11 Apr 2003 (updated 11 Apr 2003 at 12:51 UTC)
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Where Logic meets Mysticism It has always been interesting
to me, as someone who does proof theory for a living, the extent to
which many leading logicians are fascinated by mysticism.
mslicker paraphrased Betrand Russell (author of
Mysticism and Logic as well as his better known
Principia), saying "if we value logic, at some point we must
rely on axioms and these axioms are necessarilly self evident, known
without demonstration". Is this true? I don't think so, because I don't think
self-evidence is much of a reason for anything. When I look
at what Aristotle was doing (esp. in the
Prior Analytics
), it seems to me he
was putting forward a system of argument that
helped his students to find the truth and convince other people, in fact an
activity not so disimilar to what Plato condemned the Sophists for
doing: namely providing his students with a useful tool that could
be used equally for good and evil ends, rather than a system
of virtuous truths.
If logic is true, what is it true in virtue of? Is it true that if
"The moon is made of green cheese and I am a Sophist" is true, then
"The moon is made of green cheese" is true as well? If so, why? We
can say: explanations have to end somewhere, so reasonable people just
accept logic as being true. Perhaps, but that doesn't help us to see
that logic is a system of truths, rather than just a useful technique.
I think that logical axioms are a bit similar to what Joseph Campbell thought
about myths. Campbell said that myths were stories or assertions that
we tell each other, not because we believe them, but because they help
us create a framework of understanding between us. It isn't important
whether myths are true or not, and maybe the best myths are obviously
absurd, what matters is that lots of people know them and can use them
as reference points when communicating and thinking of ideas that they
would otherwise be at a loss to express. Logic I think is rather the
same, except that it is important with logic that logic doesn't lead us
into falsehood: logic must be, as Tarski put it, truth-preserving.