“How Many Unemployed Are There?” —When Fuzzy Logic Met Linguistics and Semantics

“How Many Unemployed Are There?” —When Fuzzy Logic met Linguistics and Semantics Rudolf Seising Fundamentals of Soft Computing European Centre for Soft Computing Mieres (Asturias), Spain [email protected] Abstract —This paper illuminates the first 10 years of Fuzzy Sets in section III we refer to some other papers that he had recited, and Systems (FSS) where nobody could know that this theory written, published or supervised in the decade between 1965 would be a big success in the applied sciences and technology. and 1975 and which show his intention The paper concludes Starting with the content of an (perhaps) unpublished text of with some remarks on the actuality of this question until today. Lotfi A. Zadeh, we show that, the founder of FSS expected in the period of the years 1965-1972, before Fuzzy control appeared, that this new theory would play an important role in humanities II. A (P ERHAPS ) UNPUBLISHED TEXT and social sciences. Moreover he tried to link his theory to the The paper “How Many Unemployed Are There?” starts fields of linguistics and semantics. with a version of the Sorites paradox (see fig. 1) that is asking, “How many bald man are there?” Zadeh claims: “In both cases, Keywords-Fuzzy Set Theory; historyof science, linguistics, the answer is not unique because the class of the unemployed, semantic, computer science like the class of the bald, does not have a sharply defined natural boundary which separates those who are members of I. INTRODUCTION the class from those who are not.” “How many Unemployed Are There?” is the title of a script that I found in the last year in the private archive of Lotfi A. Zadeh. Perhaps this two-pages-paper that was written at “July 5, 1971” was never published [1]. The text is of historical interest because it consolidates my view that in this time Zadeh was intended to establish FSS in humanities, arts and social sciences, notably in linguistics and semantics. [2, 3]. Already in 1969 Zadeh had notified that he did not expect the incorporation of FSS into the fields of sciences and engineering: “What we still lack, and lack rather acutely, are methods for dealing with systems which are too complex or too ill-defined to admit of precise analysis. Such systems pervade Figure 1. First page (excerpt) of Zadeh’s script [1] life sciences, social sciences, philosophy, economics, psychology and many other “soft” fields.” [4] Much later, in an The Sorites that can be traced back to the old Greek word interview that he gave in 1994, he mentioned his surprise on σορως (sorós for “heap”) used by Eubulid of Alexandria (4th the fact that Fuzzy Logic (FL) was “embraced by engineers” century BC). Already when the mathematician and philoso- and “used in industrial process controls and in ‘smart’ pher Bertrand Russell (1872-1970) quoted the Sorites he consumer products such as hand-held camcorders that cancel discussed the “bald men” (Greek: falakros, English: fallacy, out jittering and microwaves that cook your food perfectly at false conclusion) and he discussed colours: “Let us consider the touch of a single button.” ([5], see also [1, 6]) the various ways in which common words are vague, and let In that interview he also said that he had “expected people us begin with such a word as ‘red’. It is perfectly obvious, in the social sciences-economics, psychology, philosophy, since colours form a continuum, that there are shades of colour linguistics, politics, sociology, religion and numerous other concerning which we shall be in doubt whether to call them areas to pick up on it [FL]. It's been somewhat of a mystery to red or not, not because we are ignorant of the meaning of the me, why even to this day, so few social scientists have word ‘red’, but because it is a word the extent of whose discovered how useful it could be.” ([5] but see [7]) application is essentially doubtful. This, of course, is the answer to the old puzzle about the man who went bald. It is In July 1971, when Zadeh wrote “How Many Unemployed supposed that at first he was not bald, that he lost his hairs one Are There?” [1], he was intended to open the field of the new by one, and that in the end he was bald; therefore, it is argued, theory’s applications to humanities and social sciences. In there must have been one hair the loss of which converted him section II we go through Zadeh’s claims in this manuscript and into a bald man. This, of course, is absurd. Baldness is a vague conception; some men are certainly bald, some are certainly However, in these 1960s the requirement of big amounts of not bald, while between them there are men of whom it