In any discussion such as this one, lest the discussion just spin out of control (which gives everybody a giddy sense of whizzing around but eventually gets nowhere) we have to understand which definition of ambiguity we are working with.
I suggested that we work with Byers's. The is nothing coarse about Byers ambiguity. To be ambiguous in Byers sense, a situation must include two well articulated ideas that are mutually antogonistic but bound together in the same well articulated system of thought. To have achieved Byers-ambiguity is to have clarified a lot. N Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University ([email protected]) http://home.earthlink.net/~nickthompson/naturaldesigns/ http://www.cusf.org [City University of Santa Fe] > [Original Message] > From: glen e. p. ropella <[email protected]> > To: The Friday Morning Applied Complexity Coffee Group <[email protected]> > Date: 12/29/2009 4:49:08 PM > Subject: Re: [FRIAM] ambiguity and mathematics > > Quoting ERIC P. CHARLES circa 09-12-29 11:09 AM: > > Well, of course, all of this (Glen and Nick's posts) is ignoring the obvious > > fact that ambiguity is the antithesis of mathematics. > > That's just not the case. Mathematics easily captures the concept of > ambiguity. Hence, ambiguity can't be the antithesis of math. Math is a > language. Languages describe. All languages can be reflective > (circular). In English, we can describe circularity with sentences > like: "This sentence is false." In math, we can describe circularity > with sentences like: "Let X = {a,b,X}." Ambiguity is, formally, just a > type of circularity. In generic circularity, the evaluation of some > predicates on X is undefined. In ambiguous cases, the evaluation of > those predicates simply have multiple values. I.e. the mapping is 1 to > many. > > This isn't, in any interpretation, the antithesis of math. It is well > described by math, less well described by English. > > > So, how do we > > reconcile claims that ambiguity is at the heart of mathematics with the obvious > > truth that mathematicians really like producing, teaching, and preaching about > > unambiguous things? > > Because math is a _means_ not an _end_. Ambiguity is at the heart of > math because math is our attempt to disambiguate the ambiguous ... to > refine what is coarse ... to peek into the little nooks and crannies > created by our prior theorems. > > > Also, re Glen's post specifically, I think there is value in discriminating > > between accidental and intentional ambiguity. Not all claims of ambiguity is > > are claims of ignorance, sometimes situations are actually ambiguous and > > therefore claims of ambiguity are claims of knowledge. > > Again, I have to disagree. All claims of ambiguity are statements of > ignorance. Granted, we can whittle away at the ignorance and refine the > ambiguity to a very fine point (which is what Rosen does). But in the > end, ambiguity ... as Byer's and the rest of us use the term [grin] ... > means "We don't know what makes it take value X as opposed to value Y in > this evaluation." > > A great example is the square root of 4. There are 2 answers: 2 and -2. > In order to know whether the answer is 2 or -2, we need more > information. I.e. we're too ignorant to answer that question. > > > For an example of the latter, we > > might ask whether George W.'s "Free Speech Zones" were protecting people's > > freedom of speech. One possible answer to that question, one that expresses a > > good understanding of the situation, NOT severe ignorance, might be "In some > > ways it technically was, but in other ways it severely undermined freedom > > speech, so the situation is ambiguous." On a lighter note, many jokes an > > innuendo take advantage of ambiguity, and if you don't think the situation is > > ambiguous, you won't get it. For example, I once shot an elephant in my > > pajamas..... what he was doing in my bedroom I'll never know. > > It's still a statement of ignorance, though perhaps not of _severe_ > ignorance. As I said before, the use of the word "ambiguity" may well > be taken as a methodological point, not an ontological or > epistemological one. Whether "Free Speech Zone" evaluates as "protect" > xor "undermine" is definitely an expression of ignorance. Ultimately, > due to our lack of understanding of the social processes involved, we > can't state for sure whether it is one or the other. Further, we can't > even state that the two are disjoint! Perhaps one MUST undermine > freedom of speech in order to protect freedom of speech, in some > circumstances? The point is that we don't know. We are ignorant. > > In the case of shooting an elephant in pajamas, again, it's a statement > of ignorance. We can resolve it by 1 question: "Was the elephant > wearing your pajamas?" Prior to the answer, it's ambiguous. Post > answer, it's not. > > -- > glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
