FOM: Re: geometrical reasoning

[Michael Thayer]

Steve S asks an intersting question.


>
>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?

He then goes on to argue that there is no difference in a curious way:

>[S]o 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?


Maybe Steve needs to conjecture the converse of his conjecture.  For what if
there were something provable diagrammatically, which was not provable in
the system?  This would confirm Seligman's suggestion.

On a more serious note, I suspect that the problem here is one of ambiguity
in the use "formalize".  One may be formalizing in order to understand how
the system works, flaws and all; on may be formalizing in order to improve
the system.  Both are worthy projects, but they are different projects:

For example, if a formalization of geometrical reasoning had a consequence
that humans found implausible, the first project would suggest changing the
formalization to more closely comform to the system being modeled; the
second project would suggest using this knowledge to improve human
intuition.

Question:  how would you formalize the geometrical reasoning that allows a
dog to catch a Frisbee?

Michael Thayer