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Mathematical Intuitionism
Published online by Cambridge University Press: 22 October 2020
Summary
L. E. J. Brouwer, the founder of mathematical intuitionism, believed that mathematics and its objects must be humanly graspable. He initiated a program rebuilding modern mathematics according to that principle. This book introduces the reader to the mathematical core of intuitionism – from elementary number theory through to Brouwer's uniform continuity theorem – and to the two central topics of 'formalized intuitionism': formal intuitionistic logic, and formal systems for intuitionistic analysis. Building on that, the book proposes a systematic, philosophical foundation for intuitionism that weaves together doctrines about human grasp, mathematical objects and mathematical truth.
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- Online ISBN: 9781108674485Publisher: Cambridge University PressPrint publication: 12 November 2020
Bibliography
Aristotle, [1941] The Basic Works of Aristotle, McKeon, R (ed. and trans.), Random House, New York.Google Scholar
van Atten, M.[2007] Brouwer Meets Husserl: On the Phenomenology of Choice Sequences, Springer, Dordrecht.Google Scholar
van Atten, M.[2018] ‘The Creating Subject, the Brouwer-Kripke Schema, and Infinite Proofs’, Indag. Math, 29, pp. 1565–636.Google Scholar
Van Atten, M., Boldini, P., Bourdeau, M., Heinzmann, G., (eds.) [2008] One Hundred Years of Intuitionism (1907–2007), van Atten, M., et. al. (eds.), Birkhäuser.Google Scholar
van Atten, M., and van Dalen, D. [2002] ‘Arguments for the Continuity Principle’, Bull. Symb. Logic, 8, pp. 329–47.Google Scholar
van Atten, M., van Dalen, D., and Tieszen, R. [2002] ‘Brouwer and Weyl: The Phenomenology and Mathematics of the Intuitive Continuum’, Philosophia Mathematica, 10, 2, pp. 203–26.Google Scholar
Auxier, R., Anderson, D., and Hahn, L. [2015] The Philosophy of Hilary Putnam, Open Court, Chicago.Google Scholar
Becker, O. [1927] Mathematische Existenz. Untersuchungen zur Logik und Ontologie mathematischer Phänomene (Jahrbuch für Philosophie und phänomenologische Forschung), vol. 8, pp. 440–809.Google Scholar
Beeson, M. [1985] Foundations of Constructive Mathematics: Metamathematical Studies, Springer, Berlin.Google Scholar
Bernays, P. [1930] ‘Die Philosophie der Mathematik und die Hilbertsche Beweistheorie’, in Bernays [1976], pp. 17–61.Google Scholar
Bernays, P.[1976] Abhandlungen zur Philosophie der Mathematik, Wissenschaftliche Buchgesellschaft, Darmstadt.Google Scholar
Beth, E. [1947] ‘Semantical Considerations on Intuitionistic Mathematics’, Indag. Math., 9, 572–7.Google Scholar
Bezhanishvili, G., and Holliday, W. [2019] ‘A Semantic Hierarchy for Intuitionistic Logic’, Indag. Math., 30, pp. 403–69.Google Scholar
Boffa, M, van Dalen, D., and McAloon, M. (eds.) [1980] Logic Colloquium 78, North Holland, Amsterdam.Google Scholar
Bridges, D, and Richmond, F., [1987] Varieties of Constructive Mathematics, Cambridge University Press, Cambridge.Google Scholar
Brouwer, L. E. J. [1975] Collected Works, 6 (abbreviated as CW) (Heyting, A, ed.), Amsterdam, North Holland Publishing Company.Google Scholar
Brouwer, L. E. J.[1907] Over de grondslagen der wiskunde, Dissertation, 1907, University of Amsterdam. (Translated as On the Foundations of Mathematics CW pp. 11–101.)Google Scholar
