SUO: Re: Abstract Syntax & Set Theory
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BA = Bill Andersen
JA = Jon Awbrey
JA: Abstract Syntax
JA: I have noticed people increasingly bandying about
the words "abstract syntax", for instance in the
Conceptual Graph Standard (Working Draft):
JS: http://www.jfsowa.com/cg/cgstand.htm
JA: Also in the CLog papers (sorry, but the identifier "CL" has
long been pre-empted by the subject of "Combinatory Logic"):
BA: Actually, it was pre-empted 15 years ago by "Common Lisp". So what?
That was just banter, but, hysterically spiking,
CombLog beats ComLisp by many decades. We all
belive in unique resource indicia, don't we?
JA: This appears to be a poorly labelled repackaging
of a standard subject in formal language theory --
twenty years ago it was commonly referred to as
"Allied Families of Language" (AFL's), but I'm
sure the name has changed six times since then.
At any rate, an AFL by any other name is just
a category of formal languages, in other words,
a category whose objects are formal languages
and whose arrows are morphisms between them.
I think that this probably puts us outside
the ballpark of the Boys of FOL.
BA: Jon, what's the point of this? Again, so what? Even if this is a
"standard subject in formal language theory", it's work that still
needs to be done, even if it is in your view pedestrian work.
The point is that much of the "work" of reconceptualization has been done and
has been available in the standard literatures and textbooks for decades, and
AFL's were only the application du jour of category theory to problems that
arose in practical settings of programming language design. But too many
folks hereabouts are just not making use of that prior work, out of some
philosphical fixation on pure FOL or whatever, I have given up guessing.
There are lots and lots of not already been chewed problems to work on,
but we will never get to them if we keep to this flat earth logic.
BA: You are aware, I suppose, that the syntax of CL differs significantly
from the standard FOL syntax we all know and love. So, why criticize it?
You should be among the first to applaud such an effort -- if you want
something to criticize, the CL group is giving you a nice, fat,
rigorously defined target to shoot at.
I suppose it all depends on what you mean by "significantly".
For me there is not even the beginning of a new insight there.
And the stuff that is there would get in the way of everything
that I need to think about. The pages of JOSL and NDOFL are just
positivistically rife with barogue variations of this genre, none
of which ever get down to tackling the many outstanding problems
of actually using logic to do anything new and useful in applied,
computational, whether creative or humdrum, practical settings.
BA: Wondering why I bother ...
Unlike you, I have the good
fortune to know why I bother:
I am hopelessly naive.
Gadflown aspects aside, I am naive enough to try and explain why else I bother.
Society needs, for all sorts of reasons, an applied computational practical logic.
This is a thought that occurred to me thirty odd years ago, so I set to work on it.
After many fits and starts, I happened on the surprising discovery that some old dude
had already done about 98% of what was needed, so I set to work on my 2% remainders.
In the time since then, I have learned a few things about how to do this right,
in my testy but testable opinion, and yet, after two years of talking to folks
here, I find people still reinventing Prinicpia Mythematica, and other major
millstones of progress, with all of its incipidly facile misconceits intact.
Worse than that, there is not even the slightest sense anymore
of a lesson that all good programmers learned when I was a child,
of the difference between abstract mush for its own sake and the
kinds of porridge that fortifies us for tasks beyond its own bowl,
namely, the kinds of concrete syntax and efficient algoritnms that
extend our powers to solve problems and to think up brand new ones.
It is crucial for this task to get conscious, painstakingly aware,
of the difference in roles between "signs", implementable syntax,
and "objects", whether they be actual objects, imaginary objects,
or intentional objectives does not matter at the outset, so long
as one appreciates that they occupy a different role than signs,
being for the moment "out there", addressable but not nearly as
controllable, or inexistent in the present frame of reference.
This was standard common sense at one time. The sense of it
appears to be lost hereabouts.
Progress is made by recognizing problems and solving them, bit by bit.
I am oriented toward finding and fixing problems. Problems are always
thrown at us from outside our pet formalisms, hence the name "problems",
so the formalisms have to be able to adapt and evolve. But we inherited
this attitude from the school of atomic analysts that what you do instead
is build a formalism and then pretend that all the problems that it fails
to address are just not important: "You can't say that in here" becomes
its stock answer to just about everything worth saying or thinking about.
Logic is not a language.
Logic is a normative science, a body of critical reflective methods.
Languages are tools for achieving the aims of this formal science.
When the tools get in the way of thinking about what we need to
think about, then the tools have to be refit. CLog ain't it.
I am sorry if this sounds critical in a bad way.
But it's meant to be critical in the best way.
And the problems before us are critical in
the worst way.
Jon Awbrey
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