FOM: geometric proof (fwd)
Charles Silver
csilver at sophia.smith.edu
Tue Feb 23 07:48:40 EST 1999
On Mon, 22 Feb 1999, Moshe' Machover wrote:
> 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.
In a way, a diagrammatic proof could be thought of as actually
being a *better* proof. For, it shows that the actual subject matter in
the proposition to be proved doesn't really matter. The same diagram
could be used to prove any one of a number of isomorphic propositions with
differing content. Doesn't this make a diagrammatic proof "better"?
Charlie Silver
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