is not data could be difficult but Zadeh wrote that it would have been true to say they must either be bald or not bald.” ([8], p. 85). “not a very big problem” to require the “lot of data” “to Russell showed in this article from 1923 that concepts are compute the grades of membership”. Therefore he concluded vague even though there have been and continue to be many that “the approach sketched above has the potential of attempts to define them precisely: “The metre, for example, is providing a much truer measure of unemployment that is defined as the distance between two marks on a certain rod in possible with the conventional dichotomizing techniques which Paris, when that rod is at a certain temperature. Now, the divide the population into two complementary classes – the employed and the unemployed – with no provision for in- marks are not points, but patches of a finite size, so that the between categories. Needless to say, there is bound to be some distance between them is not a precise conception. Moreover, arbitrariness in the formula for computing the grades of temperature cannot be measured with more than a certain membership in the fuzzy class of the unemployed, but it should degree of accuracy, and the temperature of a rod is never quite not be difficult to devise one which would represent a broad uniform. For all these reasons the conception of a metre is consensus.” [1] Zadeh also emphasized that the cardinality of lacking in precision.” ([8], p. 86) the fuzzy class of unemployed “corresponds to the number of In [1] Zadeh linked the problems of the Sorites and “How »full-time equivalent unemployed« in the group, and as such many unemployed are there?” with his then five years old has an intuitively appealing and simple interpretation. theory of Fuzzy Sets (see fig. 2). This short manuscript shows Zadeh’s intention in the early years of his new mathematical theory FSS to present it is a proper tool in social sciences and humanities. Already in these late 1960s it is obvious that FSS depends on the used language and beyond that on the meanings of its words. In the next sections we will show these dependencies in more details. III. FUZZY LOGIC , -LANGUAGES, -SYNTAX , -SEMANTICS A. Joseph Goguen and “A Logic of Inexact Concepts” When Zadeh looked for applying FSS in different academic disciplines he kept interdisciplinary company with colleagues on the campus of Berkeley: Joseph Goguen (1941-2006) – who was a Ph. D. student of the mathematician Hans-Joachim Bremermann (1926-1996), the psychologist Eleanor Rosch Figure 2. First page (excerpt) of Zadeh’s script [1] (Heider) (born 1938) and the linguist George Lakoff (born 1941). Zadeh and Bremermann served as first and second He wrote that we can identify “the class of the reviewers for Goguens’s Ph.D. thesis “Categories of Fuzzy unemployed” with a fuzzy set (or a “fuzzy class”) and therefore Sets” [9] where Goguen generalized fuzzy sets to so-called “ L- the number of the unemployed equals the cardinality of that sets” [10]. An L-set is a function that maps the fuzzy set carrier fuzzy set. – But how can we compute this cardinality? – Zadeh X into a partially ordered set L: A: X → L. The partially ordered wrote that to this end “a two-stage process” is required: set L Goguen called the “truth set” of A. The elements of L can • First, a formula must be devised under which each thus be interpreted as “truth values”; in this respect, Goguen individual in a group is assigned a grade of then also referred to a “Logic of Inexact Concepts” [11] membership in the class of the unemployed within that group. For example, someone who has lost a job and is B. From System Theory to Computer Science actively looking for one would be assigned the grade In 1959 Zadeh became professor of electrical engineering at of membership 1. A housewife who takes a half-time Berkeley and he also was a well-known protagonist of System job to supplement her family’s income would be Theory, but then, Zadeh recalled in one of my interviews, assigned the grade of membership 0. On the other “System Theory came grown up but then computers and hand, someone who is working half-time but would computers then took over. In other words: the center of work full-time if he could get a full-time job would be attention shifted. [...] So, before that, there were some assigned the grade of membership 0.5. And so forth. universities that started departments of system sciences, The formula could be quite complex to take into departments of system engineering, something like that, but consideration a variety of factors, or it could be quite simple, as in the above example.

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