FOM: geometrical reasoning
Stephen G Simpson
simpson at math.psu.edu
Tue Feb 23 21:13:25 EST 1999
Jerry Seligman's posting of 23 Feb 1999 13:47:23 makes some useful
distinctions. I don't imagine that the continental philosophers have
gone into anything like this level of detail.
Challenge to Seligman: You suggest that the structure of diagrammatic
proofs *may perhaps* be very different from that of predicate calculus
proofs. Has the systematic study of diagrammatic proofs progressed to
where there is a preponderance of evidence on this? If so, what is
the verdict? If the verdict is as you suggest, that diagrammatic
proofs and predicate calculus proofs are structurally different, then
what are the structural features that distinguish them?
What about predicate calculus systems such as Harvey's system for
plane geometry in 1 Feb 1999 04:52:48? In this system, the
conjunctions of atomic formulas may be viewed as diagrams, so it seems
reasonable to conjecture that anything provable in this system has a
diagrammatic proof within the system. If this conjecture is true,
would that be a counterexample to what you are suggesting?
I haven't yet looked at the Barwise/Allwein volume, but I will get it
from the library tomorrow.
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