As I mentioned in my previous two posts (see here and here), it was Kurt Gödel who posited the existence of a centuries-long conspiracy to conceal Leibniz’s efforts to develop a universal symbolic language (characteristica universalis) and universal thinking machine (calculus ratiocinator). And yet, there is no reference to this conspiracy theory in Michael Kempe’s intellectual biography of Leibniz, The Best of all Possible Worlds: A Life of Leibniz in Seven Pivotal Days. Why this omission? How seriously should we take Gödel’s conjecture? And what evidence, if any, did Gödel have for reaching this remarkable conclusion? At the very least, for the reasons I provide below (and in my 2022 paper “The Leibniz Conspiracy“), Gödel’s conjecture deserves a fair hearing:

To begin (sorry, Richard!), Gödel is best known for his landmark contributions to logic and mathematics, especially his first and second incompleteness theorems,[1] as well as for reportedly discovering a logical contradiction in the U.S. Constitution.[2] In addition, during his years at the Institute for Advanced Studies (IAS) in Princeton, New Jersey, Gödel’s interests also turned to philosophy and physics. Among other things, Gödel admired the works of Gottfried Leibniz and studied them closely, “devoting endless hours to the study of Leibniz.”[3] At some point during his studies, Gödel postulated the existence of a hostile conspiracy that had caused some of Leibniz’s works to be concealed or destroyed.[4] In the words of one of Gödel’s biographers, Rebecca Goldstein, Gödel “came to believe that there was a vast conspiracy, apparently in place for centuries, to suppress the truth [about Leibniz’s writings] and make men stupid.”[5]

That Gödel, one of the most logical and rigorous thinkers of all time, was himself a proponent of such a far-fetched conspiracy theory shows us how compelling and pervasive conspiracy thinking can be. Gödel’s biographers, however, have generally dismissed Gödel’s conspiracy theory out of hand, attributing this episode to Gödel’s “paranoia” or to his many mental delusions.[6] By way of example, one scholar states: “He [Gödel] suffered delusions and personality disturbances. He became excessively paranoid, the paranoia deriving, some have conjectured, from his super-logicality and overly intense introspection. He tended to believe in secret intrigues and conspiracies.”[7] Another scholar speculates that it was Gödel’s intellectual isolation, especially after the death in 1955 of his best friend Albert Einstein, that “provided fertile sole for that rationality run amuck which is paranoia.”[8]

While it is tempting to dismiss this conspiracy theory as the product of a paranoid mind, such an ad hominem psychological explanation is too easy. After all, Gödel was not only a world-renowned logician; he had also devoted “endless hours” of study to Leibniz’s works.[9] In fact, Gödel may have first encountered the works of Leibniz as early as 1926, while he was still a student at the University of Vienna.[10] According to Karl Menger, a credible source who knew Kurt Gödel personally from their days together in Vienna, Gödel “had been most intensely interested in Leibniz”[11] and “he keenly desired to inspect Leibniz’ unpublished manuscripts and not only out of historical interest ….”[12] But to fully appreciate and assess the plausibility of this alleged conspiracy, we must revisit one of Leibniz’s most ambitious and revolutionary ideas and the supposed target of this secret cover-up, an idea that must have captured Gödel’s imagination, for in the words of one scholar:

“Gödel was fascinated by Leibniz’s ideas, to the point that others felt he was obsessed: he checked out every book on Leibniz from his university library. He believed (correctly, I would say) that Leibniz’s most important ideas (the characteristica universalis) had been nearly forgotten by society; but he also believed that this was due to a shadowy conspiracy meant to prevent the intellectual advancement of mankind.”[13]

In brief, Gottfried Wilhelm Leibniz was one of the most important logicians, mathematicians, and natural philosophers of his time. Although his most well-known contributions to the world of ideas include his discovery of differential and integral calculus, he also attempted to develop a universal logic of science and human reasoning. Specifically, Leibniz wanted to “reduce everything from imagination to analysis,”[14] or in the words of one Leibniz scholar: “Leibniz dreamt all his life of developing a ‘characteristica universalis’—a kind of ‘algebra of thought’ that would mechanize any form of factual reasoning as algebra had mechanized geometrical thought.”[15]

To the point, Leibniz was convinced that all human ideas could be reduced to a few primitive thoughts, or in the words of another Leibniz scholar, “If it were possible to map these primitive thoughts unambiguously to a list of characters, then either no one using these characters in reasoning and writing would ever err, or he or she would recognize these errors with the help of [the] most simple checks.”[16] To accomplish this ambitious project, Leibniz developed the concept of a characteristica universalis, the foundation of his general model for logical reasoning.[17]Or in the immortal words of Leibniz himself:

“We will present here, thus, a new and marvelous calculus, which occurs in all our reasonings and which is not less rigorous than arithmetic or algebra. Through this calculus, it is always possible to terminate that part of a controversy that can be determined from the data, by simply taking a pen, so that it will suffice for two debaters (leaving aside issues of agreement about words) to say to each other: Let us calculate!”[18]

Alas, as I mentioned in my previous post, one possibility is that Leibniz never described the characteristica universalis in operational detail. (Indeed, some scholars have dismissed Leibniz’s project as an absurd fantasy.[19]) Gödel, however, may have believed that Leibniz’s project was feasible. In a systematic and methodical fashion, Gödel had assembled all the relevant works of Leibniz and that is when the Austrian-American logician noticed a striking anomaly: a detailed treatment of the characteristica universalis was conspicuously absent from Leibniz’s surviving works. Was this omission a mere coincidence, or was something more nefarious at work?

