBernays65a, title = {Information and Prediction in Science}, year = 1965, editor = {S.~Dockx and P.~Bernays}, series = {Proceedings of a Symposium, Brussels, 1962}, address = {London, New York}, publisher = {Academic Press}, annote = {From: No.~70 in \cite{bo:Mueller76a}} } @Book{bo:Franchella97a, author = {Miriam Franchella}, title = {Paul Bernays' Epistemological Way towards Gonseth's Theory}, publisher = {C.U.E.M}, year = 1997, address = {Milano} } @Book{bo:Gonseth26a, author = {Ferdinand Gonseth}, title = {Les fondements des mathematiques. De la g{\'e}ometrie d'Euclide {\`a} la r{\'e}lativit{\'e} g{\'e}n{\'e}rale et {\`a} l'intuitionnisme}, publisher = {Blanchard}, year = 1926, address = {Paris}, note = {Second edition 1974} } @Book{bo:Gonseth36a, author = {Ferdinand Gonseth}, title = {Les math{\'e}matiques et la r{\'e}alit{\'e}. Essai sur la m{\'e}thode axiomatique}, publisher = {Blanchard}, year = 1936, address = {Paris}, note = {Second edition 1974} } @Book{bo:Gonseth39a, author = {Ferdinand Gonseth}, title = {Philosophie Math{\'e}matique}, publisher = {Hermann}, year = 1939, address = {Paris}, number = 837, series = ASI, note = {Second edition 1974} } @Book{bo:Gonseth41a, author = {Ferdinand Gonseth}, title = {Entretiens de Z{\"u}rich}, publisher = {Leemann \& Co.}, year = 1941, address = {Z{\"u}rich} } @Book{bo:Gonseth45-55a, author = {Ferdinand Gonseth}, title = {La g{\'e}ometrie et le probl{\`e}me de l'espace}, publisher = {Griffon}, year = {1945--55}, volume = {I--VI}, address = {Neuch\^atel} } @Book{bo:Heinzmann82a, author = {Gerhard Heinzmann}, title = {Schematisierte Strukturen. Eine Untersuchung {\"u}ber den Idoneismus Ferdinand Gonseths auf dem Hintergrund eines konstruktivistischen Ansatzes}, publisher = {Haupt}, year = 1982, address = {Bern} } @Book{bo:Hilbert28a, author = "David Hilbert", title = "Die Grundlagen der Mathematik, {\em mit Zus\"{a}tzen von Hermann Weyl und Paul Bernays}", publisher = "Teubner Verlag, Leipzig", year = 1928, volume = 5, series = "Hamburger Mathematische Einzelschriften", annote = "\cite{bo:vanHeijenoort67a}, p.~642" } @Book{bo:HilbertBernays34a, author = "David Hilbert and Paul Bernays", title = "{Grundlagen der Mathematik}", publisher = SPR, year = 1934, volume = 1, note = "2nd edition 1968.", annote = "\\ $\bullet$ No.~19 in \cite{bo:Mueller76a}" } @Book{bo:HilbertBernays39a, author = "David Hilbert and Paul Bernays", title = "{Grundlagen der Mathematik}", publisher = SPR, year = 1939, volume = 2, note = "2nd edition 1970.", annote = "\mueller{28.}" } @Book{bo:Mancosu98a, author = "Paolo Mancosu", title = "From Brouwer to Hilbert: The debate on the foundations of mathematics in the 1920s", publisher = OUP, year = 1998 } @Book{bo:Mueller76a, title = "Sets and Classes -- On the work of Paul Bernays", publisher = NH, year = 1976, editor = "Gert H.~M{\"u}ller", volume = 84, series = "Studies in logic and the foundations of mathematics" } @Book{bo:PanzaPont92a, author = {M.~Panza and J.-C.