Walter Pitts

(1923-1969)

Walter Pitts as a child taught himself logic and mathematics. At age 12 he found a copy of Bertrand Russell and Alfred North Whitehead's *Principia Mathematica* at s local library and wrote Russell a letter suggesting improvements in the first volume.

When Pitts was 15 years old, Russell was invited to the University of Chicago and Pitts attended his lectures, while living homeless near the University. Russell advised Pitts to work with Rudolf Carnap, who also attended Russell's lectures. Pitts walked into Carnap's office with a marked up copy of Carnap's famous text, *The Logical Syntax of Language*, then left without telling Carnap how to contact him. It took Carnap months to locate Pitts and give him a minor job with a modest income.

Pitts mastered Carnap's abstract logic and applied it to the neuronal structure of the brain after many discussions with Nicolas Rashevsky, who founded the *Bulletin on on Mathematical Biophysics*

Pitts started a life-long friendship with Jerome Lettvin, a pre-med student at University of Illinois in Chicago.

Warren McCulloch, twenty-five years older than Pitts, spent most of his life arguing that neurons in the brain are logic gates like those in digital computers, and that the brain can be understood as a Turing machine (a universal digital computer).

McCulloch and Pitts were thus the originators of today's widely supported "computational model of the mind." Their work became the basis of cybernetics, modeling the brain as a digital computer, and artificial intelligence, as well as "cellular automata," in which individual cells live or die according to inputs from their surrounding cells. See John Conway's "Game of Life."

In their 1943 paper, "A Logical Calculus of the Ideas Immanent in Nervous Activity," Pitts and his older colleague Warren McCulloch wrote

Because of the “all-or-none” character of nervous activity, neural events and the relations among
them can be treated by means of propositional logic. It is found that the behavior of every net can
be described in these terms, with the addition of more complicated logical means for nets
containing circles; and that for any logical expression satisfying certain conditions, one can find a
net behaving in the fashion it describes. It is shown that many particular choices among possible
neurophysiological assumptions are equivalent, in the sense that for every net behaving under
one assumption, there exists another net which behaves under the other and gives the same
results, although perhaps not in the same time. Various applications of the calculus are
discussed.
"A Logical Calculus of the Ideas Immanent in Nervous Activity," p.99

McCulloch said his ideas that neural networks are similar to arguments in propositional logic and thus to computer networks dates back many years.

Many years ago one of us, by considerations impertinent to this argument,
was led to conceive of the response of any neuron as factually equivalent to a
proposition which proposed its adequate stimulus. He therefore attempted to
record the behavior of complicated nets in the notation of the symbolic logic of
propositions. The “all-or-none” law of nervous activity is sufficient to insure
that the activity of any neuron may be represented as a proposition.
Physiological relations existing among nervous activities correspond, of
course, to relations among the propositions; and the utility of the representation
depends upon the identity of these relations with those of the logic of
propositions. To each reaction of any neuron there is a corresponding assertion
of a simple proposition. This, in turn, implies either some other simple
proposition or the disjunction of the conjunction, with or without negation, of
similar propositions, according to the configuration of the synapses upon and
the threshold of the neuron in question.
"A Logical Calculus of the Ideas Immanent in Nervous Activity," p.99

In the 1930's McCulloch had studied logic at Yale in

Frederic Fitch's course on propositional logic, based on the great

*Principia Mathematica* of

Bertrand Russell and

Alfred North Whitehead.

Fitch also was the thesis adviser for Ruth Barcan Marcus, whose work on the "necessity of identity" influenced Saul Kripke.

Despite the fact that information flows along neurons in the brain, the neural network is not a computer network, brain processes are not algorithms, there is no central processing unit (CPU) or even distributed parallel processing.

Very simply, man is not a machine and the brain is not a computer.

Nevertheless, we can regard McCulloch as the first thinker to offer a solution to the mind-body problem that "embodies" an *immaterial logical software* mind in a *material mechanical hardware* computer, as the title of his 1965 book, "*Embodiments of Mind*, suggests.

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