FOM: ordered pair: Bourbaki

Martin Davis martin at
Mon May 3 15:14:59 EDT 1999

At 07:18 PM 5/2/99 EDT, Vedasystem at wrote:

> The Bourbaki's approach to introducing notation
>for ordered pair is preferable because one cannot prove
>silly theorems like (x,y) U {x} =  (x,y).
>The Bourbaki's approach is related to abstract data types --
>the most fundamental concept on which the modern programming
>languages like Java, C++, Eiffel are based.
>Victor Makarov, Brooklyn.

Abstract data types are fine so long as concrete implementations are
possible. And once you choose a particular implementation, extraneous
irrelevant facts will appear.

It would not be difficult to produce inconsistent abstract data types.

So Makarov's analogy is fine, but he draws the wrong moral.

                           Martin Davis
                   Visiting Scholar UC Berkeley
                     Professor Emeritus, NYU
                         martin at
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