FOM: Chou vs Hersh; intuitionism and building bridges; legal logic

Torkel Franzen torkel at
Mon Mar 2 04:20:20 EST 1998

  Peter White says:

   >Of course we use Boolean logic too (you can hardly design circuits
   >without it) but I am interested in the Intuitionistic philosphy. You
   >have stated it as "the world consists of our own mental constructions",
   >but as an engineer I would state it as "I do not believe you can do
   >it until you can build it".

  This is not quite the intuitionistic philosophy. Intuitionistically,
you would say, rather, "I don't believe you can do it until you show
me how you could, in principle, build it". Thus, for example, a vivid
description of how to build a small planet, set it in orbit around the
Sun at a comfortable distance and turn it into a luxurious resort for tired
mathematicians will set you up in business from the point of view of
intuitionistic engineering.

   If we want to actually build things (or obtain actual numerical
bounds or values or instances in mathematics), we are not necessarily
helped by the intuitionistic philosophy. In practical constructive
work, we are more likely to be opportunists, using whatever methods we
can come by that actually work and yield results. But of course we
also want to have some confidence in these methods, and some would
hesitate to use a fast algorithm proved correct by non-constructive
means. It is such misgivings that intuitionism and other
constructivist schools address, rather than the engineer's hankering
to actually build things and make them work.

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