Re: SUO: Mutual Admiration Society
Pierluigi,
I certainly grant that the technical developments in logic made
a lot of progress in many respects during the 20th century.
However, the main issue is the enormous lack of progress in
many other areas:
1. Education in universities: From the middle ages to the 19th
century, logic was the first of the seven liberal arts. It was
taught to every college freshman (at least at the level of
Aristotle's syllogisms. Today, 90% of all college students have
no exposure to any form of logic, and of the remaining 5%, the
overwhelming majority have developed either an intense dislike
or at best a dismissive indiference to the notation that they
were forced to study. The tiny minority (such as you and I)
who liked the subject anyway, were able to learn it despite
all the obstacles that were put in our path.
2. Even among those people who have mastered the technical subject,
the overwhelming majority cannot map a few simple sentences from
their native language into predicate calculus notation. As you
very well know, your boss, Doug L., administers a test to all
applicants for a position your company, and everyone, even
professors of logic, are required to map some English sentences
into logic -- and the overwhelming majority of them fail the
test. Even the professors don't fully understand their own
subject.
3. And those of us who have been working to promote the use of logic
in AI and computer science in general have to fight a very strong
uphill battle against the entrenched gulf of ignorance. When I was
at IBM, I was teaching and promoting the use of Prolog. I made
quite a few converts to it, but the overwhelming attitude at IBM
was no different from the overwhelming attitude at every other
major computer systems group (in business and in universities).
Some people, such as Ted Codd, the chief promoter of relational
databases, said that he wished he had invented Prolog. But the
main DB people had already chosen SQL, which is undoubtedly one
of the worst notations for logic ever invented. Some human factors
people tested SQL against an even worse notation, and it proved
to be somewhat better -- but that is not saying much.
PM> Even "pedagogically," there seems to have been no special difficulty
> for people to handle Frege-Peano-Hilbert's "far worse" systems:
> consider the development of logic between 1879 and 1936 (the year
> without which the term 'computer science' would be non-denoting), and
> the decades since. A lot of people on several continents seem to have
> had no trouble learning what they wanted to learn.
You should delete Frege's name from that list, since nobody ever used
his notation. Hilbert used Peirce's algebraic notation, and Peano
merely changed the symbols to develop his notation. Peano gave full
credit to Peirce as the inventor of the notation, and he wrote a very
negative review of Frege's publication. That started a correspondence
between Frege and Peano, in which Frege started to reply using his own
Begriffsschrift. But Peano insisted that Frege translate it into the
algebraic form because he declared Frege's form "unreadable".
The major work in Germany had been done with Peirce's notation for
many years by Schroeder, Hilbert, Zermelo, Loewenheim, and many others.
Even today, Polish notation uses Peirce's symbols Pi and Sigma for the
quantifiers instead of Peano's symbols. When the Principia Mathematica
came out in 1910, the Germans were very unimpressed, since they had made
much further progress based on the work of Peirce and Schroeder.
Frege had no influence on that work because the major logicians
and mathematicians (Hilbert & Co.) didn't agree with his philosophy,
and they didn't like his notation.
Bottom line: Logicians today are still using Peirce's first notation
for logic (1880, 1883, 1885 -- see the references in the bibliography
at www.jfsowa.com/bib.htm ). Anyone who uses that notation should
at least take a look at what inventor thought was a better system.
John Sowa