Brahman: Absolute Consciousness in Advait (Non Dual) Vedanta Philosophy
Key Terms
Brahman
Maya
Witness Consciousness
Non-dual (Advait) Vedanta Philosophy
Philosophy
Vedic Philosophy
Subject Object
Subject Subject
Subject Meta-Subject
Absolute Consciousness
Phenomenal Consciousness
Turiya
Awareness
Adi Shankara
Sakshi
Akash and Prakash
Mayavad
Truth, Value and Freedom
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Bhattacharyya’s most remarkable idea is his notion of the Absolute as alternation. Instead of the Hegelian absolutization of the Absolute, he chose the dialectics of alternation both at transcendental and empirical levels of reality. The triple functions of consciousness in relation to its contents are: knowing, feeling, and willing. Each of them has its own formulation of the Absolute, namely truth, value, and freedom respectively. When cognition is given importance, the Absolute is viewed as truth; when emotion (devotion) is given importance, it is viewed as value; and when volition is given importance, it is viewed as freedom. These conceptions of the Absolute cannot be unified into one, because each is Absolute in turn.7 For Bhattacharyya, this alternation is not just our symbolic speakingabout the one Absolute in three distinct ways, but the very constitution (dynamics) of the Absolute.8
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
The idealist view of life and reality, which Radhakrishnan calls religion of the spirit, perceives the universe as ultimately spiritual. Brahman (Atman/ the Spirit) being the ultimate truth and the universe its self-manifestation, the spirit is our deepest self.
Radhakrishnan wanted all historical religions to transform themselves into the religion of the spirit, a spiritual vision that transforms the world and ensures human unity, universal moral order, and world peace.
Radhakrishnan tried to work out a positive account of the world by interfacing three concepts – Brahman (the Absolute), Ishvara (God), and the world. Brahman considered in its self-identity as pure consciousness is beyond all distinctions, qualifications, and descriptions. This one, absolute being, however, manifests itself as the world. The world is just one possibility of Brahman’s self-manifestation; other possibilities we may not know.
Brahman in its relation to the world is Ishvara (God). Ishvara is Brahman’s creative aspect, conceived as creator, redeemer, and judge. Immanent in the world, Ishvara guides and transforms it. Ishvara lasts as long as the world-process lasts. Although the transformation of the world is God’s action, it is essentially linked with human transformation. Despite limitations, human evolution and progress is teleological and moves toward a greater good.10 Human calling is to co-operate with the divine plan for the world’s transformation.
Typical of an Advaitin, Radhakrishnan held that our deepest self (atman) is identical to the transcendental Self (Atman) and is above transmigration. What is subject to transmigration is jiva, the empirical self. The world-process lasts until all jivas are liberated.11 When all jivas are liberated, the world will be transformed into Brahma-loka (the kingdom of God). The world and all jivas become one with God and God will be all in all. And finally the Brahma-loka, along with Ishvara, will lapse into Brahman. Thus Brahman remains the beginning and the end of the world. If and when another world-process begins is left to the freedom of Brahman.
“Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Source: “Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
Source: Advaita and the philosophy of consciousness without an object
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Key Sources of Research
“Mind/Consciousness Dualism in Sā̇ṅkhya-Yoga Philosophy.”
“Contemporary Interpretations of Shankara’s Advaita and the Affirmation of the World.”
Kaipayil, Joseph.
In Reason: Faithful and True (Essays in Honour of George Karuvelil), edited by Thomas Karimundackal and Dolichan Kollareth, 293-302. Pune: Jnana-Deepa Vidyapeeth, 2020.
1Department of Psychological and Brain Sciences, Boston University, Boston, MA 02215, USA;
2Laboratory for Information Design and Systems, Massachusetts Institute of Technology, Cambridge, MA 02139, USA †Vaibhav Tripathi, http://orcid.org/0000-0001-7520-4188 *Correspondence address. Department of Psychological and Brain Sciences, 64, Cummington Mall, Rm 149, Boston University, Boston, MA 02215, USA. Tel: +1 857-253-8491; E-mail: vaibhavt@bu.edu
Subjects: Asian Religion And Philosophy Series: SUNY series in Religious Studies Paperback : 9780791412824, 285 pages, December 1992 Hardcover : 9780791412817, 285 pages, January 1993
In: Intellectica. Revue de l’Association pour la Recherche Cognitive, n°51, 2009/1. Le continu mathématique. Nouvelles conceptions, nouveaux enjeux. pp. 169-189;
Oxford: Clarendon Press. The standard biography of Brouwer. Volume 1, The Dawning Revolution, covers the years 1881–1928, volume 2, Hope and Disillusion, covers 1929–1966.