Brouwer, L. E. J.[1908] ‘Die möglichen Mächtigkeiten’, Atti del IV Congresso Internazional dei Matematici, Romo, 6–11 Aprile 1908. Rome, Academia dei Lincei, 569–71. CW, pp. 102–4.Google Scholar
Brouwer, L. E. J.[1908A] ‘De onbetrouwbaarheid der logische principes’, Tijdschrift voor Wijsbegeerte, 2, 152–8. CW, pp. 107–11.Google Scholar
Brouwer, L. E. J.[1912] Intuitionisme en formalisme, Amsterdam, translated (by A. Dresden) as ‘Intuitionism and Formalism’, Bull. Amer. Math Soc. 20 (1913), pp. 81–96. CW, pp. 123–38.Google Scholar
Brouwer, L. E. J.[1919] ‘Intuitionistische Mengenlehre’, Jber. Deutsch. Math. Verein, 28, 203–8, Proceedings Acad. Amsterdam, 23, pp. 949–54.Google Scholar
Brouwer, L. E. J.[1923] ‘Intuitionistische Zerlegung mathematischer Grundbegriffe’, Jahresbericht der deutschen Mathematiker Vereinigung, 33: 251–6. CW, pp. 275–80.Google Scholar
Brouwer, L. E. J.[1925] ‘Zur Begründung der intuitionistischen Mathematik I’, Mathematische Annalen, 93, pp. 244–77.Google Scholar
Brouwer, L. E. J.[1927]‘Über Definitionsbereiche von Funktionen’, Mathematische Annalen, 97, 1927: 60–75. CW, pp. 390–405.Google Scholar
Brouwer, L. E. J.[1927A] ‘Virtuelle Ordnung und unerweiterbare Ordnung’, J. Reine Angew. Math., 157, 255–7. CW, pp. 406–8.Google Scholar
Brouwer, L. E. J.[1930] ‘Die Struktur des Kontinuums’, Lecture delivered in Vienna, 14 March 1928. CW, pp. 429–40.Google Scholar
Brouwer, L. E. J.[1933] ‘Willen, Weten, Spreken’, Euclides, 9, pp. 177–93. Translated as ‘Will, Knowledge and Speech’, in van Stigt [1990], pp. 418–31.Google Scholar
Brouwer, L. E. J.[1942] ‘Zum freien Werden von Mengen und Funktionen’, Proceedings of the Acad. Amsterdam, 45, pp. 322–3(= Indag. Math., 4, pp. 107–8). CW, pp. 459–60.Google Scholar
Brouwer, L. E. J.[1948] ‘Consciousness, Philosophy and Mathematics’, Proceedings of the Tenth International Congress of Philosophy, Amsterdam, 3, pp. 1235–49. CW, pp. 480–94.Google Scholar
Brouwer, L. E. J.[1948A] ‘Essenteel negatieve eigenschappen’, Proceedings of the Acad. Amsterdam, 51 1948, pp. 963–4 (= Indag. Math., 10, pp. 322–3). Translated as ‘Essentially negative properties’, in CW, pp. 478–9.Google Scholar
Brouwer, L. E. J.[1949] ‘De non-aequivalentie van de constructieve en de negatieve orderelatie in het continuum’, Proceedings of the Acad. Amsterdam, 52, pp. 122–4(= Indag. Math., 11, pp. 37–9). Translated as ‘The non-equivalence of the constructive and the negative order relation on the continuum’. CW, pp. 495–6.Google Scholar
Brouwer, L. E. J.[1950] ‘Discours Final de M. Brouwer’, Les Methodes Formelles en Axiomatique, Colloques Internationaux du Centre National de la Recherche Scientifique, Paris, page 75. CW, p. 503.Google Scholar
Brouwer, L. E. J.[1952] ‘Historical Background, Principles and Methods of Intuitionism’, South African Journal of Science, 49:139–46. CW, pp. 508–15.Google Scholar
Brouwer, L. E. J.[1954] ‘Points and Spaces’, Canadian J. for Math. 6, pp. 1–17. CW, 522–40.Google Scholar
Brouwer, L. E. J.[1955] ‘The Effect of Intuitionism on Classical Algebra of Logic’, Proc. Royal Irish Academy, Section A, 57, pp. 113–16. CW 551–4.Google Scholar
Brouwer, L. E. J.[1981] Brouwer’s Cambridge Lectures on Intuitionism (van Dalen, D, ed.), Cambridge University Press.Google Scholar
Chatzidakis, Z., Koepke, P., and Pohlers, W. (eds.), [2006] Logic Colloquium ‘02 (Lecture Notes in Logic 27), Wellesley, A. K. Peters.Google Scholar
