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Karl Menger Bibliography

Karl Menger published a total of 234 papers. There are also collections of some of his work:

• Karl Menger: Ergebnisse eines Mathematischen Kolloquiums , Egbert Dierker and Karl Siegmund (eds.), Springer, 1998. 
• Karl Menger: Selected Papers in Logic and Foundations, Didactics, Economics , D. Reidel Publishing Co. (Dordrecht, Holland), 1979. 
• Selecta Mathematica, Volume 1 and Volume 2, B. Schweizer, A. Sklar, K. Sigmund, et al. (eds.), Springer 2002/2003. 
• Unexplored Dimensions: Karl Menger on Economics and Philosophy (1923-1938) , Giandomenica Becchio (ed.), Emerald Group Publishing Limited, 2009.

The following bibliography is an extension of the one printed in the latter collection of papers.

Abbreviations of the titles of some journals used below:

AM	Annals of Mathematics
AMM	American Mathematical Monthly
AW	Anzeiger, Wiener Akademie der Wissenschaften, Mathematisch-Naturwissenschaftliche Klasse
BAMS	Bulletin of the American Mathematical Society
CRP	Comptes Rendus, Acad?mie des Sciences, Paris
ErgMK	Ergebnisse eines Mathematischen Kolloquiums
FM	Fundamenta Mathematicae
JbDMV	Jahresbericht der Deutschen Mathematiker-Vereinigung
MA	Mathematische Annalen
Mh	Monatshefte f?r Mathematik und Physik
PA	Proceedings, Royal Academy of Science, Amsterdam
PUSA	Proceedings, National Academy of Science, U.S.A.
RepMC	Reports of a Mathematical Colloquium

1921-1923

1. 'Zur Dimensions- und Kurventheorie. Unver?ffentlichte Aufs?tze aus den Jahren 1921-1923' (Published in Mh 36 (1929), 411-432.).
   1. 'Zur Theorie der Punktmengen' (Fall 1921);
   2. '?ber die Dimensionalit?t von Punktmengen' (January 1922);
      1. 'Erg?nzung' ('Supplement') to '?ber die Dimensionalit?t von Punktmengen' (February 1922);
   3. '?ber die Dimensionalitat von Punktmengen' (Fall 1922);
   4. 'Zur Theorie der Punktmengen II' (Fall 1923).
2. '?ber die Dimensionalit?t von Punktmengen, I. Teil', Mh 33 (1923), 148-160.
3. 'Einleitung' ('Introduction') to Carl Menger, Grund?tze der Volkswirtschaftslehre , 2. Auflage, Wien.

1924

1. 'Einige ?berdeckungss?tze der Punktmengenlehre', Sitzungsber. Akad. d. Wissensch. Wien, Math.-Naturw. Kl. 133, 421-444.
2. '?ber die Dimension von Punktmengen', PA 27, 639-643.
3. '?ber die Dimension von Punktmengen, II. Teil', Mh 34, 137-161.

1925

1. 'Grundz?ge einer Theorie der Kurven', PA 28, 67-71.
2. 'Grundz?ge einer Theorie der Kurven', MA 95, 277-306 (according to a note in 1970-1 (p.443) this should be 1926).

1926

1. 'Zur allgemeinen Kurventheorie', FM 10, 96-115 (according to a note in 1970-1 (p.443) this should be 1927).
2. 'Das Hauptproblem ?ber die dimensionelle Struktur der R?ume', PA 30, 138-144.
3. 'Allgemeine R?ume und Cartesische R?ume I, II', PA 29, 476-83 and 1125-1128.
4. 'Bericht ?ber die Dimensionstheorie', JbDMV 35, 113-150.
5. '?ber geod?tische Linien in allgemeinen metrischen R?umen', PA 29, 166-169.
6. '?ber regul?re Raumkurven', MA 96, 572-582. (corrected? from  1979-1 )
7. 'Zur Entstehung meiner Arbeiten ?ber Dimensions- und Kurventheorie', PA 19, 1122-1124.

1927

1. 'Bemerkungen zur zweiten Untersuchung ?ber allgemeine Metrik', PA 30, 710-714 (See 1928-2-II ).
2. 'Die Haupttheoreme der Dimensionstheorie', JbDMV 36, 8-12.
3. 'Zusammenhangsstufen und Cantorsche Mannigfaltigkeiten', PA 30, 705-709.