The Return of the Flowing Continuum
Dirk van Dalen
Intellectica, 2009/1, 51, pp.
From philosophical traditions to scientific developments: reconsidering the response to Brouwer’s intuitionism.
In: The History of Continua: Philosophical and Mathematical Perspectives. Edited by: Stewart Shapiro and Geoffrey Hellman, Oxford University Press (2021).
DOI: 10.1093/oso/9780198809647.003.0013
HERMANN WEYL ON INTUITION AND THE CONTINUUM*
John L. Bell
REFERENCES
[1]
Brouwer, L. E. J., Intuitionisme en Formalisme, Noordhoff, Groningen, 1912, 32 pp.Google Scholar
[2]
Brouwer, L. E. J., Intuitionism and formalism, Bulletin of the American Mathematical Society, vol. 20 (1914), pp. 81–96.CrossRefGoogle Scholar
[3]
Brouwer, L. E. J., Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten. Erster Teil. Allgemeine Mengenlehre, Koninklijke Nederlandse Akademie van Wetenschappen–Verhandelingen, vol. 12 (1918), no. 5, 43pp.Google Scholar
/4]
Brouwer, L. E. J., Über Definitionsbereiche von Funktionen, Mathematische Annalen, vol. 97 (1927), pp. 60–75, Also in [17], pp. 446–463.CrossRefGoogle Scholar
[5]
Feferman, S., Weyl vindicated: “Das Kontinuum” 70 years later, Termi e prospettive della logica e della filosofia della scienza contemporanee, vol. I, CLUEB, Bologna, 1988.Google Scholar
[6]
Frey, G. and Stammbach, U., Hermann Weyl und die Mathematik an der ETH Zürich. 1913–1930, Birkhäuser, 1992.Google Scholar
Hilbert, D., Die Grundlagen der Mathematik II, Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität, vol. 6 (1928), pp. 65–85.CrossRefGoogle Scholar
[9]
Hilbert, D. and Bernays, P., Die Grundlagen der Mathematik, I, Springer, Berlin, 1934.Google Scholar
[10]
Kleene, S. C., Realizability: a retrospective survey, Cambridge summer school in mathematical logic, Springer Lecture Notes in Mathematics, no. 337, Springer-Verlag, Berlin, 1973, pp. 95–112.CrossRefGoogle Scholar
[11]
Kolmogorov, , Zur Deutung der intuitionistischen Logik, Mathematische Zeitschrift, vol. 35 (1932), pp. 58–65.CrossRefGoogle Scholar
[12]
Kreisel, G., A remark on free choice sequences and the topological completeness proofs, Journal of Symbolic Logic, vol. 23 (1958), pp. 369–388.CrossRefGoogle Scholar
[13]
Lorenzen, P., Einführung in die operative Logik und Mathematik, Springer, 1955.CrossRefGoogle Scholar
[14]
Troelstra, A. S. and Van Dalen, D., Constructivism in Mathematics, vol. I, II, North-Holland, Amsterdam, 1988.Google Scholar
[15]
Van Dalen, D. and Troelstra, A. S., Projections of lawless sequences, Intuitionism and Proof Theory (Myhill, J., Kino, A., and Vesley, R., editors), North-Holland, Amsterdam, 1970, pp. 163–186.Google Scholar
[16]
Hoeven, G. van der, Projections of lawless sequences, (diss.) Mathematical Centre Tracts, Amsterdam, 1982.Google Scholar
[17]
Heijenoort, J. van, From Frege to Gödel. a source book in mathematical logic, 1879–1931, Harvard University Press, Cambridge, Mass., 1967, 660 pp.Google Scholar
[18]
Weyl, H., Das Kontinuum. Kritische Untersuchungen über die Grundlagen der Analysis, Veit, Leipzig, 1918.Google Scholar
[19]
Weyl, H., Über die neue Grundlagenkrise der Mathematik, Mathematische Zeitschrift, vol. 10 (1921), pp. 39–79.CrossRefGoogle Scholar
[20]
Weyl, H., Randbemerkungen zu Hauptproblemen der Mathematik, Mathematische Zeitschrift, vol. 20 (1924), pp. 131–150.CrossRefGoogle Scholar
[21]
Weyl, H., Die heutige Erkenntnislage in der Mathematik, Symposion, vol. 1 (1925), pp. 1–32.Google Scholar
[22]
Weyl, H., Diskussionsbemerkungen zu dem zweiten Hilbertschen Vortrag über die Grundlagen der Mathematik, Abhandlungen aus dem mathematischen Seminar der Hamburgischen Universität, vol. 6 (1928), pp. 86–88, Also in [17], pp. 480–484.CrossRefGoogle Scholar
[23]
Weyl, H., Mathematics and Logic. A brief survey serving as a preface to a review of “The Philosophy of Bertrand Russell”, American Mathematical Monthly, vol. 53(1946), pp. 2–13.CrossRefGoogle Scholar
[24]
