Abstract
In 1928 Edmund Husserl wrote that “The ideal of the future is essentially that of phenomenologically based (“philosophical”) sciences, in unitary relation to an absolute theory of monads” (“Phenomenology”, Encyclopedia Britannica draft) There are references to phenomenological monadology in various writings of Husserl. Kurt Gödel began to study Husserl’s work in 1959. On the basis of his later discussions with Gödel, Hao Wang tells us that “Gödel’s own main aim in philosophy was to develop metaphysics—specifically, something like the monadology of Leibniz transformed into exact theory—with the help of phenomenology.” (A Logical Journey: From Gödel to Philosophy, p. 166) In the Cartesian Meditations and other works Husserl identifies ‘monads’ (in his sense) with ‘transcendental egos in their full concreteness’. In this paper I explore some prospects for a Gödelian monadology that result from this identification, with reference to texts of Gödel and to aspects of Leibniz’s original monadology.
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Notes
Mahnke's work predates Gödel's technical and philosophical work. Although his writings are certainly of interest, he does not consider what a new Gödelian monadology would look like.
All of the ‘fundamental beliefs' mentioned at the end of this passage—realism about the conceptual world, the analogy of concepts and mathematical objects to physical objects, the possibility and importance of categorial intuition or immediate conceptual knowledge, and the one-sidedness of what Husserl calls "the naive or natural standpoint—were the subject of discussions I had with Wang in the nineteen eighties about Gödel and Husserl. Many of my comments below are shaped by the exchanges I had with Wang.
In the Logical Investigations and other works from this period Husserl speaks of 'categorial intuition' in connection with the objects of logic and mathematics but in later works he speaks mostly of 'eidetic intuition', i.e., intuition of essences. Both can be viewed as types of rational intuition, with eidetic intuition focused on essences in particular. I do not have space to go into the differences here but I am interested in both as species of rational intuition.
Shinji Ikeda suggested such a view in conversation.
In various writings going back to the nineteen thirties, Gödel in fact distinguishes the purely formal and relative concept of proof from the 'abstract' concept of proof as "that which provides evidence". See, e.g., Gödel (193?, p. 164, *1951, p. 318, footnote 27, *1953/1959, p. 341, footnote 20, and 1972b, p. 273, footnote).
References
Feferman S et al (eds) (1986) Kurt Gödel: collected works, vol 1. Oxford University Press, Oxford
Feferman S et al (eds) (1990) Kurt Gödel: collected works, vol II. Oxford University Press, Oxford
Feferman S et al (eds) (1995) Kurt Gödel: collected works, vol III. Oxford University Press, Oxford
Gödel K (*193?) Undecidable diophantine propositions. In: Feferman et al. (eds) 1995, pp 164–175
Gödel K (*1951) Some basic theorems on the foundations of mathematics and their implications. In: Feferman et al. (eds) 1995, pp 304–323
Gödel K (*1953/1959) III and V. Is mathematics syntax of language? In: Feferman et al. (eds) 1995, pp 334–363
Gödel K (*1961/?) The modern development of the foundations of mathematics in the light of philosophy. In Feferman et al. (eds) 1995, pp 374–387
Gödel K (1964) What is Cantor’s continuum problem? In: Feferman et al. (eds) 1990, pp 254–270. Revised version of Gödel 1947
Gödel K (1972a) On an extension of finitary mathematics which has not yet been used. In: Feferman et al. (eds) 1990, pp 271–280. Revised version of Gödel 1958
Gödel K (1972b) Some remarks on the undecidability results. In: Feferman et al. (eds) 1990, pp 305–306
Husserl E (1900–1901) Logical investigations, vols I, II (trans: 2nd edn. by Findlay JN). Routledge and Kegan Paul, London, 1973
Husserl E (1922) The London lectures (syllabus of a course of four lectures). In: McCormick P, Elliston F (eds) Husserl: shorter works. University of Notre Dame Press, pp 68–74, 1981
Husserl E (1923–1924) Erste Philosophie. Erster Teil: Kritische Ideengeschichte. Husserliana, vol 7. Nijhoff, The Hague, 1956
Husserl E (1923–1924) Erste Philosophie. Zweiter Teil: Theorie der phänomenologischen Reduktion. Husserliana, vol 8. Nijhoff, The Hague, 1959
Husserl E (1927–1928) Phenomenology (drafts of the Encyclopedia Britannica Article). In: Psychological and transcendental phenomenology and the confrontation with Heidegger (1927–1931). Kluwer, Dordrecht, pp 83–194, 1997
Husserl E (1931) Cartesian meditations. An introduction to phenomenology. English translation: (trans: Cairns D). Martinus Nijhoff, The Hague, 1960
Leibniz GW (1677) On the universal science: characteristic. In: Weiner P (ed) Leibniz: selections. Charles Scribner’s Sons, New York, 1951
Leibniz GW (1714a) Principles of nature and grace, based on reason. In: Weiner P (ed) Leibniz: selections. Charles Scribner’s Sons, 1951
Leibniz GW (1714b) Monadology. In: Weiner P (ed) Leibniz: selections. Charles Scribner’s Sons, New York, 1951
Mahnke D (1917) Eine neue Monadologie. Kantstudien Ergänzungsheft 39. Reuther and Reichard, Berlin
Mahnke D (1925) Leibnizens Synthese von Universalmathematik und Individualmetaphysik. Erster Teil. In: Jahrbuch für Philosophie und phänomenologische Forschung, vol VII, pp 304–611
Tieszen R (1992) Kurt Gödel and phenomenology. Phil Sci 59(2):176–194. Reprinted in Tieszen 2005
Tieszen R (1998) Gödel’s path from the incompleteness theorems (1931) to phenomenology (1961). Bull Symb Logic 4(2):181–203. Reprinted in Tieszen 2005
Tieszen R (2002) Gödel and the intuition of concepts. Synthese 133(3):363–391. Reprinted in Tieszen 2005
Tieszen R (2005) Phenomenology, logic, and the philosophy of mathematics. Cambridge University Press, Cambridge
Tieszen R (2006) After Gödel: mechanism, reason and realism in the philosophy of mathematics. Phil Math 14(2):229–254
Tieszen R (2010) Mathematical realism and transcendental phenomenological idealism. In: Hartimo M (ed) Phenomenology and mathematics. Springer, Berlin, pp 1–22
van Atten M, Kennedy J (2003) On the philosophical development of Kurt Gödel. Bul Symb Logic 9:425–476
Wang H (1996) A logical journey: from Gödel to philosophy. MIT Press, Cambridge
Acknowledgments
I thank Per Martin-Löf and Mark van Atten for discussion of a number of the issues. Thanks to Guillermo Rosado-Haddock for helpful editorial comments.
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See also my forthcoming book After Gödel: Platonism and Rationalism in Mathematics and Logic (Oxford University Press).
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Tieszen, R. Monads and Mathematics: Gödel and Husserl. Axiomathes 22, 31–52 (2012). https://doi.org/10.1007/s10516-011-9162-z
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DOI: https://doi.org/10.1007/s10516-011-9162-z