Robotics Reference
In-Depth Information
Similar devices were constructed for the study of the soul and the
seven deadly sins. Although these devices did not really offer any addi-
tional logical powers, the
Ars Magna
was admired by many Renaissance
clerics and commented on by such noted scholars as Wilhelm Leibniz.
Llull's writings advanced the idea that logical reasoning could be per-
formed, or at least assisted, by a mechanical process, but as Martin Gard-
ner points out, none of Llull's scientific writings added to the scientific
knowledge of his time. Nevertheless, Llull firmly believed that, by us-
ing a mechanical device to combine the terms of a logical expression, it
would be possible to discover the building blocks that could be employed
to construct logical arguments, and his beliefs inspired other pioneers in
this field.
Gottfried Wilhelm von Leibniz
Gottfried Wilhelm von Leibniz (1646-1716) was a great mathematician
and philosopher, one of the first to try to build a mechanical calcula-
tor. He was also the first to appreciate that Llull's method of logical
argument could be applied to formal logic. Although Leibniz had lit-
tle regard for Llull's work in general, he believed there was a chance it
could be extended to apply to formal logic. In a rare flight of fancy,
Leibniz conjectured that it might be possible to create a universal alge-
bra that could represent just about everything under the sun, including
moral and metaphysical truths. If this were possible then the rules of the
universal algebra would allow the creation of logical arguments to prove
anything that could be proved, to disprove anything that could be dis-
proved, and to deduce and infer. In summary, it would make it possible
to reason about anything, using the language of the universal algebra as
the language of reasoning:
All our reasoning is nothing but the joining and substituting of
characters, whether these characters be words or symbols or pic-
tures . . .
...If we could find characters or signs appropriate for expressing
all our thoughts as definitely and as exactly as arithmetic expresses
numbers or geometric analysis expresses lines, we could in all sub-
jects, insofar as they are amenable to reasoning, accomplish what is
done in Arithmetic and Geometry.
