The Linguistic Significance of the Meanings of Basic Color Terms

Linguistic Society of America The Linguistic Significance of the Meanings of Basic Color Terms Author(s): Paul Kay and Chad K. McDaniel Source: Language, Vol. 54, No. 3 (Sep., 1978), pp. 610-646 Published by: Linguistic Society of America Stable URL: http://www.jstor.org/stable/412789 . Accessed: 01/08/2011 17:55 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at . http://www.jstor.org/action/showPublisher?publisherCode=lsa. . 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MCDANIEL PAUL KAY and CHAD K Berkeley ey California, forn a Berke University Un vers tyof of Ca e there here are cons constraints ra n s on semanticc un universals versa s in n the he doma domain n oof co There are seman color; or i.e. ruc ure arise se from rom the he sstructure basicc co color or lexicons. ex cons These cons constraints ra n s ar the he types possible b e bas ypes oof poss han rather her than n the he case oof co color or aat least, unc on oof the he vvisual sua sys and function eas ra system. em Thus in ha de deterer c Sap Whorf), it iss percep perception on that Sapirr and Whor determining erm n ng percep perception on (cf. language anguage de mines m nes language. anguage he vvisual sua sys rom proper must he seman semanticc un universals versa s from In der system, em one mus properties es oof the deriving v ng the he theory n par han d discrete scre e ma continuous nuous ra rather her than mathematics, hema cs in heory oof particular cu ar the employ emp oy a con conflicts cs w with h the color or seman semantics cs thus hus con he d discretescre e model oof co sets. s The resu resulting ng mode fuzzy uzzy se ruc ura s s and genera semanticc pr feature ea ure concep generativists. v s s IIt iss primes mes shared by sstructuralists concept oof seman heor es are oof limited m ed accuracy discrete-feature scre e ea ure seman semanticc theories h s bas basiss that ha d accuracy.** argued on this INTRODUCTION nto the mean color or prov 11. Recent emp meanings ngs of words for co provides des empirical r ca research into n linguistics beliefs efs in contradicts cts two w evidence ev dence that contrad ngu st cs and the ph widely-held de y-he d be philosophy osophy thiss ev basiss to Thiss paper presents a summary of th of language. evidence, dence uses itt as a bas anguage Th basicc co color-term or-term semant model of bas construct a genera semantics, cs and exp explores ores the implicamp cageneral mode thiss mode semanticc theory model for genera ttions ons of th theory. general semant familiar arto which ch we w will present ev to most linguists evidence dence iss fam rst be The ffirst belief ef aga ngu sts against nst wh various ous so-ca so-called ed strong and weak forms as the Sap hypothesis. s There are var Sapir-Whorf r-Whorfhypothes n aall forms notion on iss that each lanbasicc not anof th thiss hypothes forms, the bas (Fishman shman 1960); in hypothesiss (F ts own idiond v dua s 'kaleidoscopic ux of impressions' d oka e doscop c fflux mpress ons its mposes on the individual's guage imposes Thiss doctr structure. Th doctrine ne emphas semanticc structure semanticc relativity at v ty of semant syncraticc semant syncrat emphasizes zes the re minimizes n m zes the ro rolee of linguistic ex ca categor universals. versa s The lexical structures, and m structures ngu st c un categorization zat on thiss arb nstance of th of co color or has often been presented as a parad paradigmatic gmat c instance arbitrary, trary n h hiss w semanticc structure structure. Thus Thus, in mpos t on of semant language-specific anguage-spec f c imposition widely-used de y-used Gleason eason cclaimed a med (1961:4) There iss a cont continuous nuous gradat textbook, G (1961:4), 'There introductory ntroductorytextbook gradation on of co other. Yet an Amer color or from one end of the spectrum to the other American can descr describing b ng itt w will list st the hues as red red, orange blue, ue purp yellow, ow green orange, ye green, b purple-or e-or someth something ng of the n the spectrum or the human percept nherenteeither ther in kind. k nd There iss noth nothing ng inherent perception on of itt ts d n th division v s on in thiss way would d compe which wh ch wou way.' compel its terature on co colororexperimentally menta y and investigating anguages exper nvest gat ng the literature Studying Study ng 20 languages additional t ona languages, Berlin n & Kay 1969 (hereafter B & K) semantics cs for 78 add term semant anguages Ber evidence dence indicating a ms of G Gleason eason and others that, contrary to the cclaims others, nd cat ng that presented ev universal versa system of bas basicc co aall languages color or categor anguages share a un categorization. zat on B & K argued universal versa bas basicc co color or categor that there are un basicc co color-term or-term categories, es and that the bas inventories nventor es of most languages me by lexicalizing anguages expand through ttime ex ca z ng these categor categories es universal versa order order. In add in nah McDaniel e has argued (1972 addition, t on