1928

1. 'Bemerkungen zu Grundlagenfragen, I-lV', JbDMV 37:
   1. '?ber Verzweigungsmengen', 213-226;
   2. 'Die mengentheoretischen Paradoxien', 298-302;
   3. '?ber Potenzmengen', 303-308;
   4. 'Axiomatik der endlichen Mengen und der elementargeometrischen Verkn?pfungsbeziehungen', 309-325.
2. 'Untersuchungen ?ber allgemeine Metrik, I-III', MA 100:
   1. 'Theorie der Konvexit?t', 75-113;
   2. 'Die Euklidische Metrik', 113-141;
   3. 'Eine n-dimensionale Metrik', 142-163.
   1. Abstracts of 1928-2 in AW 65, 14-17 and in ErgMK 1, 20-23.
3. 'Konvexit?tstheoretische Notizen: ?ber konvexe H?llen; ?ber Vollkonvexit?t; ?ber Verallgemeinerungen des Zwischenbegriffes; ?ber den Begriff der Konkavit?t', AW 65, 154-156 and ErgMK 1, 23-26.
4. 'Die Metrik des Hilbertschen Raumes', AW 65, 159-160 and ErgMK 1, 26-27.
5. 'Die Halbstetigkeit der Bogenl?nge', AW 65, 278-281.
6. 'Ein Theorem der Topologie', AW 65, 4 and ErgMK 1, 2-3.
7. 'Dimensionstheoretische Notizen: Ein Satz zur Erg?nzung der Dimensionsdefinition; ?ber schwachdimensionale Mengen; ?ber n-dimensionale Gew?chse', AW 65, 5-8 and 11-12, and ErgMK 1, 6-8.
8. 'Dimension und Zusammenhangsstufe' (with W. Hurewicz ), MA 100, 618-633.
9. Dimensionstheorie , Leipzig & Berlin, iv + 319 pp.

1929

1. '?ber die Dimension von Punktmengen, III. Teil. Zur Begr?ndung einer axiomatischen Theorie der Dimension', Mh 36, 193-218; abstr. in AW 66, 148-149.
2. 'Zur Frage nach der Herleitung des Dimensionsbegriffes aus Forderungen', AW 66, 87-90.
3. 'Allgemeine R?ume und Cartesische R?ume III. Beweis des Fundamentalsatzes', PA 32, 330-340.
4. 'Dimensionstheoretische Notizen: Ein Zerlegungssatz f?r rational-dimensionale Mengen; ?ber die nirgends dichten Teilmengen des R n ; ?ber die Summe regul?rer Kurven', AW 66, 84-87 and ErgMK 1, 6-8.
5. '?ber eine neue Definition der Bogenl?nge. Weitere Verallgemeinerung des L?ngenbegriffes', AW 66, 23-25.
6. 'Ein allgemeiner Trennungssatz', AW 65, 266-288 and ErgMK 1, 16-17.
7. 'Die allgemeine Kurventheorie', Forschungen und Fortschritte , 5, No.20, 232-233.

1930

1. 'Axiomatische Einf?hrung des Dimensionsbegriffes', in Comptes Rendus da Premier Congr?s des Math?maticiens des Pays Slaves, Warszawa 1929, pp. 57-65.
2. 'Untersuchungen ?ber allgemeine Metrik. IV. Zur Metrik der Kurven', MA 105, 466-501.
3. 'Entwurf einer neuen Theorie des Masses', ErgMK 2, 6-10 and AW 67, 12-16.
4. 'Remarques sur la Th?orie Axiomatique de la Dimension' (with C. Kuratowski ), Mh 37, 169-174.
5. 'Bemerkungen ?ber dimensionelle Feinstruktur und Produktsatz', Prac Mat.-Fizycz. 37, 77-90.
6. 'Otto Schreier', Mh 37, 1-6.
7. 'Eine dimensionstheoretische Bemerkung von O. Schreier', Mh 37, 7-12; abstr. in ErgMK 2, 1.
8. 'Antwort auf eine Note von Brouwer', Mh 37, 175-182.
9. '?ber den n-Beinsatz in lokal-zusammenh?ngenden Kontinua' (with G. N?beling ), AW 67, 86-88.
10. 'Eine neue Definition der Bogenl?nge', ErgMK 2, 11-12.
11. 'Das Botenproblem', ibid ., p. 12.
12. 'Bemerkungen von Mazurkiewicz und Tarski ?ber die Axiomatik des Dimensionsbegriffes', ibid ., p.16.
13. '?ber Mengensysteme', ibid ., pp. 16-17.
14. 'Probleme der allgemeinen metrischen Geometrie', ibid ., pp. 20-22.
15. 'Bericht ?ber die mengentheoretischen ?berdeckungss?tze', ibid ., pp. 23-27.
16. '?ber pl?ttbare Dreiergraphen und Potenzen nichtpl?ttbarer Graphen', ibid ., pp. 30-31 and AW 67, 30-31.
17. 'Einf?hrung des Komplexen in die allgemeine Metrik und metrische Untersuchungen in abstrakten Gruppen', ibid ., pp. 34-38 and AW 67, 39-44.
18. '?ber die sogenannte Konstruktivit?t bei arithmetischen Definitionen', AW 67, 257-258.
19. 'Der Intuitionismus', Bl?tter f?r Deutsche Philosophie 4, 311-325.

