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These are excerpts and elaborations from my book "The Nature of Consciousness"
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Formal Systems David Hilbert, a German mathematician of the beginning of the 20th
century, is credited with first introducing the question of whether a
mechanical procedure exists for proving mathematical theorems (fully in 1928).
His goal was to reduce Mathematics to a more or less blind manipulation of
symbols through a more or less blind execution of formal steps. Already
implicit in Hilbert's program was the idea that
such a procedure could be carried out by a machine. The discipline of formal systems was born, with the broad
blueprint that a formal system should be defined by a set of axioms (facts that
are known to be true) and a set of inference rules (rules on how to determine
the truth or falsity of a new fact, given the axioms). By applying the rules on
the axioms, one could derive all the facts that are true. A formal system employs the
language of propositions (statements that can only be true or false and can be
combined by binary operators such as not, and and or) and predicates
(statements with a variable that can be quantified existentially or
universally, i.e. can be only true or false relative to at least one value of
the variable or for every value of the variable). For example, the fact that
Piero Scaruffi is a 51-year old writer could
be expressed as: writer (Piero) AND age (Piero, 51). The fact that teachers
are poor can be expressed with the expression: "FOR EVERY x, teacher(x)
-> poor (x)"; that translates as: every individual that satisfies the
predicate "teacher" also satisfies the predicate "poor".
The fact that some teachers are obnoxious can be expressed as: "FOR AT
LEAST ONE x teacher(x) -> obnoxious (x)". The language of Logic is not
very expressive but it lends itself to logical reasoning, i.e. deduction. This generation of
mathematicians basically pushed logical calculus to the forefront of the tools
employed to investigate the world. The apparatus of formal systems became the
apparatus that one must use to have any scientific or philosophical discussion.
Implicit in their program was the belief that the laws of logic were the laws
of thought. Back to the beginning of the chapter "Machine Intelligence" | Back to the index of all chapters |
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