~Pont}, title = {Espace et horizon de r{\'e}alit{\'e}. Philosophie math{\'e}matique de Ferdinand Gonseth}, publisher = {Masson}, year = 1992, address = {Paris/Milan/Barcelone/Bonn} } @Book{bo:Peckhaus90a, author = {Volker Peckhaus}, title = {Hilbertprogramm und Kritische Philosophie}, publisher = {Vandenhoeck \& Ruprecht}, year = 1990, volume = 7, series = {Studien zur Wissenschafts-, Sozial- und Bildungsgeschichte der Mathematik}, address = {G{\"o}ttingen} } @Book{bo:vanHeijenoort67a, author = "Jean van Heijenoort", title = "{From Frege to G{\"o}del: A Sourcebook of Mathematical Logic}", publisher = "Harvard University Press", year = "1967", address = "Cambridge, Massachusetts" } @Booklet{journal:Dialectica90a, title = {Dialectica}, OPTkey = {}, OPTauthor = {}, OPThowpublished = {}, OPTaddress = {}, OPTmonth = {}, year = {1990}, note = {vol.~44, numbers~3--4}, OPTannote = {} } @Unpublished{ms:Bernays38a, author = {Paul Bernays}, title = {R{\'e}sum{\'e}}, note = {Manuscript (AJ/B/38a), Archives Henri-Poincar{\'e}, Nancy}, year = 1938 } @Unpublished{ms:Bernays38b, author = {Paul Bernays}, title = {}, note = {Manuscript (AJ/B/38b), Archives Henri-Poincar{\'e}, Nancy}, year = 1938 } @Article{re:Bernays23a, author = "Paul Bernays", title = "{Review of Aloys M\"{u}ller's `Der Gegenstand der Mathematik'}", journal = "Die Naturwissenschaften", year = 1923, volume = 11, number = 26, pages = "520-2", annote = "{\\ $\bullet$ \cite{bo:Mancosu98a}, p.~183, not listed by M\"{u}ller}" } @Article{re:Bernays36h, author = "Paul Bernays", title = "{Review of W.~V.~Quine: A reinterpretation of Sch\"{o}nfinkel's logical operators, Bulletin of the American Mathematical Society vol.~42, pp.~87--9, 1936}", journal = JSL, year = 1936, volume = 1, number = 1, pages = "42--3", month = "March", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays36i, author = "Paul Bernays", title = "{Review of Wilhelm Ackermann: Beitr\"{a}ge zum Entscheidungsproblem der mathematischen Logik, Mathematische Annalen vol.~112, pp.~419--32, 1936}", journal = JSL, year = 1936, volume = 1, number = 1, pages = "43--4", month = "March", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays36j, author = "Paul Bernays", title = "{Review of J.C.C.~McKinsey: On the independence of Hilbert and Ackermann's postulates for the calculus of propositional functions, American journal of Mathematics, vol.~58, pp.~336--44, 1936}", journal = JSL, year = 1936, volume = 1, number = 2, pages = "64--5", month = "June", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays36k, author = "Paul Bernays", title = "{Review of Alonzo Church: An unsolvable problem of elementary number theory, American journal of Mathematics, vol.~58, pp.~345--63, 1936}", journal = JSL, year = 1936, volume = 1, number = 2, pages = "73--4", month = "June", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays36l, author = "Paul Bernays", title = "{Review of Alonzo Church: A note on the Entscheidungsproblem, Journal of Symbolic Logic, vol.~1, no.~1, pp.~40--1, 1936}", journal = JSL, year = 1936, volume = 1, number = 2, pages = "74", month = "June", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays36m, author = "Paul Bernays", title = "{Review of Alonzo Church and J.B.~Rosser: Some properties of conversion, Transactions of the American Mathematical Society, vol.~39, pp.~472--82, 1936}", journal = JSL, year = 1936, volume = 1, number = 2, pages = "74--5", month = "June", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays36n, author = "Paul Bernays", title = "{Review of Gerhard Gentzen: Die Widerspruchsfreiheit der reinen Zahlentheorie, Mathematische Annalen, vol.~112, pp.~493--565, 1936}", journal = JSL, year = 1936, volume = 1, number = 2, pages = "75", month = "June", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays36o, author = "Paul Bernays", title = "{Review of M.