1931

1. 'New Foundations of Euclidian Geometry', Amer. J. of Math. 53, 721-745.
2. 'Beitr?ge zur Gruppentheorie I. ?ber einen Abstand in Gruppen', Math. Zeitschrift 33, 396-418.
3. 'Bericht ?ber metrische Geometrie', JbDMV 40, 201-219.
4. 'Some Applications of Point-Set Methods', AM 32, 739-760.
5. 'Remarks Concerning the Paper of W. L. Ayres on the Regular Points of a Continuum', Transactions Am. Math. Soc. 33, 663-667.
6. 'Ein Problem von Blaschke', AW 68, 75-76.
7. 'Eine neue Kennzeichnung der Geraden', ibid ., pp. 103-105.
8. 'Bericht ?ber ein mathematisches Kolloquium 1929/30', Mh 38, 17-38.
9. '?ber den Konstruktivit?tsbegriff (Zweite Mitteilung)', AW 68, 7-9.
10. 'Eine elementare Bemerkung ?ber die Struktur logischer Formeln', ErgMK 3, 22-23.

1932

1. Kurventheorie , edited in collaboration with G. N?beling , Leipzig, iv + 376 pp.; repr. Chelsea, New York 1967.
2. 'Neuere Methoden und Probleme der Geometrie', in Verhandlungen des internationalen Mathematiker-Kongresses, Z?rich 1932, I, pp. 310-323.
3. '?ber die Hinweise auf Brouwer in Urysohns Memoire', Wien (published by the author).
4. 'Eine Zuschrift von Karl Menger an Hans Hahn betreffend Mengers Antwort auf eine Note von Brouwer in Band 37 der Monatshefte', Mh 40, 233.
5. '?ber die lokale Dimension von Mengensummen', ErgMK 4, 1-2.
6. 'Eine NZ-Kurve', ibid ., p. 7.
7. '?ber eine Limesklasse', ibid ., p. 9.
8. 'Diskussion ?ber die Verzweigungsordnung von Fl?chenpunkten', ibid ., pp. 11-12.
9. 'Zur mengentheoretischen Behandlung des Tangentenbegriffes und verwandter Begriffe', ibid ., p. 23.
10. 'Ein ?berdeckungssatz f?r  ', ibid ., pp. 40-41.
11. 'Eine neue Kennzeichnung der Geraden', ibid ., pp. 41-43.

1933

1. 'Die neue Logik', in Krise und Neuaufbau in den Exakten Wissenschaften. F?nf Wiener Vortr?ge , Leipzig & Wien, pp. 94-122 (E. tr. 1937-6 ).
   1. 'Vorwort' ('Preface', unsigned) to Krise und Neuaufbau , pp. i-ii.
2. '?ber den imagin?ren euklidischen Raum', Tohoku Math. J. 37, 475-78.
3. 'Zur Begr?ndung einer Theorie der Bogenl?nge in Gruppen', ErgMK 5, 1-6.
4. 'Eine Bemerkung ?ber die Potenzen schwach eindimensionaler Mengen', ibid ., pp. 9-10.
5. 'Rein imagin?re R?ume, indefinite Metriken und verwandte Probleme', ibid ., pp. 16-17.
6. 'Neuer Aufbau der Vektoralgebra', ibid ., pp. 27-29.
7. 'Diskussion ?ber koordinatenlose Differentialgeometrie' (with K. G?del and A. Wald ), ibid ., pp. 25-26.