van Dalen, D. [1986] ‘Intuitionistic Logic’, in Handbook of Philosophical Logic, vol. 3, Gabbay, D and Guenther, F (eds.), D. Reidel Publishing Company, pp. 225–340.Google Scholar
van Dalen, D.[1997] ‘How Connected Is the Intuitionistic Continuum’, Journal of Symbolic Logic, 62, 4, pp. 1147–50.Google Scholar
van Dalen, D.[1999] ‘From Brouwerian Counter Examples to the Creating Subject’, Studia Logica, 62, pp. 305–14.Google Scholar
van Dalen, D.[1999a] Mystic, Geometer and Intuitionist: The Life of L.E.J. Brouwer. Volume 1, Oxford University Press.Google Scholar
van Dalen, D.[2005] Mystic, Geometer and Intuitionist: The Life of L.E.J. Brouwer. Volume 2, Oxford University Press.Google Scholar
van Dalen, D., and Troelstra, A. S. [1970] ‘Projections of Lawless Sequences’, in Kino, Myhill and Veslely [1970], pp. 163–86.Google Scholar
Del Santo, F., and Gisin, N. [2019] ‘Physics without Determinism: Alternative Interpretations of Classical Physics’, Physical Review A, 100 (062107)Google Scholar
Diaconescu, R. [1975] ‘Axiom of Choice and Complementation’, Proc. Amer. Math. Soc., 51, 176–8.Google Scholar
Dragalin, A. G. [1988] ‘Mathematical Intuitionism: Introduction to Proof Theory’, Translations of Mathematical Monographs, 67, Providence, American Mathematical Society.Google Scholar
Dummett, M. [1973] ‘The Philosophical Basis of Intuitionistic Logic’, in Logic Colloquium ’73, Rose, H. E., and Shepherdson, J. C. (eds.), Amsterdam, North Holland Publishing Company pp. 5–40, reprinted in Dummett [1978], pp. 215–47.Google Scholar
Dummett, M.[1975] ‘The Justification of Deduction’, Proceedings of the British Academy, 59, London, reprinted in Dummett [1978], pp. 290–318.Google Scholar
Dummett, M.[2000] Elements of Intuitionism, 2nd ed., Oxford University Press. (First edition 1977).Google Scholar
Gabbay, D., and Woods, J., eds. [2007] Handbook of the History of Logic, v. 8, Amsterdam, North Holland.Google Scholar
Gisin, N. [2019] ‘Indeterminism in Physics, Classical Chaos and Bohmian Mechanics: Are Real Numbers Really Real?, Erkenntnis, DOI http://doi.org/10.1007/s10670-019–00165-8Google Scholar
Gisin, N.[2019A] ‘Real Numbers Are the Hidden Variables of Classical Mechanics’, Quantum Studies: Mathematics and Foundations, DOI http://doi.org/10.1007/s40509-019–00211-8Google Scholar
Glivenko, V. [1929] ‘Sur quelques points de la logique de M. Brouwer’, Bulletin, Académie Royale de Belgique, 15, pp. 183–8.Google Scholar
Gödel, K. [1933] ‘Eine Interpretation des intuitionistischen Aussagenkalküls’, Ergebnisse eines mathematischen Kolloquiums, 4, pp. 39–40.Google Scholar
Gödel, K.[1933A] ‘Zur intuitionistischen Arithmetik und Zahlentheorie’, Ergebnisse eines mathematischen Kolloquiums, 4, 1933, pp. 34–8.Google Scholar
Gödel, K.[1958] ‘Über eine bisher noch nicht benutzte Erweiterung des finite Standpunktes’, Dialectica, 12, pp. 280–7.Google Scholar
Goodman, N., and Myhill, J. [1978] ‘Choice implies excluded middle’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 24, p. 461.Google Scholar
Griss, G. F. C. [1944] ‘Negatieloze intuitionistische wiskunde’, Verslagen. Akad. Amsterdam, 53, pp. 261–8.Google Scholar
Griss, G. F. C.[1946] ‘Negationless Intuitionistic Mathematics, I’, Proceedings of the Acad. Amsterdam, 49, pp. 1127–33 (= Indag. math., 8, pp. 675–81).Google Scholar
Griss, G. F. C.[1949] ‘Logique des mathématiques intuitionnistes sans negation’, Comptes Rendus Acad. Sci. Paris, 227, pp. 946–7.Google Scholar
