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.

  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  %%  Moshe' Machover                 | E-MAIL: moshe.machover at kcl.ac.uk %%
  %%  Department of Philosophy        | FAX (office)*: +44 171 873 2270  %%
  %%  King's College, London          | PHONE (home)*: +44 181 969 5356  %%
  %%  Strand                          |                                  %%
  %%  London WC2R 2LS                 |  * If calling from UK, replace   %%
  %%  England                         |    +44 by 0                      %%
  %%  http://www.kcl.ac.uk/kis/schools/hums/philosophy/staff/moshem.html %%
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%





More information about the FOM mailing list