FOM: Visual proofs -- two examples
csilver at sophia.smith.edu
Mon Mar 1 13:20:31 EST 1999
On Mon, 1 Mar 1999, Joe Shipman wrote:
> Moshe' Machover wrote:
> > By a harmless extension of terminology, an outline from which it is clear
> > how a proof in the strict sense can be constructed is also called a "proof".
> > Occasionally, an intuitive explanation why a proposition is true is such
> > that it can be easily converted into a proof. In such cases the intuitive
> > explanation can itself be called a "proof"--again by a harmless extension
> > or abuse of terminology. Examples of such `visual proofs' were given by
> > Shipman. But often an explanation, no matter how *intuitively* persuasive,
> > cannot be so easily converted into a proof.
> You're assuming something I'm not ready to assume yet. The reason I presented
> those two proofs was because I wanted FOMers to elucidate
> 1) what it was about THOSE proofs that made them convincing
> 2) why we are persuaded that the proofs could be "easily converted" into a
> rigorous sentential proof.
What do you mean by a "rigorous sentential proof"?
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