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

Stephen G Simpson simpson at
Sat Feb 28 22:25:34 EST 1998

I welcome Ching-Tsun Chou's posting of 27 Feb 1998 20:06:39.  To my
way of thinking, we FOMers need more of Chou's applications-oriented
or engineering perspective.  In my posting of 26 Feb 1998 21:20:44 I
criticized intuitionism and constructivism, but my comments also
apply, mutatis mutandis and in spades, to Hersh's social
constructivist variant.  (Of course I do not mean to imply that
Hersh's ideas have anything like the coherence and fruitfulness of
those of Brouwer and Bishop.)

Vaughan Pratt 27 Feb 1998 06:47:40 wrote:

 > Double negation as a transformation is much more than formalism.

I think that Vaughan misunderstood my points in 26 Feb 1998 21:20:44
about philosophical motivation.  I concede that the double negation
transform is well motivated from the viewpoint of intuitionistic
logic, in much the way that Vaughan said.  My point was a different,
more philosophical one.

My point in a nutshell was that philosophical constructivism ("the
world consists of our own mental constructions") is incompatible with
philosophical realism ("the world exists independently of and prior to
our consciousness of it").  And I believe this is one reason why
intuitionistic mathematics has been received less than
enthusiastically by bridge-builders and professional mathematicians.
Another, perhaps related, reason is that intuitionist and
construcivist theorem formulations are often clumsy compared to
classical ones.

Vaughan wrote:

 > It has been my impression from having dealt with a lot of lawyers
 > over the last twenty years that the logic of the legal profession
 > is rarely Boolean, 

Interesting!  This came up a couple of weeks ago when I was having
dinner at a truly pleasant restaurant called Biribisi (near one of the
train stations in Torino, Italy) with a group of people including the
category theorist Benson.  I pointed out that, in modern high-profile
US trials such as cousin O.J.'s, when the lawyers say that their
client is "not guilty", they are not claiming that their client didn't
commit the crime.  They are merely claiming that they have methods for
undercutting any purported proof that he committed it.  (One of the
methods used in the O.J. trial was jury selection.)  Legal logic may
indeed be in a sense intuitionistic, because in a courtroom the mental
state of the jurors and the rules of evidence and other procedures may
sometimes matter more than the truth.  Benson had a good laugh at
this.  He also said that "not proven guilty" is an allowable verdict
in some Scottish legal code.  All this was after a few bottles of

Vaughan wrote:

 > Boolean logic is a Procrustean bed of a particularly constraining
 > kind.

Perhaps classical logic is somewhat constraining.  But is this bad?
Lawyers deal with proof and rules of evidence, pollsters deal with
public opinion, but bridge-builders et al deal with truth and facts
and therefore accept classical laws such as Av~A.  Aren't you glad
they do?  For instance, Ching-Tsun Chou (posting of 27 Feb 1998
20:06:39) is an engineer at Intel.  Aren't you glad that Chou uses
Boolean logic and classical mathematics?  Do you think the Pentium
chip would work if the Intel engineers switched to some other kind of
logic and/or mathematics?

-- Steve Simpson

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