~Wajsberg: Untersuchung \"{u}ber Unabh\"{a}ngigkeitsbeweise nach der Matrizenmethode, Wiadom\'{o}sci matematycze, vol.~41, pp.~33--70, 1936}", journal = JSL, year = 1936, volume = 1, number = 2, pages = "75--6", month = "June", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays37g, author = "Paul Bernays", title = "{Review of Raphael M.~Robinson: The theory of classes. A modification of von Neumann's system, Journal of Symbolic Logic, vol.~2, pp.~29--36, 1937}", journal = JSL, year = 1937, volume = 2, OPTnumber = "", pages = "168", OPTmonth = "", annote = "{\\ $\bullet$ not listed by M\"{u}ller, (no. and month missing)}" } @Article{re:Bernays37h, author = "Paul Bernays", title = "{Review of R.~Feys: Directions nouvelles de la logistique aux \'{E}tats-Unis, Revue n\'{e}oscolastique de philosophie, vol.~40, pp.~398--411, 1937}", journal = JSL, year = 1937, volume = 2, OPTnumber = "", pages = "175", OPTmonth = "", annote = "{\\ $\bullet$ not listed by M\"{u}ller, (no. and month missing)}" } @Article{re:Bernays39b, author = "Paul Bernays", title = "{Review of Frederic B.~Fitch: The consistency of ramified Principia, Journal of Symbolic Logic, vol.~3, pp.~140--9, 1938}", journal = JSL, year = 1939, volume = 4, number = 2, pages = "97--8", OPTmonth = "", annote = "{\\ $\bullet$ not listed by M\"{u}ller, (month missing)}" } @Article{re:Bernays40i, author = "Paul Bernays", title = "{Review of Albert Lautmann: Essai sur les notions de structure et d'existence en math\'{e}matiques, Actualit\'{e}s scientifiques et industrielles, Hermann \& C$^{ie}$, Paris, 1938, pp.~590--1}", journal = JSL, year = 1940, volume = 5, number = 1, pages = "20--2", month = "March", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays40j, author = "Paul Bernays", title = "{Review of Barkley Rosser: On the consistency of Quine's New foundations for mathematical logic, Journal of Symbolic Logic, vol.~4, pp.~15--24, 1939}", journal = JSL, year = 1940, volume = 5, number = 1, pages = "32--33", month = "March", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays40k, author = "Paul Bernays", title = "{Review of Leopold L\"{o}wenheim: Einkleidung der Mathematik im Schr\"{o}derschen Relativkalkul, Journal of Symbolic Logic, vol.~5, pp.~1--15, 1940}", journal = JSL, year = 1940, volume = 5, pages = "127--128", annote = "{\\ $\bullet$ \cite{bo:vanHeijenoort67a}, p.~631, not listed by M\"{u}ller}" } @Article{re:Bernays40l, author = "Paul Bernays", title = "{Review of Kurt G\"{o}del: The consistency of the axiom of choice and of the generalized continuum-hypothesis, Proceedings of the National Academy of Science, vol.~24, pp.~556-7, 1938}", journal = JSL, year = 1940, volume = 5, number = 3, pages = "116--7", month = "September", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays40m, author = "Paul Bernays", title = "{Review of Kurt G\"{o}del: Consistency-proof for the generalized continuum, Proceedings of the National Academy of Science, vol.~25, pp.~220--4, 1939}", journal = JSL, year = 1940, volume = 5, number = 3, pages = "117--8", month = "September", annote = "{\\ $\bullet$ not listed by M\"{u}ller}" } @Article{re:Bernays40n, author = "Paul Bernays", title = "{Review of Kurt G\"{o}del: Consistency proof for the generalized continuum-hypothesis, Proceedings of the National Academy of Sciences 25, 556-7, 1939}", journal = JSL, year = 1940, volume = 5, pages = "17-18", annote = "{\\ $\bullet$ \cite{bo:vanHeijenoort67a}, p.