The Beginnings of Digital Culture - Digital Culture - page 13

Boole made a number of brilliant contributions to mathematics,
but his most famous was to be found in his topics The Mathematical
Analysis of Logic 13 and An Investigation of the Laws of Thought . 14
In these works he successfully applied algebraic methods to logic,
thus allowing logical relations to be calculated in a mathematical
manner. One of Boole's insights was that his algebraic logic worked
using only two numerical values, , which could stand respec-

tively for the universe and nothing. Within Boole's system it is
possible to deduce any result from these terms, the variables x , y , z
etc. and the standard operators, +, -,

1 and 0

. Boole's symbolic logic was
highly influential on later generations of logicians and mathemati-
cians, and indirectly contributed to the conception of the modern
digital computer. More directly, Boole's logic also contributed to
the development of binary switching systems for telephone switch-
boards before the Second World War and, after, to the building of
logical circuits. Much of the work examining the applications of
Boolean logic to telephone switching relays was undertaken by MIT
student Claude Shannon, who was also largely responsible for the
post-war development of Information Theory.
Boole's work in Symbolic Logic was, in fact, anticipated by the
seventeenth century philosopher Gottfried Leibniz, who was one of
the most important and influential thinkers of his period, and whose
interests ranged across science, mathematics, politics and meta-
physics. Starting with his Dissertatio de arte combinatoria of

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, 15
he was concerned with the dream of a perfect, logical language. To
this end Leibniz worked on a number of schemes involving the use
of numbers to represent concepts, which could then be manipu-
lated to determine whether statements were true or false. This was
paralleled by his interest in calculating machines, which he built,
and which he saw as being able to undertake some of these logical
processes of induction, as well as his development of binary nota-
tion. His ambitious programme for logic proved to be unrealizable
in both practical and philosophical terms. It also marked a return to

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