That is one of the chapter headings of Michael Kempe’s intellectual biography of G. W. Leibniz: The Best of all Possible Worlds: A Life of Leibniz in Seven Pivotal Days (see p. 96 of Kempe’s book). To the point, as I mentioned yesterday, this “global formula” refers to the great German polymath’s Heraclean efforts to develop a working blueprint for a universal thinking machine as well as a “universal symbolic language” (p. 37) to express mathematical, scientific, and metaphysical concepts in order to automate the process of knowledge production and scientific discovery.

But as Michael Kempe notes in Chapter 4 of his beautiful new book (from which the chapter heading quoted above is taken), Leibniz was unable to complete this ambitious project during his lifetime. This observation, however, begs the key question: how much was Leibniz able to accomplish? After all, Leibniz began to work on this project as early as 1666, when he published his Art of Combinations (Dissertatio de arte combinatoria), and he presumably continued to work on his universal thinking machine until his death many decades later in 1716.

There are two possibilities. One is a conspiracy, as no less an authority than Kurt Gödel conjectured. Although this sounds like a rather remote, if not far-fetched, possibility, as I mentioned in my previous post it was Gödel who posited the existence of a centuries-long conspiracy to conceal Leibniz’s efforts to develop his universal thinking machine. On this view, Leibniz was able to carry out, if only partially, his ambitious project, but it was subsequently suppressed by a group of his shadowy enemies.

The other possibility, however, is more benign and thus more plausible. According to Kempe, for example, Leibniz’s decades-long efforts simply stalled out, so to speak, for the main stumbling block for the German polymath was this: how to reduce ideas into formal symbols? For reference, below are three of the most relevant passages from the English-language translation of Kempe’s book:

“But what’s still largely missing [from Leibniz’s efforts to develop a universal thinking machine] are concepts and methods for converting nonnumerical information into numerical values. Words have meanings, refer to things or facts, express a sense. Numbers are meaning-neutral.” (p. 111)

“[Leibniz] is looking for clues to the problem of how to connect nonnumerical and purely numerical information.” (p. 119)

“What is crucial for Leibniz is … the formalization of reality by means of symbols.” (Ibid.)

As a result, Kempe presents the following alternative conjecture: “… Leibniz should be associated not only with the programmatic idea of a universal method for answering all manner of questions by means of formulas, but also with the suspicion that this might not be possible to an unlimited extent.” (Kempe 2024, p. 121) In other words, Leibniz just gave up! Why? Because he was unable to find a way of “formaliz[ing] reality by means of symbols” (p. 119), i.e. he was unable to convert ordinary human language into well-defined symbols.

But what if Kempe’s conjecture, however plausible and reasonable-sounding, is wrong, and what if Gödel’s more malevolent and crazy conjecture of a conspiracy is closer to the truth? I will explore this possibility in my next few posts …