Griss, G. F. C.[1950] ‘Negationless Intuitionistic Mathematics, II,’ Proceedings of the Acad. Amsterdam, 53, pp. 456–63 (= Indag. math., 12, pp. 108–15).Google Scholar
van Heijenoort, J. (ed.) [1967] From Frege to Gödel: A Source Book in Mathematical Logic, 1897–1931, Cambridge, MA, Harvard University Press.Google Scholar
Hesseling, D. E. [2003] Gnomes in the Fog: The Reception of Brouwer’s Intuitionism in the 1920’s, Basel, Birkhäuser Verlag.Google Scholar
Heyting, A. [1925] Intuitionistische Axiomatiek der Projectieve Meetkunde, Groningen, Noordhoff.Google Scholar
Heyting, A.[1930] ‘Die formalen Regeln der intuitionistischen Logik,’ Sitzungsberichte der preuszischen Akademie von Wissenschaften, phys. math. Kl., pp. 42–56.Google Scholar
Heyting, A.[1930A] ‘Die formalen Regeln der intuitionistischen Mathematik,’ Sitzungsberichte der preuszischen Akademie von Wissenschaften, phys. math. Kl., pp. 57–71, 158–169.Google Scholar
Heyting, A.[1966] Intuitionism: An Introduction, 2nd rev. ed., Amsterdam, North Holland Publishing Company. (First edition 1956, Third Edition 1971).Google Scholar
Heyting, A.[1969] Review of J. L. Destouches, ‘Sur la Mecanique Classique et l’Intuitionisme’, J. Symb. Logic, 34, p. 307.Google Scholar
Hilbert, D. [1923] ‘Die logischen Grundlagen der Mathematik,’ Mathematische Annalen, 88, 151–65.Google Scholar
Hilbert, D.[1926] ‘Über das Unendliche’, Mathematische Annalen 95, 161–90. Translated in van Heijenoort, (ed.) [1967], pp. 369–92.CrossRefGoogle Scholar
Hilbert, D., and Ackermann, W. [1928] Grundzüge der theoretischen Logik, 1st ed., Berlin, Springer.Google Scholar
van der Hoeven, G. F. [1981] Projections of Lawless Sequences, Ph.D. Thesis, Amsterdam, University of Amsterdam.Google Scholar
Husserl, E. [1913] ‘Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie’ in Jahrbuch für Philosophie und phänomenologischen Forschung, 1. Translated by W. Boyce-Gibson as Ideas: General Introduction to Pure Phenomenology, New York, Macmillan, 1931.Google Scholar
Husserl, E.[1948] Erfarhung und Urteil: Untersuchungen zur Genealogie der Logik, Langrebe, L (ed.), Hamburg, Classen & Goverts. Translated by J. Churchil and K. Ameriks as Experience and Judgment, Northwestern University Press, Evanston, 1973.Google Scholar
van Inwagen, P. [2012] ‘What Is an Ontological Category,’ in Novak, Novotny, Prokop, and Svoboda [2012], pp. 11–24.CrossRefGoogle Scholar
Kant, I. [1929] Immanuel Kant’s Critique of Pure Reason, N. K. Smith (trans.) London, Macmillan.Google Scholar
Kino, A., Myhill, J., and Vesley, R. E. (eds.), [1970] Intuitionism and Proof Theory, North Holland.Google Scholar
Kleene, S. C. [1945] ‘On the Interpretation of Intuitionistic Number Theory’, J. Symb. Logic, 10, pp. 109–24.Google Scholar
Kleene, S. C.[1973] ‘Realizability: A Retrospective Survey’, in Mathias and Rogers [1973].Google Scholar
Kleene, S. C., and Vesley, R. [1965] Foundations of Intuitionistic Mathematics, Amsterdam, North Holland.Google Scholar
Kolmogorov, A. N. [1932] ‘Zur Deutung der intuitionistischen Logik’, Mathematische Zeitschrift, 35, 58–65.Google Scholar
Kreisel, G. [1958] ‘A Remark on Free Choice Sequences and the Topological Interpretation’, Journal of Symbolic Logic, 23, 369–88.Google Scholar
Kreisel, G.[1967] ‘Informal Rigour and Completeness Proofs’, in Lakatos [1967], pp. 138–86.Google Scholar
Kreisel, G.[1968] ‘Lawless Sequences of Natural Numbers’, Compositio Mathematica, 20, 222–48.Google Scholar
