SUO: Re: Common Logic Standard
Jon,
You can't get people from where they are to where you think that
they should be without providing a bridge. The CL standard is such
a bridge. To repeat my previous refrain, it is not sufficient, but
it is necessary.
Jon Awbrey wrote:
> It is not necesary to buy the "philosophy of logic" (POL) that is
> currently packaged with FOL as though indiscernible from it, and it
> is not necessary to stick oneself with the traditional syntax as if
> it makes no difference to both human conceptual clarity and machine
> computational efficiency.
I certainly agree. The CL standard will have no philosophical
assertions of any kind. It will not make any claims about the
conceptual clarity or computational efficiency of one notation or
another. On that topic, it is entirely neutral. Its only purpose
is to provide a model-theoretic semantics for a common abstract
syntax and the grammar rules for several different concrete syntaxes.
And by the way, the basis for model theory was stated by Aristotle,
developed in detail by the medieval Scholastics, and adopted by Peirce
to demonstrate the soundness of his rules of inference for existential
graphs. In his famous paper, Tarski acknowledged Aristotle, but he
had to fight a hard battle against Frege's claim that truth was too
vague a concept to be used as a basis for logic. That is just one
point I make when I try to inform logicians that their subject would
have been much further advanced if Frege and Russell had never existed.
> It has disserved students and society for a hundred years now to keep
> selling them a degraded concrete syntax that renders them incapable
> of tackling any significant problem that logic might be called on
> to help with, all the while vaunting themselves to such heights
> of delusion in their imaginary powers to "express", after the
> fact, the things that others have had to sweat it out to
> discover by almost any other means possible. The only
> kind of necessary condition that you are talking about
> here is the necessary end of an insufficient means.
I agree. That notation, with some minor modifications by Peano,
was Peirce's first method for representing all of first-order
logic. He later discovered a far better system, which he called
his "chef d'oeuvre", and which I have been teaching and preaching
to students for over 20 years.
Whenever I show people Peirce's EGs, they ask "Why didn't they teach
us logic this way in college?" And I have to answer that their poor
benighted teachers had never read the literature of their own specialty.
There is an enormous gulf of ignorance out there, and somehow, one has
to bring people from where they are to a higher plane of consciousness.
But all teaching of any kind must start at the point, for better or
worse, where the students happen to be.
The easiest students to teach are the ones who have never been spoiled
by their teachers. Second best are the students who have been exposed
to logic by inadequate teachers and have come to hate it. If you can
get the attention of those students for at least one hour, you can
lead them to the light.
> Whitehead was pretty much a hapless tag-along, but Wittgenstein had
> a bigger hand in the deal than I ever suspected. In 1913, Russell was
> actually on the point of trying to deal with a number of significant
> issues, like what it means to believe a proposition, when LW's
> lambasting devastated him personally and discouraged him from
> continuing in that direction, never mind that he would have been
> lightyears ahead to read Peirce's work on the topic, at least he was
> trying to break out of Flatopia.
Whitehead was by far the better mathematician, and he viewed his
part of the project as a continuation of his 1898 book _Universal
Algebra_, which is worth looking at for its historical development.
I don't blame him for Russell's errors in the foundations because
he tried to keep them out of the PM entirely (which he did in the
first edition). After Russell produced the second edition in 1925
(which was mostly a correction of typos in the technical parts with
a greatly expanded introduction), Whitehead publicly announced that
he had no part in the revision, and he privately denounced the
introduction as "too Wittgensteinian".
As for Wittgenstein, his first book was an attempt to work out the
foundations of Russell's logical atomism, which he did in an admirably
consistent reductio ad absurdum, and for which he spent the rest
of his life doing penance -- by pointing out the "grave mistakes"
(schwere Irrtuemer) in it.
> As long as you contribute to the impression that "It's all the same
> FOL" in whatever syntax happens to strike the individaul fancy,
> you are not helping to point out the critical differences in POL that
> prevent logic as it is posed today from reconnecting with inquiry in
> the sciences, the humanities, and in everyday problem-solving.
You have to give the devil his due. It is indeed correct to observe
that the expressive power of the first-order parts of Frege's
Begriffschrift, Peirce's algebraic notation, and Peirce's graphs
are logically equivalent. Peirce himself pointed that out many times.
And that is exactly what the CL standard is intended to do.
The task of "reconnecting logic with inquiry..." is extremely
important, but it has no place whatever in an ISO standards document.
The point of the document is to demonstrate a fact that most logicians
and computer scientists are not aware of: an algebraic notation and
a graph notation can have identical expressive power. Just getting
that point through their pointy little heads is a major victory.
And until you drive that point home, you can't even get their
attention on any more substantive issue.
> A hundred years of wasted time and effort have shown it.
> There is no choice but going back to the viable sources,
> of which Peirce provides us with just one of several.
I certainly agree. But you can't lead people back to the source
by making them so angry that they install email filters that send
your messages to the trash bin.
John Sowa