The Prehistory: From Leibniz to the Turing Machine
This text is a preview of History of the Reception of Hegel, volume II, to be published in 2026 by Reflexivity Press.
Leibniz’s Dream: Calculemus!
The dream of mechanizing thought is old. Gottfried Wilhelm Leibniz, in the seventeenth century, devised a “characteristica universalis” — a universal sign language in which all thoughts could be expressed. And a “calculus ratiocinator” — a calculus with which all truths could be computed.
Leibniz’s vision: when people argue, they should say, “Let us calculate!” (Calculemus!) The dispute would resolve itself like an arithmetic problem. No rhetoric, no persuasion, only calculation.
This remained a dream. Leibniz could develop neither the universal language nor the calculus. But the dream continued to have an effect. The formal logic of the nineteenth century — Boole, Frege, Russell — was a step in this direction. And the computer science of the twentieth century was another.
Alan Turing and the Universal Machine
In 1936, Alan Turing proved something astonishing: there exists a machine that can compute any computable function. The “Turing machine” is an abstract model — an infinite tape with symbols, a read/write head that moves and alters symbols, a finite set of rules.
This simple machine can compute everything that is computable at all. Not just arithmetic — also word processing, image editing, chess, everything. The Turing machine is the theoretical foundation of the computer.
But Turing also proved something negative: there are problems that no Turing machine can solve. The most famous is the “halting problem”: one cannot, in general, decide whether a program will ever halt or run forever. There are principled limits to computability.
The philosophical question forces itself upon us: is human thinking a Turing machine? Can humans solve problems that no machine can solve? Or are we, too, “merely” very complex computational processes?
The Turing Test
In 1950, Turing posed the question: “Can machines think?” And he gave a pragmatic answer: if a machine behaves in a conversation such that one cannot distinguish it from a human, then it “thinks” — at least operationally.
This is the Turing test: a person communicates via a screen with an unknown interlocutor. If they cannot decide whether it is a human or a machine, the machine has passed the test.
The test is behaviorist: it does not ask about the machine’s inner experience, only about its outward behavior. That is its strength and its limit. The strength: it avoids metaphysical speculation about “true consciousness.” The limit: it might mistake a perfect simulation for genuine thinking.