Kreisel, G., and Troelstra, A. S. [1970] ‘Formal Systems for Some Branches of Intuitionistic Analysis’, Annals of Mathematical Logic, 1, 229–387.Google Scholar
Kretzman, N. (ed.) [1982] Infinity and Continuity in Ancient and Medieval Thought, Ithaca, Cornell University Press.Google Scholar
Kripke, S. A. [1965] ‘Semantical Analysis of Intuitionistic Logic, I,’ in Crossley, J and Dummett, M (eds.), Formal Systems and Recursive Functions: Proceedings of the Eighth Logic Colloquium, Oxford, July 1963, North Holland, pp. 92–130.Google Scholar
Kripke, S. A.[2019] ‘ Free Choice Sequences: A Temporal Interpretation Compatible with Acceptance of Classical Mathematics’, Indag. Math., 30, pp. 492–9.CrossRefGoogle Scholar
Kushner, B. [1985] Lectures on Constructive Mathematical Analysis, Providence, AMS Publications.Google Scholar
Lakatos, I. (ed.), [1967] Problems in the Philosophy of Mathematics, Amsterdam, North Holland.Google Scholar
Lévy, P. [1927] ‘Logique classique, Logique brouwerienne et Logique mixte’, Académie Royale de Belgique, Bulletins de la Classe des Sciences, 5–13, pp. 256–66.Google Scholar
Lopez-Escobar, E. G. K. [1981] ‘Equivalence between Semantics for Intuitionism, I’, Journal of Symbolic Logic, 46, pp. 773–80.Google Scholar
Martino, E. [2018] Intuitionistic Proof Versus Classical Truth: The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics, Berlin, Spinger.Google Scholar
Mathias, A., and Rogers, H. (eds.) [1973] Cambridge Summer School in Mathematical Logic, August 1–21, 1971, Berlin, Springer.CrossRefGoogle Scholar
McCarty, D. C. [1984] Realizability and Recursive Mathematics, Department of Computer Science, Report CMU-CS-84–131, Pittsburgh, Carnegie Mellon University.Google Scholar
McKinsey, J., and Tarski, A. [1948] ‘Some Theorems about the Sentential Calculi of Lewis and Heyting’, J. Symb. Logic, 13, pp. 1–15.Google Scholar
Miller, F. D. ‘Aristotle Against the Atomists’, in Kretzman, N. (ed.) [1982] pp. 37–86.Google Scholar
Myhill, J. [1967] ‘Notes Towards an Axiomatization of Intuitionistic Analysis,’ Logique et Analyse, 9, pp. 280–97.Google Scholar
Myhill, J.[1970] ‘Formal Systems of Intuitionistic Analysis, II’, in Kino, Myhill and Vesley [1970], pp. 151–62.Google Scholar
Myhill, J.[1973] ‘Some Properties of Intuitionistic Zermelo-Fraenkel Set Theory’, in Mathias and Rogers [1973], pp. 206–31.Google Scholar
Novak, L., Novotny, D., Prokop, S., and Svoboda, D. (eds.), [2012] Metaphysics: Aristotelian, Scholastic, Analytic, Frankfurt, Ontos Verlag (in cooperation with Studia Neoaristotelica).Google Scholar
Parsons, C. [2014] ‘The Kantian Legacy in Twentieth-Century Foundations of Mathematics’, in Parsons [2014A], pp. 11–39.Google Scholar
Parsons, C.[2014A] Philosophy of Mathematics in the Twentieth Century: Selected Essays, Cambridge, Harvard University Press.Google Scholar
Posy, C. J. [1976] ‘Varieties of Indeterminacy in the Theory of General Choice Sequences’, Journal of Philosophical Logic, 5, pp. 91–132.Google Scholar
Posy, C. J.[1977] ‘The Theory of Empirical Sequences,’ Journal of Philosophical Logic, 6, pp. 47–81.Google Scholar
Posy, C. J.[1980] ‘On Brouwer’s Definition of Unextendable Order’, History and Philosophy of Logic, 1, pp. 129–49.Google Scholar
Posy, C. J.[1982] ‘A Free IPC is a Natural Logic: Strong Completeness for Some Intuitionistic Free Logics’ (Topoi, v. 1 (1982), pp. 30–43; reprinted in J. K. Lambert (ed.), Philosophical Applications of Free Logic, Oxford University Press, 1991).Google Scholar
