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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Tue, 30 Sep 2008 11:33:32 -0500
Message-id: <7ECC3CE7-261E-40EB-8A6F-BD1611D59704@xxxxxxx>

On Sep 30, 2008, at 1:25 AM, Rob Freeman wrote:


So Peirce invented both the quincuncial projection and FOL?

Is FOL only useful to people who live in the northern hemisphere too?

No! Please don't justify! I'm sure if the navigator keeps a truer
model of the world in mind, it is possible to make the necessary

Just as when we finally start to look at a more fundamental topology
for meaning it will surely be possible to relate that to one or other
logical simplification at will

If we persist in ignoring the curvature of the Earth in all our
discussions of flat maps, of course, life will appear very puzzling

I don't think there is any danger of logic being "ignored" in this
forum. But I would like to invite those hitherto limited to one or
other logical projection to consider a more fundamental topology for
meaning. Not instead of logic, you understand. Just enough, in the
first instance, to make some of the "intractable" aspects of logic (in
its applications to meaning?) a big more "tractable".

This all sounds very, you know, intriguing, like the blurb on the dustjacket of a fantasy novel. But you never actually tell us what you are talking about, Rob. You just keep making indirect allusions to deep "problems" and hidden "pitfalls" and your preferences for a more "geometric" approach to... well, to something, though Im still not sure what exactly.  And when we challenge you to come out and actually say something, as Chris did, you instantly retreat into a huffy "lets not argue about trifles" stance.  One is inevitably led to guess that you don't actually have anything substantive to say. All you do is stand at the edge of the work site and make sniffy noises about how the foundations are in the wrong place. As one of the workers, I herby invite you to put on a hard hat and actually try doing something. Then we might be willing to take some notice. But until you do, your suggestions to 'consider a more fundamental topology' will fall on - well, not deaf, but closed - ears. 

As a start, what do you actually mean by the phrase 'topology of meaning' ? That sounds great until one actually thinks about it. Topology is a branch of mathematics concerned with structures which are preserved under continuous transformations. So, is your point that at some fundamental level, semantics should be concerned with continuous invariants? If so, how do you deal with the immediate fact that virtually all languages, natural and artificial, are conveyed in media which use a non-continuous "space" of discrete glyphs or syllables, one with only a trivial topology? (BTW, this applies to cartographic maps also.) 

Second, what are some of the "intractable" aspects of logic (in its application to meaning), that give you such pause? Just name a few, in order that we poor blinkered logically trained folk may be able to glance in the right direction in order to perceive the error of our ways. 

Variations of "many-body theory" (e.g. Vector Symbolic Architectures,
Chris Anderson's "Google") offer an interesting solution.

First, tell us what the problem is that these might be solutions to. 


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