An ark built of straight logs cut with equilateral triangular cross
sections would be hard to build and more difficult to build than
necessary. Construction would be easier with quads and the design
would be more flexible. (01)
Sounds like the SW. (02)
-- doug (03)
On Wed, November 10, 2010 3:43, Godfrey Rust said:
> 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 -----
> From: Alex Shkotin
> To: [ontolog-forum]
> 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 .
>
>
> But as Kronecker said in 1886, "Die ganzen Zahlen hat der liebe Gott
> 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
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
>
>
>
> ______________________________________________________________________
> This email has been scanned by the MessageLabs Email Security System.
> For more information please visit http://www.messagelabs.com/email
> ______________________________________________________________________
>
>
>
> ------------------------------------------------------------------------------
>
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
> Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
> Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
> Shared Files: http://ontolog.cim3.net/file/
> Community Wiki: http://ontolog.cim3.net/wiki/
> To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
> To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx
> (04)
=============================================================
doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (05)
"I speak as an American to the leaders of my own nation. The great
initiative in this war is ours. The initiative to stop it must be ours."
- Dr. Martin Luther King Jr.
============================================================= (06)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (07)
|