Re: On FOM, free Boolean algebras are semantic, not syntactic

Re: On FOM, free Boolean algebras are semantic, not syntactic

[Michael Barr]

[Note from moderator: with apologies for intervening twice in one day,
I'll forward Mike's note with thanks and the information that the list
will be untended until Sunday. That the categories list is lively is a
reflection of its many excellent contributors. The moderation consists
almost entirely of deciding which conference announcements are of at least
some interest. To be precise we've been operating for 10001 internet years
- just getting going.]

Let me second Vaughan's commendation of Bob.  I don't think it has been
two decades quite (maybe 15 years) but of all the mailing lists I am aware
of this is the one that is most vigorous and useful.  Most seem to have
fallen into disuse and Vaughan reports on another one that seems to be too
tightly moderated.  I don't actually know if Bob really moderates them but
this one is the best I have seen.

Michael

On Tue, 2 Oct 2007, Vaughan Pratt wrote:

>
> [Note from moderator: Thanks Vaughan...]
>
> This is a short note to express my appreciation for Bob Rosebrugh's
> quiet but effective management of this list over a great many years (are
> we up to two decades yet, Bob?)  When things have been going swimmingly
> long enough it becomes hard to picture what an alternative universe
> might have been like.
>
> But not impossible.  A few days ago I signed up again for the
> Foundations of Mathematics mailing list after many years away from it,
> thinking that maybe it had improved since I left it.
>
> When someone posted a message claiming that well-formed formulas needed
> to be presented inductively and that this requirement was giving him
> great angst, and someone else responded with a pointer to a 61-page
> paper explaining how to define syntax using category theory, I responded
> with a contrarian post, illustrated with a short definition of wff using
> only sets, inclusion, functions, and linear orders, with no mention of
> induction.  Central to the definition was the notion of wff as a
> function 2^P --> 2, recognizable as an element of the free Boolean
> algebra on P (here the set of predicates appearing in the wff) but
> without actually saying "free Boolean algebra."
>
> My post was rejected for submission on the ground that it was "deemed
> inappropriate by the moderator," with the further explanation that I was
> "confusing the entirely syntactic notion of formula with semantic notions."
>
> Either the (anonymous) moderator has never seen a representation of a
> free Boolean algebra, or views all algebras including the free ones as
> semantics and hence unfit for posting on FOM in connection with the
> definition of wff.
>
> A slightly more convincing ground for rejection might have been that
> 2^X --> 2 is the set of terms at X of the monad for Boolean algebras,
> and that anyone familiar with the Kleisli construction would see right
> away that I was just trying to disguise the associated inductive
> definition of wff by semantic smoke and mirrors.  To which I would have
> responded first with Sol Feferman's question, "What rests on what?", and
> second with "It was you who picked the initial adjunction for that
> monad, how do you know I didn't have the final one in mind?"
>
> Had the anonymous moderator at least mentioned Kleisli we might have had
> a basis for debating the appropriateness of the rejection on such
> grounds, though it becomes unpleasant to have to spend more time
> defending a submission to a faceless moderator than writing it in the
> first place.
>
> Absent such I concluded that FOM had fallen into ignorant hands, making
> it little more than a time sink for MOPDAL21, Members Of the Project to
> Drag Archaic Logic into the 21st century.  With such decisions, those of
> FOM's moderators still having a reputation to maintain would do well to
> keep their rejection messages anonymous.
>
> So again, thank you Bob for making this list an enjoyable free-for-all
> of ideas.  Things would have been less fun if you'd decided that
> anything outside the scope of CTWM was heresy unfit for posting.
>
> And thank you for *never* telling me I'm confused.  Even though you may
> have suspected it on many occasions, some even apparent to me.
>
> Vaughan Pratt
>
>

On FOM, free Boolean algebras are semantic, not syntactic

[Vaughan Pratt]

[Note from moderator: Thanks Vaughan...]

This is a short note to express my appreciation for Bob Rosebrugh's
quiet but effective management of this list over a great many years (are
we up to two decades yet, Bob?)  When things have been going swimmingly
long enough it becomes hard to picture what an alternative universe
might have been like.

But not impossible.  A few days ago I signed up again for the
Foundations of Mathematics mailing list after many years away from it,
thinking that maybe it had improved since I left it.

When someone posted a message claiming that well-formed formulas needed
to be presented inductively and that this requirement was giving him
great angst, and someone else responded with a pointer to a 61-page
paper explaining how to define syntax using category theory, I responded
with a contrarian post, illustrated with a short definition of wff using
only sets, inclusion, functions, and linear orders, with no mention of
induction.  Central to the definition was the notion of wff as a
function 2^P --> 2, recognizable as an element of the free Boolean
algebra on P (here the set of predicates appearing in the wff) but
without actually saying "free Boolean algebra."

My post was rejected for submission on the ground that it was "deemed
inappropriate by the moderator," with the further explanation that I was
"confusing the entirely syntactic notion of formula with semantic notions."

Either the (anonymous) moderator has never seen a representation of a
free Boolean algebra, or views all algebras including the free ones as
semantics and hence unfit for posting on FOM in connection with the
definition of wff.

A slightly more convincing ground for rejection might have been that
2^X --> 2 is the set of terms at X of the monad for Boolean algebras,
and that anyone familiar with the Kleisli construction would see right
away that I was just trying to disguise the associated inductive
definition of wff by semantic smoke and mirrors.  To which I would have
responded first with Sol Feferman's question, "What rests on what?", and
second with "It was you who picked the initial adjunction for that
monad, how do you know I didn't have the final one in mind?"

Had the anonymous moderator at least mentioned Kleisli we might have had
a basis for debating the appropriateness of the rejection on such
grounds, though it becomes unpleasant to have to spend more time
defending a submission to a faceless moderator than writing it in the
first place.

Absent such I concluded that FOM had fallen into ignorant hands, making
it little more than a time sink for MOPDAL21, Members Of the Project to
Drag Archaic Logic into the 21st century.  With such decisions, those of
FOM's moderators still having a reputation to maintain would do well to
keep their rejection messages anonymous.

So again, thank you Bob for making this list an enjoyable free-for-all
of ideas.  Things would have been less fun if you'd decided that
anything outside the scope of CTWM was heresy unfit for posting.

And thank you for *never* telling me I'm confused.  Even though you may
have suspected it on many occasions, some even apparent to me.

Vaughan Pratt