1934

1. 'Ist die Quadratur des Kreises l?sbar?', in Alte Probleme - Neue L?sungen in den exakten Wissenschaften. F?nf  Wiener Vortr?ge, Zweiter Zyklus , Leipzig & Wien, pp. 1-28.
   1. 'Nachwort' ('Postscript', signed K.M.) to Alte Probleme - Neue L?sungen , pp. 117-122.
2. 'Bericht ?ber neueste Ergebnisse der metrischen Geometrie', in Comptes Rendus du Deuxi?me Congr?s des Math?maticiens des Pays Slaves, Praha 1934, pp. 116-117.
3. 'Eine Bemerkung ?ber L?ngenmengen', ErgMK 6, 1-2.
4. Remarks in the Discussion of K. Schlesinger's Modification of  the Walras - Cassel Production Equations and A. Wald's Solution of the Modified Equations, ibid ., pp. 18-20.
5. 'Ein Satz ?ber endliche Mengen mit Anwendungen auf die formale Ethik', ibid ., pp. 23-26.
6. 'Bernoullische Wertlehre und Petersburger Spiel', ibid ., pp. 26-27.
7. 'Hans Hahn', ibid ., pp. 40-44.
8. 'Das Unsicherheitsmoment in der Wertlehre. Betrachtungen in Anschluss an das sogenannte Petersburger Spiel', Zeitschrift f?r National?konomie 5, 459-485 (E. tr. 1967-1 ).
   1. 'Bemerkungen' ('Remarks') to 'Das Unsicherheitsmoment in der Wertlehre', Zeitschrift f?r National?konomie 6, 283-285 (E. tr. 1967-1 ).
9. Moral, Wille und Weltgestaltung , Wien, iv + 143 pp.

1935

1. 'Hans Hahn', FM 24, 317-320.
2. 'Metrische Geometrie und Variationsrechnung', FM 25, 441-458.
3. 'Sull' Indirizzo di Idee e sulle Tendenze Principali del Colloquio Matematico di Vienna', Ann. Scuola Norm. Sup., Pisa 4, 1-13.
4. 'Sur un Th?or?me G?n?ral du Calcul des Variations', CRP 201, 705-707.
5. 'Algebra der Geometrie. Zur Axiomatik der projektiven Verkn?pfungsbeziehungen', ErgMK 7, 11-12.
6. '?ber die  -Metrik und  -Bogenl?nge', ibid ., pp. 13-14.
7. 'Programmatisches zur Anwendung der metrischen Geometrie auf die Variationsrechnung', ibid ., pp. 40-51.

1936

1. 'New Foundations of Projective and Affine Geometry. Algebra of Geometry' (in collaboration with F. Alt and O. Schreiber ), AM 37, 456-482.
2. 'Calcul des Variations dans les Espaces Distanci?s G?n?raux', CRP 222, 1007-1009.
3. 'Courbes Minimisantes Non-Rectifiables et Champs G?n?raux des Courbes Admissibles dans le Calcul de Variations', ibid ., pp. 1648-1650.
4. 'Metric Methods in Calculus of Variations', in Congres International des Mathematiciens, Oslo 1936, II, pp. 45-46.
5. 'New Ways in Differential Geometry', ibid ., pp. 171-173.
6. 'Bemerkungen zu den Ertragsgesetzen', Zeitschrift f?r National?konomie 7, 25-26 (E. tr. 1954-3 ).
   1. 'Weitere Bemerkungen zu den Ertragsgesetzen', ibid ., pp. 388-397 (E. tr. 1954-3 ).
7. 'Einige neuere Fortschritte in der exakten Behandlung sozialwissenschafflicher Probleme', in Neuere Fortschritte in den exakten Wissenschaften. F?nf Wiener Vortr?ge. Dritter Zykius , Leipzig & Wien, pp. 103-132.
8. 'Vorwort' ('Preface') to Friedrich Waismann, Einf?hrung in das mathematische Denken. Die Begriffsbildung der modernen Mathematik , Wien, pp. iii-iv. (E. tr. Introduction to Mathematical Thinking by T. J. Benach, New York, 1951). Reprinted as 1959-5 (E. tr.) and  1996-1 (German).

