FOM: Boolean algebra vs Boolean ring

Stephen G Simpson simpson at
Tue Mar 10 18:04:34 EST 1998

Vaughan Pratt writes:
 > From: Stephen G Simpson 1/31/98 4:04PM
 > >Note first that Boolean algebras are not isomorphic to Boolean rings.
 > This is only true for those who find the distinction useful, which
 > many people don't. 

And we might also say that the above statement of Pratt is only true
for those who identify "truth" with "that which I find useful".
(Pragmatist politicians?)  :-)

Seriously, my statement about Boolean algebras vs Boolean rings is
true (for everybody!), and the distinction is useful for all
mathematicians.  If we adopt a "what's true for you isn't necessarily
true for me" standpoint (i.e. a solipsist philosophy), we will never
be able to have a rational discussion.

Despite the rampant subjectivism inherent in Vaughan Pratt's comments,
I'm going to patiently try to continue the discussion:

Vaughan, you have made a rather confusing statement.  And I suspect
that you made it deliberately, in order to confuse the issue.  In
order to try to untangle this, and to make sure there is some basis
for rational discussion, let's go back to standard mathematics that we
should all be able to agree on.  For a start, could you please state
your definitions of Boolean ring and Boolean algebra?  After you have
stated them, I'll compare them with definitions that are usual in
textbooks.  And we'll try to come to some agreement.  After that,
we'll examine whether they are isomorphic.

-- Steve

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