~631, not listed by M\"{u}ller; compare with \cite{re:Bernays40l}}" } @Article{re:MacLane40a, author = {Saunders MacLane}, title = {Review of \cite{bo:Gonseth39a}}, journal = JSL, year = 1940, volume = 5, number = {77--78} } @Article{re:MacLane42a, author = {Saunders MacLane}, title = {Review of \cite{bo:Gonseth41a}}, journal = JSL, year = 1942, volume = 7, number = {35--37} } @PhdThesis{th:Bernays12a, author = "Paul Bernays", title = "{\"{U}ber die Darstellung von positiven, ganzen Zahlen durch die primitiven, bin\"{a}ren quadratischen Formen einer nicht-quadratischen Diskriminante}", school = {G\"{o}ttingen}, year = 1912, annote = "\\ $\bullet$ No.~2 in \cite{bo:Mueller76a}" } @Misc{th:Bernays18b, author = "Paul Bernays", title = "{Beitr\"{a}ge zur axiomatischen Behandlung des Logik-Kalk\"{u}ls}", howpublished = "{Habilitationsschrift, Universit\"{a}t G\"{o}ttingen}", year = 1918, note = "{Unpublished typescript.}", annote = "{\\ $\bullet$ \cite{bo:Mancosu98a}, p.~183, not listed by M\"{u}ller}" } %%% Added by RZ %%% @ARTICLE{ar:Ackermann24, author = {Wilhelm Ackermann}, year = 1924, title = {Begr\"undung des ``tertium non datur'' mittels der {H}ilbertschen {T}heorie der {W}iderspruchsfreiheit}, journal = ma, volume = 93, pages = {1--36} } @Article{ar:Ackermann40, author = {Wilhelm Ackermann}, title = {Zur {W}iderspruchsfreiheit der {Z}ahlentheorie}, journal = ma, year = 1940, volume = 117, pages = {162--194} } @BOOK{bo:HilbertAckermann28, author = {David Hilbert and Wilhelm Ackermann}, year = 1928, title = {Grundz{\"uge} der theoretischen {L}ogik}, publisher = {Springer}, address = {Berlin} } @PHDTHESIS{th:Behmann18, author = {Heinrich Behmann}, year = 1918, title = {Die {A}ntinomie der transfiniten {Z}ahl und ihre {A}ufl\"osung durch die {T}heorie von {R}ussell und {W}hitehead}, school = {Universit\"at G\"ottingen}, type = {Dissertation}, note = {352 pp.} } @article{ar:Behmann22, author = {Heinrich Behmann}, year = 1922, title = {Beitr\"{a}ge zur {A}lgebra der {L}ogik, insbesondere zum {E}ntscheidungsproblem}, journal = {Mathematische Annalen}, volume = 86, pages = {163--229} } @ARTICLE{ar:Mancosu99, author = {Paolo Mancosu}, year = {1999}, title = {Between {R}ussell and {H}ilbert: {B}ehmann on the foundations of mathematics}, journal = bsl, volume = 5, number = 3, pages = {303--330} } @Article{ar:Mancosu03, author = {Paolo Mancosu}, title = {The {R}ussellian Influence on {H}ilbert and His school}, journal = {Synthese}, year = 2003, volume = 137, pages = {59--101} } @ARTICLE{ar:vonNeumann27, author = {Johann von Neumann}, year = 1927, title = {Zur {H}ilbertschen {B}eweistheorie}, journal = mathz, volume = 26, pages = {1--46} } @Article{ar:Schroeder-Heister02, author = {Peter Schr{\"o}der-Heister}, title = {Resolution and the origins of structural reasoning: early proof-theoretic ideas of {H}ertz and {G}entzen}, journal = {Bulletin of Symbolic Logic}, year = 2002, volume = 8, pages = {246--265} } @ARTICLE{ar:Sheffer13, author = {Henry Maurice Sheffer}, year = 1913, title = {A set of five independent postulates for boolean algebras, with application to logical constants}, journal = {Transactions of the American Mathematical Society}, volume = 14, pages = {481--488} } @ARTICLE{ar:Sieg99, author = {Wilfried Sieg}, title = {Hilbert's Programs: 1917--1922}, year = {1999}, volume = {5}, number = {1}, pages = {1--44}, journal = bsl } @Article{ar:Zach99, author = {Richard Zach}, title = {Completeness before {P}ost: {B}ernays, {H}ilbert, and the development of propositional logic}, journal = bsl, year = 1999, volume = 5, number = 3, pages = {331--366} } @article{ar:Zach03, author = {Richard Zach}, title = {The practice of finitism. {E}psilon calculus and consistency proofs in {H}ilbert's {P}rogram}, journal = {Synthese}, year = {2003}, volume = {137}, pages = {211-259} } @article{ar:Zach04, author = {Richard Zach}, title = {Hilbert's ``{V}erungl\"uckter {B}eweis,'' the first epsilon-theorem, and consistency proofs}, journal = {History and Philosophy of Logic}, year = 2004, volume = 25, pages = {79--94} } @BOOK{bo:vanHeijenoort67, editor = {Jean van Heijenoort}, year = 1967, title = {From {F}rege to {G}{\"o}del. {A} Source Book in Mathematical Logic, 1897--1931}, publisher = {Harvard University Press}, address = {Cambridge, Mass.} } @BOOK{bo:Mancosu98, editor = {Paolo Mancosu}, year = 1998, title = {From {B}rouwer to {H}ilbert. {T}he Debate on the Foundations of Mathematics in the 1920s}, booktitle = {From Brouwer to Hilbert}, publisher = {Oxford University Press}, address = {Oxford and New York} } @ARTICLE{ar:Hilbert28, author = {David Hilbert}, year = 1928, title = {Die {G}rundlagen der {M}athematik}, journal = {Abhandlungen aus dem Seminar der Hamburgischen Universit{\"a}t}, volume = 6, pages = {65-85}, note = {{E}nglish translation in \cite[464--479]{bo:vanHeijenoort67}}, englishtitle = {The foundations of mathematics} } @BOOK{bo:Ewald96, editor = {William Bragg Ewald}, year = 1996, title = {From {K}ant to {H}ilbert. {A} Source Book in the Foundations of Mathematics}, volume = 2, publisher = {Oxford University Press}, address = {Oxford and New York} } @ARTICLE{ar:Hilbert22, author = {David Hilbert}, year = 1922, title = {Neubegr{\"u}ndung der {M}athematik: {E}rste {M}itteilung}, journal = {Abhandlungen aus dem Seminar der Hamburgischen Universit{\"a}t}, volume = 1, pages = {157--77}, note = {{E}nglish translation in \cite[198--214]{bo:Mancosu98} and \cite[1115--1134]{bo:Ewald96}}, englishtitle = {The new grounding of mathematics. {F}irst report} } @ARTICLE{ar:Hilbert23, author = {David Hilbert}, year = 1923, title = {Die logischen {G}rundlagen der {M}athematik}, journal = ma, volume = 88, pages = {151-165}, note = {{E}nglish translation in \cite[1134--1148]{bo:Ewald96}}, englishtitle = {The logical foundations of mathematics} } @BOOK{bo:HilbertBernays39, author = {David Hilbert and Paul Bernays}, year = 1939, title = {Grundlagen der {M}athematik}, volume = 2, publisher = {Springer}, address = {Berlin} } @Article{ar:Gentzen36, author = {Gerhard Gentzen}, title = {Die {W}iderspruchsfreiheit der reinen {Z}ahlentheorie}, journal = ma, year = 1936, volume = 112, pages = {493--565}, note = {{E}nglish translation in \cite[132--213]{bo:Gentzen69}} } @BOOK{bo:Gentzen69, author = {Gerhard Gentzen}, editor = {M. E. Szabo}, year = 1969, title = {The Collected Papers of {G}erhard {G}entzen}, booktitle = {The Collected Papers of {G}erhard {G}entzen}, publisher = {North-Holland}, address = {Amsterdam} } @Article{ar:Lowenheim15, author = {Leopold L\"{o}wenheim}, title = {\"{U}ber {M}\"oglichkeiten im {R}elativkalk\"{u}l}, journal = ma, year = 1915, pages = {447--470}, note = {English translation in \cite[228--251]{bo:vanHeijenoort67}} }