McDan (1972, highly gh y constra constrained, ned un n the human percept universals versa s are inherent nherent in color. or The 1974, MS 1974 MS)that these un perception on of co * We have bene benefited ed grea he ma matters ers d discussed scussed here from rom the he ideas deas oof John greatlyy regard regarding ng the Brent Ber Janet Dougher Bill Woo Berlin, n Jane Atkins, A k ns Bren Dougherty, y Cra Craigg Mo Molgaard, gaard Sue Thompson Wooten, en and an Thompson, B or LANGUAGE named George Lako Lakoff. anonymous reader for 610 LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 611 color co or percept resultt of a common set of neurophys perception on of aall peop peoples es iss the resu neurophysiological o og ca McDaniel e suggests that these pan-human neurophys processes, and McDan processes neurophysiological o og ca basiss of the un universal versa patterns in n the mean basicc co processes are the bas color or meanings ngs of bas terms. terms We argue nd direct rect oppos Gleason eason and other re then, in argue, then relativists, at v sts that the opposition t on to G human percept color or offers an exp perception on of co explanation anat on of why Eng English sh speakers segment the vvisual sua spectrum as they do-and why furthermore,speakers of other languages why, furthermore anguages exhibit exh b t the limited m ted and systemat ternat ve segmentat color or space systematicc set of aalternative segmentations ons of the co that they do do. Work with th a b basicc co color-term or-term Working ng w biologically o og ca y based understand understanding ng of bas natural re relations at ons that ex semantics, semant cs we can show the natura exist st between the numerous co color or n h differentiated fferent ated co color or term categories categor es encoded in highly gh y d terminologies, no og es such as Eng English, sh and the fewer categor n languages with th less ess d differentiated fferent atedand and therefore categories es encoded in anguages w n extens extension on of the arguments advanced superficially superf c a y ssimpler mp er term Thus, in terminologies. no og es Thus ex ca categor color or as a parad K, we present the lexical by B & K categorization zat on of co paradigmatic gmat cexamp example, e not of the re of semantic semant c of but the existence ex stence of b relativity at v ty structures, structures biologically o og ca y based semanticc un semant universals. versa s A second w belief ef in n linguistics widespread despread be ngu st cs and the ph philosophy osophy of language, anguage data the reviewed rev ewed doctrine ne that there ex exist st u challenged cha enged by ultimate t mate here, iss the doctr here semanticc pr semant which ch are DISCRETEent entities. t es These un units ts are ca primes mes wh called ed semant semanticc 'features' features by both European and Amer American can structura structuralist stschoo markers or schools, s and 'markers' 'distinguishers' d st ngu shers by Katz (1964 follow fo ow h (1964, 1966)and 1966) and those generat who generative ve linguists ngu sts him. m Although A though there are differences fferencesbetween are, of course between structura structuralist stand course, major d and standard theories es as to how semant semanticc pr generative generat ve theor primes mes are comb combined ned into nto the mean meanings ngs of words or larger units, ts unt until recent arger linguistic ngu st c un recentlyy there was near nearlyy un universal versa agreement that aall semant semanticc pr primes mes are d e non-cont discrete, screte i.e. non-continuous, nuous ent entities. t es When we say that semant semanticc pr primes mes have been cons considered dered to be d discrete screte ent entities, t es we mean that ewed as propert they have been vviewed that are pred properties esthat predicable cab e of th n an aall-or-none things ngs in -or-none fashion. fash on Th Thiss tac tacitt prem n the common p premise se iss d reflected ected in directly rect y ref notation on plus/minus us m nus notat of semant semanticc features features. When [+round] or [-human] iss wr written, tten itt indicates nd cates that roundness and human humanity ty are be being ng taken as propert properties es wh which ch are ssimply mp y pred predicable cab e or not pred of someth predicable cab eof something ng be being ng ta talked ked about about. These propert properties es are not treated in n the d discrete-feature screte-featuretheory theory as pred predicable cab e of someth something ng TOA TO A DEGREE DEGREE.11 In d discussions scuss ons of the d discrete-feature screte-featuretheory nd theory, as in discussions scuss ons of semant semanticc re relativat vdomain n of co color or iss often used as a parad ity, ty the doma paradigm gm examp example. e In Katz Katz'ss theory theory, one of the major re relationships at onsh ps that may ex exist st between d discrete screte semant semanticc features iss that of antonymy antonymy. For Katz (1966:195 ff ff.), ) two linguistic ngu st c express expressions ons are antonymous just iff they have read readings ngs that are identical dent ca except