1937

1. 'Metric Methods in Calculus of Variations', PUSA 23, 224-250.
2. 'What Is the Calculus of Variations and What Are Its Applications?', Scientific Monthly 44, 250-253; repr. in The World of Mathematics II, edited by J. R. Newman, New York 1956, pp. 886-890.
3. 'A Note on a Previous Paper "New Foundations of Projective and Affine Geometry" 'with F. Alt . (See 1936-1 ), AM 38, 450.
4. 'La G?om?trie des Distances at Ses Relations avec les Autres Branches des Math?matiques', L'Enseignement Math?matique 35, 348-372.
5. 'An Exact Theory of Social Relations and Groups', in Report of Third Annual Research Conference on Economics and Statistics, Cowles Commission for Research in Economics, Colorado Springs , pp. 71-73.
6. 'The New Logic', Philosophy of Science 4, 299-336 (E. tr., with revisions, of 1933-1 by H. B. Gottlieb and J. K. Senior). Reprinted as 1996-2 .

1938

1. 'Non-Euclidian Geometry of Joining and Intersecting', BAMS 44, 821-824.
2. 'Axiomatique Simplifi?e de l'Alg?bre de la G?om?trie Projective', CRP 206, 306-308.
3. 'A Foundation of Projective Geometry', Proceedings, Indiana Academy of Science 47, 189-191.
4. 'A Symposium on the Algebra of Geometry and Related Subjects', Science 87, 324.
5. 'An Abstract Form of the Covering Theorems of Topology', AM 39, 794-803.
6. 'New Foundation of Non-Euclidian, Affine, Real Projective and Euclidian Geometry', PUSA 24, 486-490.
7. 'Nouvelle Base pour le D?veloppement de la G?om?trie de Bolyai et Lobatchefski', CRP 206, 458-460.
8. 'Une Forme Abstraite du Th?or?me de Borel-Lebesgue G?n?ralis?', ibid ., pp. 563-565.
9. 'Introduction' to L. M. Blumenthal, Distance Geometries , University of Missouri Studies 13, Columbia, Missouri, pp. 7-10.
10. 'An Exact Theory of Social Groups and Relations', American Journal of Sociology 43, 790-798.

1939

1. 'A Logic of the Doubtful. An Optative and Imperative Logic', RepMC 1, 53-64.
2. 'A Theory of Length and Its Applications to the Calculus of Variations', PUSA 25, 474-478.
3. 'On Cauchy's Integral Theorem in the Real Plane', ibid ., pp. 621-625.
4. 'On Necessary and on Sufficient Conditions in Elementary Mathematics', School, Science and Mathematics , 631-642.
5. 'On Linear Sets in Metric Spaces' (with A. N. Milgram ), RepMC 1, 16-17.

1940

1. 'Three Lectures on Mathematical Subjects', The Rice Institute Pamphlet 27:
   1. 'Analysis and Metric Geometry', 1-40;
   2. 'On Algebra of Geometry and Recent Progress in Non-Euclidian Geometry', 41-79;
   3. 'Topology without Points', 80-107. (corrected? from 1979-1 )
2. 'On Shortest Polygonal Approximations to a Curve', RepMC 2, 33-38.
3. 'On Green's Formula', PUSA 26, 660-664.
4. 'Redundancies in the Classical Treatment of the Cauchy-Riemann Conditions', RepMC 2, 45-48.

1942

1. 'Statistical Metrics', PUSA 28, 535-537.
2. 'Projective Generalization of Metric Geometry' (abstract), BAMS 48, 833.

1943

1. 'What Is Dimension?' AMM 50, 2-7.
2. 'Differential Equations', in Practical Mathematics , edited by R. S. Kimball, New York, Issue 9, vol.8, pp. 513-540.

1944

1. Algebra of Analysis , Notre Dame Mathematical Lectures 3, Notre Dame, Indiana, 50 pp.
2. 'Tri-Operational Algebra', RepMC 5/6, 3-10.
3. 'Projective Generalizations of Metric Geometry', ibid ., pp. 60-76.
4. 'On the Teaching of Differential Equations', AMM 51, 392-395.
5. 'Why Study Mathematics?', Al-Geo-Trig (Central Catholic High School, Toledo, Ohio) 7, 5-6.
6. 'On the Relation between the Calculus of Probability and Statistics', in Notre Dame Mathematical Lectures 4, Notre Dame, Indiana, pp. 44-53.

1945

1. 'D?finition Intrins?que de la Notion de Chemin', CRP 221, 739-741.
2. 'Methods of Presenting e and  ', AMM 52, 28-33.

1946

1. 'New Projective Definitions of the Concepts of Hyperbolic Geometry', RepMC 7, 20-28.
2. 'General Algebra of Analysis', ibid ., pp. 46-60.
3. 'Analysis without Variables', J. Symbol. Log . 11, 30-31.

