- From: Jon Awbrey <jawbrey@oakland.edu>
- Date: Mon, 29 Jan 2001 00:24:13 -0500
- To: Arisbe <arisbe@stderr.org>, RDF Logic <www-rdf-logic@w3.org>, SemioCom <semiocom@listbot.com>, Stand Up Ontology <standard-upper-ontology@ieee.org>
- CC: Robert Meersman <Robert.Meersman@vub.ac.be>, Seth Russell <seth@robustai.net>, Matthew West <Matthew.R.West@is.shell.com>, Mary Keeler <mkeeler@u.washington.edu>

¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤ Arisbeans, Resourcerors, SemioComrades, Stand Up Ontologists, | Why is it necessary to reflect on signs? | Why not just talk about the objects alone? | Why not just use signs without mentioning them? I cannot get together a sufficient amount of concentration to even think of dealing with these questions in any kind of a systematic way right now, but I keep being reminded of them by the bits and snatches of commentary that I am able to scan on our various lists, so maybe I can try to chip away at them as I see the different aspects of the problem come up. One thing that my conversation with Matthew brought back to mind was this old but persistent observation of mine that we actually make use of set theory in radically different ways, depending on whether it happens to be sets of objects, in general, or sets of signs, as a special case, on which we are focussed at the moment in question. As for sets of objects in general, being human, we are really greedy, and we tend to chafe at any sorts of prior constraints that might be laid on what we have the power to encompass by our surveys of things. As for sets of signs in that role, being human, we have finite powers to control, to determine, to discern, to fashion, and to resolve them, and so what I have in mind here is the sorts of bounds that we accept in the computational sciences, in contra-distinction from mathematics, where our imagination knows no bounds, comparatively speaking, anyway. Here, if we want to be practical, we constrain the sets of signs that we adopt to the "finitely generated" varieties, like formal languages that are au fond founded on a finite alphabet, lexicon, or vocabulary. It was this "differential deployment" of set theory that I had in mind a while ago when I quoted this observation of a founder of the subject: | That the word "set" is being used indiscriminately | for completely different notions and that this is | the source of the apparent paradoxes of this young | branch of science, that, moreover, set theory itself | can no more dispense with axiomatic assumptions than | can any other exact science and that these assumptions, | just as in other disciplines, are subject to a certain | arbitrariness, even if they lie much deeper here -- | I do not want to represent any of this as something new. | | ~~ Julius König, 1905 Well, I do not want to represent it as anything new, either -- far less so now! -- and I do not believe that the situation with set theory has changed all that much since the days of this subject's first dawn, except for a dubious distinction that the glory of the theory has made us forget how to make such easy and obvious and simple observations. So what!? So I reckon that our failure to distinguish just which column of the sign-theoretic ledger that we are using our set theories "to make book on" or "to keep accounts by", is one of the things that is currently causing the greatest number of failures to communicate in several of the present discussion groups. And I think that a modicum of attention to this "pragmatic" factor, dealing with how the set theory is being set, with what aim, on what basis, in what context, and so on, might just permit us to untangle a few old knots. It Could Happen ... Jon Awbrey Refs: http://ltsc.ieee.org/logs/suo/msg00884.html http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Konig_Julius.html ¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤

Received on Monday, 29 January 2001 00:23:56 UTC