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Cover Quote: April 1968

It has been pointed out by A. M. Turing in 1937 and by W. S. McCulloch and W. Pitts in 1943 that effectively constructive logics, that is, intuitionistic logics, can be best studied in terms of automata. Thus logical propositions can be represented as electrical networks or (idealized) nervous systems. Whereas logical propositions are built up by combining certain primitive symbols, networks are formed by connecting basic components, such as relays in electrical circuits and neurons in the nervous system. A logical proposition is then represented as a “Black box” which has a finite number of inputs (wires or nerve bundles) and a finite number of outputs. The operation performed by the box is determined by the rules defining which inputs, when stimulated, cause responses in which outputs, just as a propositional function is determined by its values for all possible assignments of values to its variables. There is one important difference between ordinary logic and the automata which represent it. Time never occurs in logic, but every network or nervous system has a definite time lag between the input signal and the output response. A definite temporal sequence is always inherent in the operation of such a real system. This is not entirely a disadvantage. For example, it prevents the occurence of various kinds of more or less overt vicious circles (related to non-constructivity, impredicativity, and the like) which represent a major class of dangers in modern logical systems. It should be emphasized again, however, that the representative automaton contains more than the content of the logical proposition which it symbolizes to be precise, it embodies a definite time lag.



- John von Neumann
Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components, 1956
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