1948

1. 'The Topology of the Triangle Inequality', Revista de Ciencias 50, 155-165. (corrected? from 1979-1 )
2. 'Stieltjes Integrals Considered as Lengths', Annales , Soci?t? Polonaise Math . 21, 173-175.
3. 'Fundamental and Applied Research in Geometry', Illinois Tech Engineer 13, 13-14 and 38-46.
4. 'Independent Self-Dual Postulates in Projective Geometry', RepMC 8, 81-87.
5. 'Aristotelian Demonstration and Postulational Method' (with Y. R. Simon ), The Modern Schoolman , 25, 190-192.

1949

1. 'What Paths Have Length?', FM 36, 109-118.
2. 'Modern Geometry and the Theory of Relativity', in Albert Einstein: Philosopher-Scientist , The Library of Living Philosophers VII, edited by P. A. Schilpp, Evanston, Illinois, pp. 459-474.
3. 'Generalized Vector Spaces I. The Structure of Finite-Dimensional Spaces', Canadian J. of Math . 1, 94-104.
4. 'Self-Dual Fragments of the Ordinary Plane', AMM 56, 545-546. (crrected? from 1979-1 )
5. 'La G?om?trie Axiomatique de l'Espace Projectif', CRP 228, 1273-1274.

1950

1. 'The Projective Space', Duke Math. J. 17, 1-14.
2. 'The Mathematics of Elementary Thermodynamics', American J. of Physics 18, 89-103.

1951

1. 'Probabilistic Theories of Relations', PUSA 37, 178-180.
2. 'Ensembles Flous et Fonctions Al?atoires', CRP 232, 2001-2003.
3. 'Espaces Vectoriels G?n?raux, Topologies Triangulaires, Transformations Lin?aires G?n?ralis?es, CRP 232, 2176-2178.
4. 'Probabilistic Geometry', PUSA 37, 226-229.

1952

1. 'The Formative Years of Abraham Wald and His Work in Geometry', Annals of Math. Statistics 23, 14-20.
2. 'A Topological Characterization of the Length of Paths', PUSA 38, 66-69.
3. 'Une Th?orie Axiomatique G?n?rale des D?terminants', CRP 234, 1941-1943.
4. You Will Like Geometry. A Guide Book for the Ill. Inst. of Tech. Geometry Exhibition at the Museum of Science and Industry , Chicago, 36 pp.
5. Calculus. A Modern Approach (mimeographed), Chicago, xxv + 255 pp.

1953

1. 'On the Design of Grouping Problems and Related Intelligence Tests', J. of Educational Psychology 44, 275-287.
2. 'The Ideas of Variable and Function', PUSA 39, 956-961.
3. Calculus. A Modern Approach (mimeographed), 2nd enlarged edition, Chicago, xxiv+ 304 pp. (crrected? from 1979-1 )

1954

1. 'Variables de Diverses Natures', Bulletin Sciences Math . 78, 229-234.
2. 'Is Calculus a Perfect Tool?', J. of Engineering Education 45, 261-264.
3. 'The Logic of the Laws of Return. A Study in Meta-Economics', in Economic Activity Analysis , edited by O. Morgenstern, New York, pp. 419-481 (E. tr. of 1936-6 and 6a by O. Eckstein).
4. 'Tossing a Coin', AMM 61, 634-636.
5. G?om?trie G?n?rale , M?morial d. Sci. Math. 124, Paris, 81 pp.
6. 'On Variables in Mathematics and in Natural Science', British J. Philosophy of Science 5, 134-142.
7. 'A Simple Definition of Analytic Functions and General Multifunctions', PUSA 40, 819-821.
8. 'Remarks to L. Sommer's Translation of Bernoulli's "Exposition of a New Theory on the Measurement of Risk" ', Econometrica 22, pp. 28, 31-32 and 34.

1955

1. 'Random Variables from the Point of View of a General Theory of Variables', in Proceedings, Third Berkeley Symposium on Math. Statistics and Probability II, Berkeley & Los Angeles, pp. 215-229. (according to MathSciNet this appeared in 1956)
2. 'The Behavior of a Complex Function at Infinity', PUSA 41, 512-513.
3. 'Generalized Derivatives and Expansions' (with S. S. Sh? ), ibid ., pp. 591-595.
4. Calculus. A Modern Approach , Boston, xviii + 354 pp.

