Posts Tagged ‘fuzzy logic’
From time to time I receive invitations to contribute to various “encyclopedias.” Recent examples include an entry on “confidence intervals” in the International Encyclopedia of Statistical Science (Springer, 2010) and an entry on “uncertainty” in the Encyclopedia of Human Behavior (Elsevier, 1994, 2012). The latter link goes to the first (1994) edition; the second edition is due out in 2012. I’ve duly updated and revised my 1994 entry for the 2012 edition.
Having been raised by a librarian (my mother worked in the Seattle Public Library for 23 years), I’m a believer in the value of good reference works. So, generally I’m willing to accept invitations to contribute to them. These days there is a niche market even for non-digital works of this kind, and of course the net has led to numerous hybrid versions.
Despite the fact that such invitations are regarded as markers of professional esteem, they don’t count for much in the university system where I work because they aren’t original research publications. Same goes for textbooks. Thus, for my younger academic colleagues, writing encyclopedia entries or, worse still, writing textbooks actually can harm their careers. They understandably avoid doing so, which leaves it to older academics like me.
Some of these encyclopedias have interesting moments on the world stage. The International Encyclopedia of Statistical Science has been said to have set a record for the number of countries involved (105, via the 619 contributing authors). Its editors were nominated for the 2011 Nobel Peace Prize, apparently the first time any statisticians had received this honor. Meanwhile, V.S. Ramachandran, editor of the Encyclopedia of Human Behavior, was selected by Time Magazine as one of the world’s most influential people of 2011.
However, I digress. The Sage Encyclopedia of Philosophy and the Social Sciences is an intriguing proposal for a reference work that bridges these two intellectual cultures. I regard this aim as laudable, and I’m fortunate insofar as the areas where I work have a tradition of dialogs linking philosophers and social scientists. So, I was delighted to be asked to provide an entry on “agnotology, ignorance and uncertainty”. There is, however, a bit of a catch.
The guidelines for contributors state that “Entries should be written at a level appropriate for students who do not have an extensive background either in philosophy or the social sciences and for academics from other disciplines… it is essential that a reader versed in philosophy only or mostly, or alternatively, in social sciences, should gain by reading entries that aim at expanding their knowledge of concepts and theories as these have developed in the complementary area.” All of this is supposed to be achieved for a treatment of “agnotology, ignorance and uncertainty” in just 1,000 words, with a short list of “further readings” at the end. All of my posts in this blog thus far exceed 1,000 words (gulp). Can I be sufficiently concise without butchering or omitting crucial content?
Here’s my first draft (word count: 1,018). See what you think.
AGNOTOLOGY, IGNORANCE AND UNCERTAINTY
“Agnotology” is the study of ignorance (from the Greek “agnosis”). “Ignorance,” “uncertainty,” and related terms refer variously to the absence of knowledge, doubt, and false belief. This topic has a long history in Western philosophy, rooted in the Socratic tradition. It has a considerably shorter and, until recently, sporadic treatment in the human sciences. This entry focuses on relatively recent developments within and exchanges between both domains.
A key starting-point is that anyone attributing ignorance cannot avoid making claims to know something about who is ignorant of what: A is ignorant from B’s viewpoint if A fails to agree with or show awareness of ideas which B defines as actually or potentially valid. A and B can be identical, so that A self-attributes ignorance. Numerous scholars thereby have noted the distinction between conscious ignorance (known unknowns, learned ignorance) and meta-ignorance (unknown unknowns, ignorance squared).
The topic has been beset with terminological difficulties, due to the scarcity and negative cast of terms referring to unknowns. Several scholars have constructed typologies of unknowns, in attempts to make explicit their most important properties. Smithson’s book, Ignorance and Uncertainty: Emerging Paradigms, pointed out the distinction between being ignorant of something and ignoring something, the latter being akin to treating something as irrelevant or taboo. Knorr-Cetina coined the term “negative knowledge” to describe knowledge about the limits of the knowable. Various authors have tried to distinguish reducible from irreducible unknowns.
Two fundamental concerns have been at the forefront of philosophical and social scientific approaches to unknowns. The first of these is judgment, learning and decision making in the absence of complete information. Prescriptive frameworks advise how this ought to be done, and descriptive frameworks describe how humans (or other species) do so. A dominant prescriptive framework since the second half of the 20th century is subjective expected utility theory (SEU), whose central tenet is that decisional outcomes are to be evaluated by their expected utility, i.e., the product of their probability and their utility (e.g., monetary value, although utility may be based on subjective appraisals). According to SEU, a rational decision maker chooses the option that maximizes her/his expected utility. Several descriptive theories in psychology and behavioral economics (e.g., Prospect Theory and Rank-Dependent Expected Utility Theory) have amended SEU to render it more descriptively accurate while retaining some of its “rational” properties.
