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That logical reasoning is, in some sense, computation -or, more
properly, that it can be formalized and validated by controllable
means- is now an accepted idea, clearly explained in the writings of
1920's logicians (Hilbert or Herbrand, to name two) and
actually mechanized in the 1960's. But the notion was advanced in
the l7th century by Hobbes, who wrote in 1655 that "reasoning is
but reckoning", and by Leibniz, who thought in 1658 (and wrote
in 1666) that, in the future, philosophers would settle their
disputes as accountants do, just by taking pens and calculators
(abaci) and proclaiming "let us compute!". Leibniz explicitly
stated that this was Llull's dream made true. It really was. Llull
had anticipated this in 1274 by noting that, to convert muslims (a
current worry), public disputations were fruitless (the ones
attempted in the 1260's ended circularly, with nobody
convinced), so one had to find a mechanism to prove and generate
truths in such a way that, once everyone agreed on the assumptions,
the objectivity of the procedure would force all to accept the
conclusions. The elaboration of such a mechanism took his lifetime's
efforts. Though Leibniz explained the idea in concise and appealing
terms, Llull himself could have suscribed his admirer's formulation,
stated 400 years later. Moreover, Llull's "mechanism" was not
a merely abstract procedure; it was supported by truly "mechanical"
means, his rotating concentric rings. Now easily dismissed as banal
toys, they were the first such devices on offer. From this elementary
mechanism, and by simple mechanical manipulations, a whole heuristic
followed and a deductive chain of truths was combinatorially generated,
to be later explored and validated.
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