1956

1. 'On the Formulation of Certain Arithmetical Questions' (with H. J. Curtis ), The Mathematics Teacher 49, 528-530.
2. 'Calculus 1950 - Geometry 1880', Scripta Mathematica 22, 89-96 and 203-206.
3. 'What Are Variables and Constants?', Science 123, 547-548.
4. 'Why Johnny Hates Math', The Mathematics Teacher 49, 578-584.
5. 'What Are x and y ?', Math. Gazette 40, 246-255.

1957

1. The Basic Concepts of Mathematics. A Companion to Current Textbooks on Algebra and Analytical Geometry. Part I. Algebra , Chicago, vii + 95 pp. (corrected? from 1979-1 )
2. 'Multiderivatives and Multi-Integrals', AMM 64, 58-70; Supplement to L. R. Ford on His Seventieth Birthday (Sixth H. E. Slaught Memorial Paper).

1958

1. 'Optimal Differences in Computing Probable Derivatives', Journal de Math?matiques Pures et Appliqu?es 38, 245-252.
2. 'Rates of Change and Derivatives', FM 46, 89-102.
3. 'Is w a Function of u ?', Colloquium Mathematicum 6, 41-47.
4. 'New Approach to Teaching Intermediate Mathematics', Science 127, 1320-1323.

1959

1. 'An Axiomatic Theory of Functions and Fluents', in Symposium on the Axiomatic Method , edited by L. Henkin, P. Suppes and A. Tarski, Amsterdam, pp. 454-473.
2. 'Gulliver in the Land without One, Two, Three', Math. Gazette 43, 241-250.
3. 'On Probabilistic Metrics and Numerical Metrics with Probability 1' (with Berthold Schweizer and Abe Sklar ), Czechoslovak Math. J. 9, 459-466.
4. 'Mensuration and Other Mathematical Connections of Observable Material', in Measurement, Definitions and Theories , edited by C. W. Churchman and P. Ratoosh, New York, pp. 97-128.
5. 'Preface' to Friedrich Waismann, Introduction to Mathematical Thinking , New York, 1959 (reprint of E. tr. of 1936-8 )

1960

1. 'Gulliver's Return to the Land without One, Two, Three', AMM 67, 641-648.
2. 'Introduction' to Ernst Mach, The Science of Mechanics , 6th American edition, La Salle, Ill., pp. iii-xxi.
3. 'Gulliver in Applyland', Eureka , No. 23, 5-8.
4. 'A Counterpart of Occam's Razor in Pure and Applied Mathematics. Ontological Uses', Synthese 12, 415-428.

1961

1. 'A Counterpart of Occam's Razor in Pure and Applied Mathematics. Semantic Uses', Synthese 13, 331-349.
2. 'What Is Length?' (with Frank Henmueller ), Philosophy of Science 28, 172-177.
3. 'The Algebra of Functions: Past, Present, Future', Rendiconti di Matematica 20, 409-430.
4. 'Frammenti Piani Autoduali e Relative Sostituzioni', Rendiconti Acc. Naz. di Lincei 30, 713-717.
5. 'Variables, Constants, Fluents', in Current Issues in the Philosophy of Science , edited by H. Feigl and O. Maxwell, New York, pp. 304-313 and 316-318.
6. 'Eine Algebra der Funktionen', Nachr. ?sterr. Math. Ges . 15 No. 68/69, 99-100.

1962

1. 'A Group in the Substitutive Algebra of the Calculus of Propositions', Archiv. d. Math . 13, 471-478.
2. 'On Compositive Functions of Matrices', Annali di Matematica Pura e Applicata 58, 69-84.
3. 'Function Algebra and Propositional Calculus', in Self-Organizing Systems , edited by M. C. Yovits, G. T. Jacobi and G. D. Goldstein, Washington, D.C., pp. 525-532.

1963

1. 'A Self-Dual Theory of Real Determinants' (with F. Kozin ), Publ. Math. Debrecen 10, 123-127.
2. 'Postulates for the Substitutive Algebra of the 2-Place Functors in the 2-Valued Calculus of Propositions' (with Martin Schultz ), Notre Dame J. on Formal Logic 4, 188-192.
3. 'Calculus of Variations', in Harper Encylopedia of Science I, New York & Evanston, pp. 195-196.

