Mind, Body, World- Foundations of Cognitive Science, 2013a

Truth tables, and the truth-value system that they support, are very powerful. They
can be used to determine whether any complex expression, based on combinations
of primitive propositions and primitive logical operations, is true or false (Lewis,
1932). In the next section we see the power of the simple binary truth-value system,
because it is the basis of the modern digital computer. We also see that bringing this
system to life in a digital computer leads to the conclusion that one must use more
than one vocabulary to explain logical devices.
2.3 From the Formal to the Physical
The short story The Dreams in the Witch-house by Lovecraft (1933) explored the
link between mathematics and magic. The story explained how a student discovers
that the act of writing out mathematical equations can alter reality. This alteration
provided an explanation of how the accused Salem witch Keziah Mason escaped her
seventeenth-century captors:
She had told Judge Hathorne of lines and curves that could be made to point out
directions leading through the walls of space to other spaces and beyond. . . . Then
she had drawn those devices on the walls of her cell and vanished. (Lovecraft,
1933, p. 140)
This strange link between the formal and the physical was also central to another
paper written in the same era as Lovecraft’s story. The author was Claude Shannon,
and the paper’s title was “A symbolic analysis of relay and switching circuits”
(Shannon, 1938). However, his was not a work of fiction. Instead, it was a brief version
what is now known as one of the most important master’s theses ever written
(Goldstine, 1993). It detailed the link between Boolean algebra and electrical circuits,
and showed how mathematical logic could be used to design, test, and simplify
circuits. “The paper was a landmark in that it helped to change digital circuit
design from an art to a science” (p. 120).
Shannon had a lifelong interest in both mathematics and mechanics. While
his most influential papers were mathematical in focus (Shannon, 1938, 1948), he
was equally famous for his tinkering (Pierce, 1993). His mechanical adeptness led
to the invention of a number of famous devices, including Theseus, a mechanical
maze-solving mouse. Later in his career Shannon seemed to take more pride in the
gadgets that he had created and collected than in his numerous impressive scientific
awards (Horgan, 1992).
Shannon’s combined love of the mathematical and the mechanical was evident
in his education: he completed a double major in mathematics and electrical
engineering at the University of Michigan (Calderbank & Sloane, 2001). In 1936, he
was hired as a research assistant at MIT, working with the differential analyzer of
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