On Sat, Dec 15, 2007 at 09:29:00AM -0800, Dennis Thomas wrote:
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It seems to me that as valid as mathematics may be for the purposes of engineering, architecture, other worldly purposes, and as a tool for analytical thinking, that it's requirement for self-consistency automatically negates its capacity to faithfully model the natural universe and its ever changing landscape.
Well, just about anything can "seem" to be true if you don't submit it to evidence, analysis, or argument. The only idea here in danger of being "automatically negated" is your unargued suggestion that "faithfully" modeling the natural universe requires some sort of (non-mathematical?) system that can tolerate inconsistency. You further hint that this has something to do with change. There is a vast literature on the logical representation of time, change, causation and dynamic information generally. Are you unaware of this? Or do you actually have arguments that demonstrate convincingly (or that even vaguely suggest) that (a) none of the current approaches to dynamic information can "faithfully model the natural universe" and (b) the reason for this is the "requirement for self-consistency" in mathematics? Indeed, can you even *say* what you mean by the requirement for self-consistency? And are you aware that, in fact, there are rigorous mathematical systems designed to tolerate inconsistency?
As indicated by the previous comments and articles, imagery and its co-partner imagination, trump mathematics.
Ontology is a (nascent) engineering science. Mathematical logic is the mathematical foundation of ontological engineering. It is no more "trumped" by imagery and imagination than is the calculus "trumped" by them in physics or mechanical engineering. These are utterly orthogonal. Imagery and imagination play critical roles in solving problems in physics, mechanical engineering, and ontology alike. It is mathematics that then provides the means to turn images and imaginings -- our *ideas* -- into theory and thence into concrete solutions to real problems. This talk of the one trumping the other is nothing short of a retreat to mysticism.
So isn't the quest for universal ontological formalism in the face of 215 industries that operate within and across 200 recognized countries that speak at least 80 different languages, all idiosyncratic and all evolving, presents a similar problem for ontologists?
No one is looking for a universal ontological formalism.
Can it be that 100% reliance upon self-consistent logic can ever be the foundation for formal ontologies, when logic automatically precludes human enculturation, beliefs and values?
This reminds me of an ad I once saw in college. I don't recall what it was an ad for, but it consisted of a picture of Einstein with the caption: "With the cold certainty of mathematics, Einstein proved that we live in a world of relative values."
The comment above exhibits the same confusion. Logic no more precludes belief and values than it precludes, say, enjoying your morning coffee. Logic is a tool, a powerful means to represent information and to reason with it formally -- anything that can be expressed in language, including our most cherished beliefs and values, can be represented in logic. (Indeed, there is a very large literature on *logics* of belief.) The challenge is to get those representations right and to be able to share and extract information from them efficiently given certain inherent computational limitations to automated reasoning.
A lot in this thread seems to me to stem from simple ignorance of what mathematical logic is and of its foundational role in ontological engineering.
Chris Menzel
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