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).
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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