To be continued (footnotes are below the fold) …

---

[1] See generally Georg Kreisel, “Kurt Gödel, 28 April 1906–14 January 1978”, Biographical Memoirs of Fellows of the Royal Society, vol. 26 (1980), pp. 148–224.

[2] See generally F. E. Guerra-Pujol, “Gödel’s loophole”, Capital University Law Review, Vol. 41 (2013), pp. 637–673, which surveys the various accounts of Gödel’s alleged discovery of a contradiction or loophole in the Constitution.

[3] Yourgrau (2005), p. 182. Also, for a brief summary of Leibniz’s contributions to logic and mathematics, see Dawson (1997), p. 39. In addition, Dawson (1997, p. 237) explains the relevance of Leibniz’s ideas to Gödel’s First Incompleteness Theorem. The First Incompleteness Theorem first appeared as “Theorem VI” in Gödel’s 1931 paper “On Formally Undecidable Propositions of Principia Mathematica and Related Systems I.” See Gödel (1931), translated in Heijenoort (1967).

[4] See Karl Menger, “Memories of Kurt Gödel”, pp. 222-223, in Louise Golland, et al., editors, Reminiscences of the Vienna Circle and the Mathematical Colloquium, Springer Science (1994), pp. 200-236.

[5] Rebecca Goldstein, Incompleteness: The Proof and Paradox of Kurt Gödel, Norton (2005), p. 48 (internal quotation marks omitted).

[6] See ibid., p. 48. See also John W. Dawson, Jr., Logical Dilemmas: The Life and Work of Kurt Gödel, A. K. Peters (1997), p. 107 & p. 137; Theoni Pappas, “The paranoia of Kurt Gödel”, in Theoni Pappas, Mathematical Scandals, World Wide Publishing/Tetra (1997), pp. 26–34; and Palle Yourgrau, A World Without Time: The Forgotten Legacy of Gödel and Einstein, Basic Books (2005), p. 15.

[7] Philip J. Davis, “The ‘here’ and the ‘there’ of mathematics: Kurt Gödel”, Society for Industrial and Applied Mathematics News, Vol. 30, No. 8 (1997), available at https://perma.cc/G6PG-728L.

[8] Goldstein, op. cit., p. 48. It is worth noting, however, that Gödel postulated this worldwide anti-Leibniz conspiracy as early as 1939, when Gödel was at the height of his mental powers. See Menger, “Memories of Kurt Gödel”, op. cit., pp. 222-223.

[9] Yourgrau, op. cit., p. 182. In addition, Karl Menger has attested that Gödel had become deeply involved in the study of Leibniz. See Dawson (1997), p. 107. See also ibid., p. 166: “That the study of Leibniz was the primary focus of Gödel’s attention during the years 1944-45 is attested both by IAS Bulletin nos. 11 and 12 and by entries in Morgenstern’s diary.” (Oskar Morgenstern and Gödel were both faculty members at the Institute of Advanced Studies in Princeton, New Jersey, and by all accounts, they were close friends for many decades.)

[10] Dawson, op. cit., p. 39.

[11] Karl Menger, “Vignettes of the Members of the [Vienna] Circle in 1927”, p. 71, in Golland, op. cit., pp. 54-73.

[12] Menger, “Memories of Kurt Gödel”, op. cit., p. 210.

[13] Douglas Summers Stay, “Gödel and Leibniz”, Machinamenta (Oct. 23, 2012), available at https://perma.cc/62LZ-A3WA.

[14] Leibniz (1690e), quoted in Victor Blåsjö, Transcendental Curves in the Leibnizian Calculus: Studies in the History of Mathematical Enquiry, Elsevier (2017), p. 14 & p. 218, n.17.

[15] Blåsjö, op. cit., p. 14.

[16] Volker Peckhaus, “Calculus ratiocinator versus characteristica universalis? The two traditions in logic, revisited”, History and Philosophy of Logic, Vol. 25 (2004), pp. 3-14, p. 6.

[17] Leibniz’s work draws a distinction between a lingua characterica (or characteristica universalis), a universal language of thought, and a calculus ratiocinator, a calculus of reasoning. See generally Pechkaus, op. cit.

[18] Leibniz (1875–1890), vol. 7, pp. 64-65; translation from Dascal (2008), p. 41, quoted in Blåsjö, op. cit., p. 14 & p. 218, n.18. The original reads as follows: “Itaque profertur hic calculus quidamnovus et mirificus, qui in omnibus nostris ratiocinationibus locum habet, et qui non minus accurate procedit quam Arithmetica aut Algebra. Quo adhibito semper terminari possint controversiae quantum ex datis eas determinari possibile est, manu tantum ad calamum admota, ut sufficiat duos disputantes omissis verborum concertationibus sibi invicem dicere: calculemus.” See Blåsjö, op cit., 218, n.18.

[19] Compare G. H. R. Parkinson, Leibniz: Philosophical Writings (translation by Mary Morris), J. M. Dent (1973), p. ix: “Leibniz’s views about the systematic character of all knowledge are linked with his plans for a universal symbolism, a Characteristica Universalis. This was to be a calculus which would cover all thought, and replace controversy by calculation. The ideal now seems absurdly optimistic.”