Posy, C. J.[1991] ‘Mathematics as a Transcendental Science’, in T. M. Seebohm, D. Follesdal, and J. N. Mohanty (eds.), [1991].Google Scholar
Posy, C. J.[2000] ‘Epistemology, Ontology and the Continuum’, in Grosholz and Breger, pp. 199–219.Google Scholar
Posy, C. J.[2008] “Brouwerian Infinity”, in van Atten, et. al. (eds.) [2008] pp. 21–36.Google Scholar
Posy, C. J.[2015] ‘Realism, Reference and Reason: Remarks on Putnam and Kant’, Auxier et al. [2015], pp. 565–98.Google Scholar
Posy, C. J.[Forthcoming] ‘Kant and Brouwer: Two Knights of the Finite’, in Posy and Rechter, [Forthcoming].Google Scholar
Posy, C., and Rechter, O. (eds.), [Forthcoming] Kant’s Philosophy of Mathematics: Vol. 2, Reception and Influence, Cambridge University Press.Google Scholar
Rasiowa, H., and Sikorski, R. [1963] The Mathematics of Metamathematics, Warsaw, Panstwowe Wydawnictowo Naukow.Google Scholar
Rathjen, M. [2006] ‘Choice Principles in Constructive and Classical Set Theories’, in Chatzidakis et al., [2006] pp. 299–326.Google Scholar
Rogers, H., [1967] Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York.Google Scholar
Seebohm, Th., Follesdal, D., and Mohanty, J. N. (eds.), [1991] Phenomenology and the Formal Sciences, the Center for Advanced Research in Phenomenology, and Kluwer Academic Publishers.Google Scholar
Shapiro, S. (ed.), [2005] The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press.Google Scholar
Specker, E. [1949] ‘Nicht konstrukiv bewiebare Sätze der Analysis’, Journal of Symbolic Logic, 14, 145–58.Google Scholar
Spector, C. [1962] ‘Provably Recursive Functionals of Analysis; a Consistency Proof of Analysis by an Extension of Principles Formulated in Current Intuitionistic Mathematics’, in Recursive Function Theory, Proc., Pure Mathematics, pp. 1–27.Google Scholar
de Swart, H. C. M. [1976] ‘Another Intuitionistic Completeness Proof,’ Journal of Symbolic Logic, 41, 1976, pp. 644–62.Google Scholar
Tennant, N.[2020] ‘Does Choice Really Imply Excluded Middle? Part I: Regimentation of the Goodman – Myhill Result, and Its Immediate Reception,’ Philosophia Mathematica, 28, pp. 139–171.Google Scholar
Tennant, N.[Forthcoming] ‘Does Choice Really Imply Excluded Middle? Part II: Historical, Philosophical, and Foundational Reflections on the Goodman – Myhill Result,’ Philosophia Mathematica, forthcoming.Google Scholar
Troelstra, A. S. [1969] Principles of Intuitionism, Lecture Notes in Mathematics, 95, Berlin, Springer.Google Scholar
Troelstra, A. S.[1977] Choice Sequences: A Chapter of Intuitionistic Mathematics, Oxford University Press.Google Scholar
Veldman, W. [1976] ‘An Intuitionistic Completeness Theorem for Intuitionistic Predicate Logic,’ Journal of Symbolic Logic 41.Google Scholar
Voorbraak, F. P. J. M. [1987] ‘Tensed Intuitionistic Logic’, Logic Group Preprint Series, No. 17, Philosophy Department, Utrecht, University of Utrecht.Google Scholar
Wavre, R., [1926] “Logique formelle et logique empiriste,” Revue de Métaphysique et de Morale, 33, pp. 65–75.Google Scholar
Weyl, H. [1917] Das Kontinuum, Kritische Untersuchungen über die Grundlagen der Analysis, Berlin, Teubner.Google Scholar
Weyl, H.[1921] ‘Über die neue Grundlagenkrise der Mathematik’, Mathematische Zeitschrift, 10, 39–79.Google Scholar
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