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Gödel’s Last Loop

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Notes

  1. This (if any) is the reason adduced in all biographical accounts, which by and large depend on [2] (compare, for instance, the relevant sentences in [2, p. 16] and [9, p. 133], the latter quoted in turn in [7, p. 250]), expanded to a full biography in [3]. However, a complex pathological profile like Gödel’s easily allowed for a final radicalization of his anorexia, whatever the motive (if any): read, in [1, p. 6], the opinions of the psychiatrist who followed him in his last years and of the physician attending him in his last days at Princeton Hospital.

  2. In [3, p. 255], a different connection is put forward. The complete argument is worth quoting: “Unable to escape from the inner logic of his paranoia—to adopt, as it were, a ‘metatheoretical’ perspective—he succumbed to starvation in the grip of his obsessive fear of being poisoned. Like the actions of an inhabitant of one of the timeless universes he had envisioned, his death equally was, and was not, of his own volition.” Gödel firmly held that the world is deterministic, that free will is an illusion, and that change is not objective.

  3. On the grounds that “the criterion for distinguishing between Gödelian and non-Gödelian design defects or flaws in the Constitution is the presence of ‘self-reference’” [8, p. 650], it has been argued that the inconsistency Gödel found in the United States constitution, allowing for a dictatorship to arise, is that the amending procedure is an article of the constitution itself, and hence can be amended in order to make constitutional changes easy (as a matter of fact, this is a flaw of almost all constitutions). Gödel never revealed what this inconsistency was. The several versions of the related anecdote found in Gödel’s biographies—such a proliferation of versions is surprising, since the only primary source appears to be Morgenstern’s account—can also be read in [8, pp. 644–646].

References

  1. S. Budiansky. Journey to the Edge of Reason: The Life of Kurt Gödel. Oxford University Press, 2021.

  2. J. W. Dawson. Kurt Gödel in sharper focus. Mathematical Intelligencer 6:4 (1984), 9–17.

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  3. J. W. Dawson. Logical Dilemmas: The Life and Work of Kurt Gödel. A K Peters, 1997.

  4. K. Gödel. Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik 38 (1931), 173–198, reprinted and translated in [6], I, pp. 145–195.

  5. K. Gödel. An example of a new type of cosmological solutions of Einstein’s field equations of gravitation. Reviews of Modern Physics 21 (1949), 447–450, reprinted in [6], II, pp. 190–198.

  6. K. Gödel. Collected Works. I–V. Oxford University Press, 1986–2003.

  7. R. Goldstein. Incompleteness: The Proof and Paradox of Kurt Gödel. W. W. Norton & C., 2005.

  8. F. E. Guerra-Pujol. Gödel’s loophole. Capital University Law Review 41 (2013), 637–673.

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  9. H. Wang. Reflections on Kurt Gödel. MIT Press, 1995.

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Correspondence to Fabio Acerbi.

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Acerbi, F. Gödel’s Last Loop. Math Intelligencer (2024). https://doi.org/10.1007/s00283-024-10341-6

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