Excerpt from Warren S. McCulloch, “What Is a Number, that a Man May Know It, and a Man, that He May Know a Number?” (1960)
Please remember that we are not now concerned with the physics and chemistry, the anatomy and physiology, of man. They are my daily business. They do not contribute to the logic of our problem. Despite Ramon Lull’s combinatorial analysis of logic and all of his followers, including Leibniz with his universal characteristic and his persistent effort to build logical computing machines, from the death of William of Ockham logic decayed. There were, of course, teachers of logic. The forms of the syllogism and the logic of classes were taught, and we shall use some of their devices, but there was a general recognition of their inadequacy to the problems in hand. […] The difficulty is that they had no knowledge of the logic of relations, and almost none of the logic of propositions. These logics really began in the latter part of the last century with Charles Peirce as their great pioneer. As with most pioneers, many of the trails he blazed were not followed for a score of years. For example, he discovered the amphecks — that is, “not both … and …” and “neither … nor …”, which Sheffer rediscovered and are called by his name for them, “stroke functions”.
It was Peirce who broke the ice with his logic of relatives, from which springs the pitiful beginnings of our logic of relations of two and more than two arguments. So completely had the traditional Aristotelian logic been lost that Peirce remarks that when he wrote the Century Dictionary he was so confused concerning abduction, or apagoge, and induction that he wrote nonsense. Thus Aristotelian logic, like the skeleton of Tom Paine, was lost to us from the world it had engendered. Peirce had to go back to Duns Scotus to start again the realistic logic of science. Pragmatism took hold, despite its misinterpretation by William James. The world was ripe for it. Frege, Peano, Whitehead, Russell, Wittgenstein, followed by a host of lesser lights, but sparked by many a strange character like Schroeder, Sheffer, Gödel, and company, gave us a working logic of propositions. By the time I had sunk my teeth into these questions, the Polish school was well on its way to glory.
In 1923 I gave up the attempt to write a logic of transitive verbs and began to see what I could do with the logic of propositions. My object, as a psychologist, was to invent a kind of least psychic event, or “psychon”, that would have the following properties: First, it was to be so simple an event that it either happened or else it did not happen. Second, it was to happen only if its bound cause had happened — shades of Duns Scotus! — that is, it was to imply its temporal antecedent. Third, it was to propose this to subsequent psychons. Fourth, these were to be compounded to produce the equivalents of more complicated propositions concerning their antecedents.
In 1929 it dawned on me that these events might be regarded as the all-or-none impulses of neurons, combined by convergence upon the next neuron to yield complexes of propositional events. (McCulloch 1965, 7–9).
- McCulloch, Warren S. (1961), “What Is a Number that a Man May Know It, and a Man, that He May Know a Number?”, Ninth Alfred Korzybski Memorial Lecture, General Semantics Bulletin, Numbers 26 and 27, pp. 7–18, Institute of General Semantics, Lakeville, CT. Reprinted in Embodiments of Mind, pp. 1–18. Online (1) (2).
- McCulloch, Warren S. (1965), Embodiments of Mind, MIT Press, Cambridge, MA.