From: Christopher Menzel <cmenzel@tamu.edu>

Date: Wed, 01 Aug 2007 11:05:10 -0500

To: "[ontolog-forum] " <ontolog-forum@ontolog.cim3.net>

Cc: SW-forum <semantic-web@w3.org>

Message-id: <673338F5-DC2B-408F-A1ED-648ACF8B55BA@tamu.edu>

Date: Wed, 01 Aug 2007 11:05:10 -0500

To: "[ontolog-forum] " <ontolog-forum@ontolog.cim3.net>

Cc: SW-forum <semantic-web@w3.org>

Message-id: <673338F5-DC2B-408F-A1ED-648ACF8B55BA@tamu.edu>

> Duane: > You are right. This goes to the heart of the issue of "vicious > circularity" that Whitehead and Russell had thought was sorted with > Principia Mathematica, No, actually, the vicious circularity of which Russell (mostly) and Whitehead spoke didn't have anything whatever to do with whatever it was that Duane was talking about. The so-called Vicious Circle Principle, which was implemented in the ramified type theory of Principia Mathematica, put constraints on the acceptable range of the quantifiers in a class definition, and its purpose was the avoidance of semantic paradoxes like the Liar Paradox and Richard's Paradox. (Basically, the VCP placed the blame for the paradoxes on the use of nonconstructive class definitions in which quantifiers ranged over the very classes of which the classes being defined were themselves members. Such definitions are in fact ubiquitous (and generally quite harmless) in classical mathematics.) > until Kurt Gödel came along and demolished their shiny, perfect, > world. I will have to disagree. In fact, Gödel's results didn't really have any particular bearing on the central philosophical motivations of Principia Mathematica, viz., the avoidance of semantic paradox, which PM managed to do quite well. It was in fact Ramsay who had already shown several years before Gödel's 1931 paper that PM was an inadequate foundation for classical mathematics unless it adopted a very unintuitive principle known as the Axiom of Reducibility. And even then, to my knowledge, Russell and Whitehead never claimed that PM would provide a logically *complete* foundation for mathematics. Gödel's theorems had a far greater impact on Hilbert's program, which (somewhat anachronistically put) explicitly sought a complete, consistent, computationally decidable foundation for all of mathematics. Gödel's work did effectively show that goal to be unattainable in principle even for elementary arithmetic, let alone all of mathematics, and its implications are directly relevant to the goals of modern computational ontology. -chris > An ontology is not just some self-referencing and self-sustaining > model that is somehow "complete"; it points out to the real world, > as you rightly say. > > > Peter > > -----Original Message----- > From: ontolog-forum-bounces@ontolog.cim3.net [mailto:ontolog-forum- > bounces@ontolog.cim3.net] On Behalf Of Duane Nickull > Sent: 31 July 2007 16:05 > To: [ontolog-forum]; John F. Sowa > Cc: 'SW-forum' > Subject: Re: [ontolog-forum] Current Semantic Web Layer Cake > > On 7/31/07 12:46 PM, "Azamat" <abdoul@cytanet.com.cy> wrote: > >> The real semantics or meanings of any symbolism or notation is >> defined by >> ontology; for this is the only knowledge domain studying the Being of >> Everything which is, happens and relates. > > Not trying to start a nit picky argument, but I had always thought > that real > semantics are defined by how a term is used and what it is linked > to in a > physical world (which of course can be captured and expressed in an > ontology). Otherwise any ontology is just a huge circular > reference (like > the english dictionary when void of any grounding. > > How can one define and convey the true meaning of spicy food, heat, > pain etc > without the corresponding grounding experience? > > DuaneReceived on Wednesday, 1 August 2007 16:06:14 UTC

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