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

equivalent. Shannon noted that the basic properties of the two-valued logic were
true of his logical interpretation of switches: “Due to this analogy any theorem of
the calculus of propositions is also a true theorem if interpreted in terms of relay
circuits” (p. 714).
x
A
x
y
B
x
y
C
Figure 2-1. (A) An electrical switch, labelled x. (B) Switches x and y in series. (C)
Switches x and y in parallel.
The practical implication of Shannon’s (1938) paper was that circuit design and
testing was no longer restricted to hands-on work in the physical domain. Instead,
one could use pencil and paper to manipulate symbols using Boolean logic, designing
a circuit that could be proven to generate the desired input-output behaviour.
Logical operations could also be used to ensure that the circuit was as simple as
possible by eliminating unnecessary logical terms: “The circuit may then be immediately
drawn from the equations” (p. 713). Shannon illustrated this technique with
examples that included a “selective circuit” that would permit current when 1, 3, or
4—but not 0 or 2—of its relays were closed, as well as an electric combination lock
that would only open when its 5 switches were depressed in a specific order.
Amazingly, Shannon was not the first to see that electrical circuits were logical
in nature (Burks, 1975)! In 1886, Charles Peirce wrote a letter to his student
Alan Marquand suggesting how the latter’s logic machine (Marquand, 1885) could
be improved by replacing its mechanical components with electrical ones. Peirce
provided diagrams of a serial 3-switch circuit that represented logical conjunction
(and) and a parallel 3-switch circuit that represented logical disjunction (or).
Peirce’s nineteenth-century diagrams would not have been out of place in Shannon’s
twentieth-century paper.
Multiple Levels of Investigation 31