FOM: geometric proof (fwd)
Moshe' Machover
moshe.machover at kcl.ac.uk
Mon Feb 22 15:55:37 EST 1999
At 10:32 am -0700 21/2/99, Reuben Hersh wrote:
>A proof by diagram is holistic, it gives an insight or a grasp into the
>
>whole theorem. It is more likely to be understood, remembered, and used
>in
>
>further problem solving or research than a very detailed logical argument
>
>that is impossible to keep in mind at once.
>
>Logic and diagrams supplement each other. There's no competition unless
>one
>
>takes on an imperialistic attitude that says, my way or nothing.
The trouble with a `proof' by diagram is that it is not at all clear *what
proposition* is being proved.
At best, a `proof' by diagram can perhaps establish that *if conditions
such as those exemplified by the diagram hold* then such and such a
consequence follows. But what are those conditions?
In other words, a `proof' by diagram `proves' A --> B but doesn't tell us
what A is.
It is thereore not a proof at all, but may be a useful tool for discovering
the right--or some reasonable--conditions A under which A --> B can really
be proved.
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