Weyl, H., Selecta Hermann Weyl, Birkhäuser, Basel, 1956.Google Scholar
Bibliography
Aristotle, [1941] The Basic Works of Aristotle, McKeon, R (ed. and trans.), Random House, New York.Google Scholar
van Atten, M., [2002] On Brouwer, Thomson, Wadsworth, London.Google Scholar
van Atten, M.[2007] Brouwer Meets Husserl: On the Phenomenology of Choice Sequences, Springer, Dordrecht.CrossRefGoogle Scholar
van Atten, M.[2018] ‘The Creating Subject, the Brouwer-Kripke Schema, and Infinite Proofs’, Indag. Math, 29, pp. 1565–636.CrossRefGoogle 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.CrossRefGoogle Scholar
van Atten, M., and van Dalen, D. [2002] ‘Arguments for the Continuity Principle’, Bull. Symb. Logic, 8, pp. 329–47.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Bell, J., [1988] Toposes and Local Set Theories, Oxford University Press, Oxford.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.CrossRefGoogle Scholar
Bishop, E. [1967] Foundations of Constructive Analysis, McGraw Hill.Google Scholar
Boffa, M, van Dalen, D., and McAloon, M. (eds.) [1980] Logic Colloquium 78, North Holland, Amsterdam.Google Scholar
Borel, E. [1898] Leçons sur la Theorie des Fonctions, Paris, Gauthier-Villars.Google Scholar
Bridges, D, and Richmond, F., [1987] Varieties of Constructive Mathematics, Cambridge University Press, Cambridge.CrossRefGoogle 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.CrossRefGoogle Scholar
Brouwer, L. E. J.[1927]‘Über Definitionsbereiche von Funktionen’, Mathematische Annalen, 97, 1927: 60–75. CW, pp. 390–405.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Del Santo, F., and Gisin, N. [2019] ‘Physics without Determinism: Alternative Interpretations of Classical Physics’, Physical Review A, 100 (062107)CrossRefGoogle Scholar
Dewey, J. [1938] Logic: The Theory of Inquiry, New York, Holt.Google Scholar
Diaconescu, R. [1975] ‘Axiom of Choice and Complementation’, Proc. Amer. Math. Soc., 51, 176–8.CrossRefGoogle Scholar
Dragalin, A. G. [1988] ‘Mathematical Intuitionism: Introduction to Proof Theory’, Translations of Mathematical Monographs, 67, Providence, American Mathematical Society.CrossRefGoogle 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.[1978] Truth and Other Enigmas, Harvard University Press.Google Scholar
Dummett, M.[1978A] ‘Realism’ in [1978], pp. 145–65.Google Scholar
Dummett, M.[1991] The Logical Basis of Metaphysics, Harvard University Press.Google Scholar
Dummett, M.[1993] The Seas of Language, Oxford University Press.Google Scholar
Dummett, M.[2000] Elements of Intuitionism, 2nd ed., Oxford University Press. (First edition 1977).Google Scholar
Fraenkel, A. [1923] Einleitung in die Mengenlehere, 2nd ed., Berlin, Springer.CrossRefGoogle Scholar
Gabbay, D., and Woods, J., eds. [2007] Handbook of the History of Logic, v. 8, Amsterdam, North Holland.CrossRefGoogle 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.CrossRefGoogle Scholar
Goodman, N., and Myhill, J. [1978] ‘Choice implies excluded middle’, Zeitschrift für mathematische Logik und Grundlagen der Mathematik, 24, p. 461.CrossRefGoogle 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.CrossRefGoogle 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.[1967] Remarks on Kreisel [1967] in Lakatos [1967].Google Scholar
Heyting, A.[1969] Review of J. L. Destouches, ‘Sur la Mecanique Classique et l’Intuitionisme’, J. Symb. Logic, 34, p. 307.CrossRefGoogle 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.Google 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.CrossRefGoogle Scholar
Kleene, S. C.[1952] Introduction to Metamathematics,Princeton, van Nostrand.Google Scholar
Kleene, S. C.[1973] ‘Realizability: A Retrospective Survey’, in Mathias and Rogers [1973].CrossRefGoogle 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.CrossRefGoogle Scholar
Kreisel, G. [1958] ‘A Remark on Free Choice Sequences and the Topological Interpretation’, Journal of Symbolic Logic, 23, 369–88.CrossRefGoogle Scholar
