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And it rained logics for 40 days and nights. And
God said unto his servant Berners-Lee, "Build you an ark made of
triples..."
----- Original Message -----
Sent: Wednesday, November 10, 2010 8:04
AM
Subject: Re: [ontolog-forum] Fwd:
Breaking News: Google supportsGoodRelations
JS: "Bottom line: God made FOL, and Peirce was his
prophet."
Under bottom line: And people prove theorem that the tower of
Babel may be build. And begin they. And God punish them by
NLs.
Alex
2010/11/10 John F. Sowa <sowa@xxxxxxxxxxx>
Patrick,
That paper isn't available on the WWW:
> Well, but for a non-burning bush origin for FOL, see:
Ferreirós, José > (2001), "The Road to Modern Logic-An
Interpretation", Bulletin of > Symbolic Logic 7 (4): 441–484,
doi:10.2307/2687794, > http://jstor.org/stable/2687794 .
gemacht,
alles andere ist Menschenwerk". [The dear God made the
whole numbers,
everything else is the work of man.]
I believe that one can make a
very strong case that FOL can be
considered the equivalent for logic as
the natural numbers for
mathematics. It is a subset of every
natural language, and it
is simpler to specify than any of its
subsets.
In any case, the paper you cited is not available on the
WWW. But the
abstract seems to discuss the work that Peirce did in
the years from
1897 to 1906, but everybody else ignored:
>
Among the latter, one may emphasize the spirit of modern axiomatics,
>
the situation of foundational insecurity in the 1920s, the resulting
>
desire to find systems well-behaved from a proof-theoretical point
>
of view, and the metatheoretical results of the 1930s. Not
surprisingly,
> the mathematical and, more specifically, the
foundational context in
> which Firs-Order-Logic matured will be seen
to have played a primary
> role in its shaping.
First of all,
FOL was born mature in the versions by Frege and Peirce.
It is true that
Frege had a better formalized axiomatization in 1879
than Peirce had in
1885. But their versions are equivalent to every
version invented
since then.
I certainly agree that the axiomatization by Frege, a
version of
which Whitehead and Russell adopted for PM, was not bad for
1879,
but it was horribly cumbersome. And the version presented in
PM
probably made more people hate logic than any other system
ever
inflicted on poor, innocent students.
But in 1897, Peirce
developed the existential graphs, which have
the simplest axiomatization,
proof procedure, and model theory
ever discovered:
1. The
only axiom for EGs is a blank sheet of paper, and Peirce's
rules of inference are a streamlined version of natural deduction,
which Gentzen invented over 30 years later.
2. Peirce
also invented a very simple and elegant model theory for
EGs, which he called _endoporeutic_ (for outside-in evaluation).
Nobody understood Peirce's endorporeutic until Hintikka's
student Pietarinen showed that it was a version of Game
Theoretical Semantics.
3. Every other common
axiomatization and proof procedure invented
for FOL can be
shown to be derived theorems or derived rules
of inference
from Peirce's system.
4. But as Frithjof Dau showed, Peirce's
rules are strictly more
powerful than the other common
proof procedures: certain proofs
that take exponential time
with those methods can be proved
in polynomial time with
Peirce's rules. (The case he showed
was for cut-free
proofs with Gentzen's clauses, but there
would be similar
kinds of proofs for other cases as well.)
For a brief summary of
Peirce's system, see his own tutorial:
http://www.jfsowa.com/peirce/ms514.htm
Bottom line:
God made FOL, and Peirce was his prophet.
John
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