FOM: geometrical reasoning
Stephen G Simpson
simpson at math.psu.edu
Mon Feb 22 15:48:35 EST 1999
Jacques Dubucs 20 Feb 1999 04:42:15 writes:
> A reasonably argumented exegetical discussion on this point is
> probably out the scope of FOM, but arguments could be produced to
> show that Kant had quite different ideas in the mind, with effect
> that geometrical reasoning is genuinely irreducible to logical one.
Continental philosophers want to claim that geometry is illogical. I
think it's time to challenge this in a pointed way.
Dr. Dubucs, you keep saying that geometrical reasoning is irreducible
to logical reasoning. Could you please post, here on FOM, an example
of a piece of geometrical reasoning which, according to you, is not
reducible to logical reasoning? Such an example would definitely be
within the scope of the FOM list. It would be a counterexample to what
I in 19 Feb 1999 19:30:06 called `the logicist thesis'.
In my view, the example that you gave in your posting of 16 Feb 1999
09:48:52, namely Euclid's construction of an equilateral triangle,
will not do, because Euclid's proof *is* reducible to logical
reasoning. It can be formalized in the predicate calculus,
specifically Tarski's 1959 elementary geometry (or Friedman's
elementary diagrammatic geometry of 1 Feb 1999 04:52:48, for that
matter).
-- Steve
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