FOM: Tarski's elementary geometry
Stephen G Simpson
simpson at math.psu.edu
Mon Feb 22 17:01:59 EST 1999
Harvey Friedman writes:
> Forgive me, but I think that Steve missed the main point of my FOM
> posting of 4:52AM 2/1/99, More Axiomatization of Geometry.
Yes, I probably did miss the point, because I didn't understand the
significance of the diagrammatic conditions. But Harvey, I think many
other people missed the point too, because you didn't highlight the
diagrammatic aspect enough. You need to be more agressive about these
things! :-)
> ... what I do in my posting is give simple purely geometric
> axioms. One uses only conjunctions of atomic formulas without
> equality, involving only equidistance. Thus the axiomatizations are
> purely diagrammatic.
Would it be fair to say that your system directly and cogently
formalizes geometrical/diagrammatic reasoning, within the predicate
calculus?
How is this related to the book by Barwise and Allwein entitled
`Logical Reasoning With Diagrams'? (I haven't read this book, but I
will get it out of the library in a few days.) How is it related to
Manders' work? (Has Manders published anything on this?)
Does your posting help to refute the continental philosophers' claim
that geometrical reasoning is not reducible to logical reasoning?
-- Steve
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