Kreisel, G.[1967] ‘Informal Rigour and Completeness Proofs’, in Lakatos [1967], pp. 138–86.CrossRefGoogle Scholar
Kreisel, G., and Troelstra, A. S. [1970] ‘Formal Systems for Some Branches of Intuitionistic Analysis’, Annals of Mathematical Logic, 1, 229–387.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Martin-Löf, P. [1984] Intuitionistic type theory, Naples, Bibliopolis.Google Scholar
Martino, E. [2018] Intuitionistic Proof Versus Classical Truth: The Role of Brouwer’s Creative Subject in Intuitionistic Mathematics, Berlin, Spinger.CrossRefGoogle 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
McCarty, D. C.[2005] ‘Intuitionism in Mathematics’, in Shapiro [2005], pp. 356–86.CrossRefGoogle Scholar
McKinsey, J., and Tarski, A. [1948] ‘Some Theorems about the Sentential Calculi of Lewis and Heyting’, J. Symb. Logic, 13, pp. 1–15.CrossRefGoogle 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.CrossRefGoogle Scholar
Myhill, J.[1973] ‘Some Properties of Intuitionistic Zermelo-Fraenkel Set Theory’, in Mathias and Rogers [1973], pp. 206–31.CrossRefGoogle Scholar
Novak, L., Novotny, D., Prokop, S., and Svoboda, D. (eds.), [2012] Metaphysics: Aristotelian, Scholastic, Analytic, Frankfurt, Ontos Verlag (in cooperation with Studia Neoaristotelica).CrossRefGoogle Scholar
Parsons, C. [2014] ‘The Kantian Legacy in Twentieth-Century Foundations of Mathematics’, in Parsons [2014A], pp. 11–39.CrossRefGoogle Scholar
Parsons, C.[2014A] Philosophy of Mathematics in the Twentieth Century: Selected Essays, Cambridge, Harvard University Press.CrossRefGoogle Scholar
Placek, T. [1999] Mathematical Intuitionism and Intersubjectivity, Kluwer.CrossRefGoogle Scholar
Posy, C. J. [1976] ‘Varieties of Indeterminacy in the Theory of General Choice Sequences’, Journal of Philosophical Logic, 5, pp. 91–132.CrossRefGoogle Scholar
Posy, C. J.[1977] ‘The Theory of Empirical Sequences,’ Journal of Philosophical Logic, 6, pp. 47–81.CrossRefGoogle Scholar
Posy, C. J.[1980] ‘On Brouwer’s Definition of Unextendable Order’, History and Philosophy of Logic, 1, pp. 129–49.CrossRefGoogle 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.CrossRefGoogle Scholar
Posy, C. J.[2005] ‘Intuitionism and Philosophy’, in Shapiro [2005], pp. 318–55CrossRefGoogle Scholar
Posy, C. J.[2007] ‘Free Logics’, in Gabbay and Woods [2007], pp. 633–80.CrossRefGoogle Scholar
Posy, C. J.[2008] “Brouwerian Infinity”, in van Atten, et. al. (eds.) [2008] pp. 21–36.CrossRefGoogle 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
Prawitz, D. [1965] Natural Deduction, Stockholm, Almqvist and Wiksell.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.CrossRefGoogle 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.CrossRefGoogle Scholar
Shapiro, S. (ed.), [2005] The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press.CrossRefGoogle Scholar
Specker, E. [1949] ‘Nicht konstrukiv bewiebare Sätze der Analysis’, Journal of Symbolic Logic, 14, 145–58.CrossRefGoogle 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.CrossRefGoogle Scholar
van Stigt, W. [1990] Brouwer’s Intuitionism, Amsterdam, North Holland.Google Scholar
de Swart, H. C. M. [1976] ‘Another Intuitionistic Completeness Proof,’ Journal of Symbolic Logic, 41, 1976, pp. 644–62.CrossRefGoogle Scholar
Takeuti, G. [1987] Proof Theory, 2nd ed., Amsterdam, North Holland.Google Scholar
Tennant, N. [1997] The Taming of the True, Oxford University Press.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.CrossRefGoogle 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.CrossRefGoogle Scholar
Troelstra, A. S.[1977] Choice Sequences: A Chapter of Intuitionistic Mathematics, Oxford University Press.Google Scholar
Troelstra, A. S.[1983] ‘Analyzing Choice Sequences’, J. Phil. Logic, 12, 197–260.CrossRefGoogle 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.CrossRefGoogle Scholar