The second concern is the nature and genesis of unknowns. While many scholars have treated unknowns as arising from limits to human experience and cognitive capacity, increasing attention has been paid recently to the thesis that unknowns are socially constructed, many of them intentionally so. Smithson’s 1989 book was among the earliest to take up the thesis that unknowns are socially constructed. Related work includes Robert Proctor’s 1995 Cancer Wars and Ulrich Beck’s 1992 Risk Society. Early in the 21st century this thesis has become more mainstream. Indeed, the 2008 edited volume bearing “agnotology” in its title focuses on how culture, politics, and social dynamics shape what people do not know.
Philosophers and social scientists alike have debated whether there are different kinds of unknowns. This issue is important because if there is only one kind then only one prescriptive decisional framework is necessary and it also may be the case that humans have evolved one dominant way of making decisions with unknowns. On the other hand, different kinds of unknowns may require distinct methods for dealing with them.
In philosophy and mathematics the dominant formal framework for dealing with unknowns has been one or another theory of probability. However, Max Black’s ground-breaking 1937 paper proposed that vagueness and ambiguity are distinguishable from each other, from probability, and also from what he called “generality.” The 1960’s and 70’s saw a proliferation of mathematical and philosophical frameworks purporting to encompass non-probabilistic unknowns, such as fuzzy set theory, rough sets, fuzzy logic, belief functions, and imprecise probabilities. Debates continue to this day over whether any of these alternatives are necessary, whether all unknowns can be reduced to some form of probability, and whether there are rational accounts of how to deal with non-probabilistic unknowns. The chief contenders currently include generalized probability frameworks (including imprecise probabilities, credal sets, belief functions), robust Bayesian techniques, and hybrid fuzzy logic techniques.
In the social sciences, during the early 1920’s Keynes distinguished between evidentiary “strength” and “weight,” while Knight similarly separated “risk” (probabilities are known precisely) from “uncertainty” (probabilities are not known). Ellsberg’s classic 1961 experiments demonstrated that people’s choices can be influenced by how imprecisely probabilities are known (i.e., “ambiguity”), and his results have been replicated and extended by numerous studies. Smithson’s 1989 book proposed a taxonomy of unknowns and his 1999 experiments showed that choices also are influenced by uncertainty arising from conflict (disagreeing evidence from equally credible sources); those results also have been replicated.
More recent empirical research on how humans process unknowns has utilized brain imaging methods. Several studies have suggested that Knightian uncertainty (ambiguity) and risk differentially activate the ventral systems that evaluate potential rewards (the so-called “reward center”) and the prefrontal and parietal regions, with the latter two becoming more active under ambiguity. Other kinds of unknowns have yet to be widely studied in this fashion but research on them is emerging. Nevertheless, the evidence thus far suggests that the human brain treats unknowns as if there are different kinds.
Finally, there are continuing debates regarding whether different kinds of unknowns should be incorporated in prescriptive decision making frameworks and, if so, how a rational agent should deal with them. There are several decisional frameworks incorporating ambiguity or imprecision, some of which date back to the mid-20th century, and recently at least one incorporating conflict as well. The most common recommendation for decision making under ambiguity amounts to a type of worst-case analysis. For instance, given a lower and upper estimate of the probability of event E, the usual advice is to use the lower probability for evaluating bets on E occurring but to use the upper probability for bets against E. However, the general issue of what constitutes rational behavior under non-probabilistic uncertainties such as ambiguity, fuzziness or conflict remains unresolved.
Bammer, G. and Smithson, M. (Eds.), (2008). Uncertainty and Risk: Multidisciplinary Perspectives. London: Earthscan.
Beck, Ulrich (1999). World Risk Society. Oxford: Polity Press.
Black, M. (1937). Vagueness: An exercise in logical analysis. Philosophy of Science, 4, 427-455.
Gardenfors, P. and Sahlin, N.-E. (Eds.), (1988). Decision, Probability, and Utility: Selected Readings. Cambridge, UK: Cambridge University Press.
Proctor, R. and Schiebinger, L. (Eds.), (2008). Agnotology: The Making and Unmaking of Ignorance. Stanford, CA: Stanford University Press.
Smithson, M. (1989). Ignorance and Uncertainty: Emerging Paradigms. Cognitive Science Series. New York: Springer Verlag.
Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities. London: Chapman Hall.
Written by michaelsmithson
July 9, 2011 at 11:25 am