Calculemus is not a thought experiment but a program: Gottfried Wilhelm Leibniz's project of building a language of signs in which every thought would have an exact expression and every piece of reasoning could be checked the way a sum is checked. It is the origin myth that symbolic AI told about itself, and it is also the scene with which Santelli (2026) opens his essay on doomers and "hyperos."
The dream
In "The Art of Discovery" (1685), a text he never published, Leibniz asks why we err so easily outside mathematics. In geometry every step can be tested by reducing it to numbers; in physics, metaphysics or ethics, it cannot. The remedy is to make our reasonings as tangible as those of mathematicians, so that when a dispute arises we can simply say: "Let us calculate, without further ado, in order to see who is right" (Leibniz, 1685/1951, p. 51).
The project had two parts, later named the characteristica universalis (an alphabet of primitive concepts) and the calculus ratiocinator (mechanical rules for combining them). The ambition was vast. Leibniz claims that "all the results of reasoning can be determined in numerical fashion," and that where the data do not settle a question one could still compute "the degree of probability" (1685/1951, p. 51). Hence this legendary's dual type, Symbolic and Probabilistic. With such a calculus, he promises, it would be impossible to make a mistake "except willfully" (1685/1951, p. 52). Nor did he stop at theory: in 1673 he presented a calculating machine of his own design in London.
Heirs
The lineage is long. Boole set out in 1854 to write the laws of thought as an algebra (Boole, 1854); Frege opened his Begriffsschrift (1879) by invoking Leibniz's idea, though he judged it too gigantic for any attempt to get past the preliminaries. In the history recounted by Buckner (2024), McCulloch and Pitts idolized Leibniz and his innate logical calculus when they showed that networks of simple neurons could compute propositional logic (2024, p. 9) (see McCulloch–Pitts neuron). Norbert Wiener, in Cybernetics (1948), chose him as the patron saint of cybernetics. And the GOFAI described by Haugeland (1985) (the Logic Theorist, expert systems) is Leibniz's dream running on real computers.
Where it broke
The hardest blow came from logic itself. Hilbert had asked for a mechanical procedure to decide the validity of any formula (the Entscheidungsproblem). Gödel (1931) proved that no consistent, recursively axiomatized formal system containing elementary arithmetic proves all arithmetical truths, and Church (1936) and Turing (1936) showed that the procedure Hilbert wanted does not exist. As Santelli (2026) puts it, the dream not only failed to carry mathematical certainty into every domain; it showed that it cannot be generalized even within mathematics. Santelli adds that these limits do not prove that humans have powers denied to every machine; they prove that intelligence does not reduce to an algorithm.
The dream today
The irony is that the AI that finally talks is no calculus ratiocinator. Large language models are children of connectionism: in Santelli's phrase, they are grown, not built, and they stumble over sums that a pocket calculator handles effortlessly. The dream returns by two routes. One is engineering: today's assistants hand calculations and checks over to symbolic tools, and reasoning models are trained on rewards that a formal verifier can compute. The other is almost eschatological: Pressman (2023) sees in current AI Leibniz's impending "posthumous victory," since two people in disagreement will soon be able to say "let us calculate" and ask the machine; constitutional AI, he writes, "is already nearly there." Between the tool and the oracle there is a long way, and it pays not to confuse them.