Turing test human from the automaton. Descartes fails to consider the possibility that future automata might be able to overcome such insufficiency, and so does not propose the Turing test as such, even if he prefigures its conceptual framework and criterion. Denis Diderot formulates in his "Pensées philosophiques" a Turing-test criterion: "If they find a parrot who could answer to everything, I would claim it to be an intelligent being without hesitation." This does not mean he agrees with this, but that it was already a common argument of materialists at that time. According to dualism, the mind is non-physical (or, at
Church–Turing thesis three formally-defined classes of computable functions coincide with the "informal" notion of an effectively calculable function. Since, as an informal notion, the concept of effective calculability does not have a formal definition, the thesis, although it has near-universal acceptance, cannot be formally proven. Since its inception, variations on the original thesis have arisen, including statements about what can physically be realized by a computer in our universe (physical Church-Turing thesis) and what can be efficiently computed (Church–Turing thesis (complexity theory)). These variations are not due to Church or Turing, but arise from later work in complexity theory and digital physics.