FOM: geometrical reasoning

[Stephen G Simpson]

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