1964

1. 'On Substitutive Algebra and Its Syntax', Zeitschr. f. math. Logik und Grundlagen d. Math . 10, 81-104. (corrected from 1979-1 )
2. 'Superassociative Systems and Logical Functions', MA 157, 278-295.

1965

1. 'A Characterization of Weierstrass Analytic Functions', PUSA 54, 1025-1026.
2. 'Analytische Funktionen', Wissensch. Abh. Forschungen d. Landes Nordrhein-Westfalen 33, 609-612. (according to MathSciNet this appeared in 1966)
3. 'Une Caract?risation des Fonctions Analytiques', CRP 261, 4968-4969.

1966

1. 'Weierstrass Analytic Functions', MA 167, 177-194.
2. 'Two Theorems on the Generation of Systems of Functions' (with H. Ian Whitlock ), FM 58, 229-240. (corrected? from 1979-1 )

1967

1. 'The Role of Uncertainty in Economics', in Essays in Mathematical Economics in Honor of O. Morgenstern , edited by M. Shubik, Princeton, pp. 211-231 (E. tr. of 1934-8 and 8a by W. Schoellenkopf and W. G. Mellon).

1968

1. 'General Algebraic Equations and Functional Equations', Equationes Mathematicae 1, 281.

1970

1. 'Introduction', 'Projective and Related Structures' (Part 2) and 'Curve Theory' (Part 4), in Studies in Geometry (with Leonard M. Blumenthal ), San Francisco, pp. iv-vii, 135-223 and 391-506.
2. 'Mathematical Implications of Mach's Ideas: Positivistic Geometry. The Clarification of Functional Connections', in Ernst Mach. Physicist and Philosopher , Boston Studies in the Philosophy of Science VI, edited by R. S. Cohen and R. J. Seeger, Dordrecht, pp. 107-125.

1971

1. 'The New Foundation of Hyperbolic Geometry', in A Spectrum of Mathematics , edited by J. C. Butcher, Auckland, pp. 86-97.
2. 'The Geometry Relevant to Modern Education', in Educational Studies in Mathematics IV, edited by H. Freudenthal, Dordrecht, pp. 1-17. Reprinted in The Teaching of Geometry at the Pre-College Level , edited by H. O. Steiner, Dordrecht, pp. 225-241.

1972

1. 'Bericht ?ber metrische Geometrie', in Geometrie , Wege der Forschung 177, edited by K. Strubecker, Darmstadt, pp. 371-395.
2. '?sterreichischer Marginalismus und mathematische ?konomie', Zeitschrift f. National?konomie 32, 19-28.

1973

1. 'Austrian Marginalism and Mathematical Economics', in Carl Menger and the Austrian School of Economics , edited by J. R. Hicks and W. Weber, Oxford, pp. 38-60 (Expanded E. tr. of 1972-2 by the author).

1974

1. Morality, Decision and Social Organization. Toward a Logic of Ethics , Vienna Circle Collection VI, pp. vi and 118 edited by Henk. L. Mulder, D. Reidel, Dordrecht Boston, 115 pp. (E. tr. with minor revisions of 1934-9 by the author based on work by E. van der Schalie, and a 1974 postscript pp. 93-115).

1979

1. Selected Papers in Logic and Foundations, Didactics, Economics , D. Reidel, Dordrecht Boston,  xii + 341 pp.

1980

1. 'Language and Mathematics' in Language, Logic, and Philosophy (Proc. Fourth Internat. Wittgenstein Sympos., Kirchberg am Wechsel, 1979) , Vienna, pp. 21-26.
2. 'Vorwort' ('Preface') to Hans Hahn, Empiricism, Logic, and Mathematics . Philosophical papers edited by Brian McGuinness (E. tr. by Hans Kaal). Vienna Circle Collection XIII, D. Reidel, Dordrecht Boston.

1981

1. 'On the Origin of the n -Arc Theorem', J. of Graph Theory 5, 341-350.

1983

1. 'On social groups and relations', Mathematical Social Sciences 6, 13-26.

1996

1. 'Vorwort' ('Preface') to Friedrich Waismann, Einf?hrung in das mathematische Denken. Die Begriffsbildung der modernen Mathematik , Wien, pp. iii-iv. (E. tr. Introduction to Mathematical Thinking by T. J. Benach, New York, 1951). Reprint of 2nd 1947 edition of 1936-8 .
2. 'The New Logic', Read. Philos. , Logical empiricism at its peak, 141-178, New York (reprint of 1937-6 ).