that that, where one read reading ng has a semant semanticc feature from a (prev (previously ous y spec specified) f ed) antonym set set, the other read reading ng has a d different fferentfeature feature from that same set set. Katz (1964:532) exemp exemplifies f esantonymous antonymous lexical ex ca items tems as fo follows: ows: 'There There are many spec special a an relations a ons be antonymy onymy re between ween words and express expressions. ons One examp examplee iss the he re relation a on oof "sex "sex-antonymy an onymy "". A pa pairr oof lexical ex ca items ems iss SEX SEX-ANTONYMOUS ANTONYMOUS just us in n case den ca pa ha where one has the they hey have identical paths hs excep except that he seman semanticc marker (Male) Ma e the he oother her has the he seman semanticc marker (Female). Fema e Some instances ns ances are are: woman and man bride de and groom man; br groom; aunt and unc aun uncle; e cow and bu bull. The ma majority or y oof an antonymous onymous lexical ex ca items ems are no not se setss oof 1For recen cha enges o h s v ew see Lako 1972 F more 1975 Kay 1975b 612 LANGUAGE, VOLUME 54, NUMBER 3 (1978) but se setss oof n hereare are the he spec ex ca items, pairs pa rs bu n-tuples. up es For examp example, e there ems one species-antonymous es an onymouslexical on. cub, puppy species-antonymous es an onymous n being: ng ch child, d cub kitten, en cygne examplee oof a spec examp n-tuple up e be puppy, k cygnet, and so on here are n ems that ha are d ex ca items Moreover, there Moreover n-tuples up es oof lexical distinguisher-wise s ngu sher w se an antonymous, onymous ee.g., g the he n color or ad orm an red, orange n-tuple up e oof ssimple adjectives ec ves (blue, b ue ye yellow, ow green orange). These form mp e co green, red he pa associated a ed w with h each iss identical den ca excep or the he antonymous an onymous n path h assoc n-tuple up e because the except for which ch d differentiates eren a es that ha co color or ad rom the he oothers.' hers distinguisher d s ngu sher wh adjective ec ve from Katz here proposes that ye n the blue ue each has ass green, and b yellow, ow green assigned gned to itt in a semanticc component of the grammar a d semant called ca ed discrete screte feature feature, distinguisher, d st ngu sher which wh ch d terms. color or terms distinguishes st ngu shes itt from each of the others and from the rema remaining n ng co a The inadequacy of such treatment is s when one considers cons ders nadequacy apparent compound color co or terms such as ye self-contradicf-contrad cyellow-green ow-green or b blue-green. ue-green These terms are not se Katz'ss treatment theirr mean treatment, and the tory, as one m tory might ght deduce from Katz meanings ngs are re relatively at ve y which wh ch is s is s blue b ue to some transparent: someth something ng 'blue-green' b ue-green degree and green to some degree Thiss and re below ow show that the meanrelated ated observat observations ons deve degree. Th developed oped be color co or of basic bas c terms can not with th d semanticc be discrete screte semant ings ngs accuratelyy represented w accurate features. We propose instead features the nstead that co color or categor like ke categories, es neurophysiological neurophys o og ca non-discrete screte underliee them continuous nuous funct them, are cont functions; ons; and that a non-d processes that under in n this th s the most concise conc se and instance nstance set formalism, forma sm adequate fuzzy theory, prov theory provides des color or terms semantics cs of bas basicc co terms. description descr pt on of the semant thiss ana discussion scuss on of the genera Preliminary Pre m nary to th analysis ys s and further d general linguistic ngu st c of basic bas c color-term co or-term is s it t review ew some of the ssignificance gn f cance semantics, semant cs necessary to rev researchfrom wh which ch our understand of co color or anthropological anthropo og ca and psycho psychological og ca researchfrom understanding ngof semanticc categorization categor zat on has deve developed. oped In ?2 ?2, the majorf majorfindings nd ngs of B & K regard regarding ngsemant and deve n bas universals versa s in basicc co color-term or-term vocabu vocabularies ar es are summar summarized. zed developmental opmenta un Thiss sect Th section on aalso certain n inadequacies in n so d discusses scusses certa the nadequac es original or g na ana analysis ys s that can now be corrected corrected. In ?3 we offer a brief br ef ?3, summary of current theory and research color or percept regarding regard ng the neurophys neurophysiological o og ca bases of co perception on as they are re relevant evant to McDaniel's McDan e s understanding understand ng psychophysiological psychophys o og ca rere-interpretation nterpretat onand and exp explanation anat on of B & K K. Our currentana n ??4-5 current analysis ys s iss presented in ??4-5, where the work of B & K and of McDan McDaniel e iss integrated with th new data from recent ffield e d stud studies es of bas basicc co ntegrated w colororterm systems This Th s eads to a reformu reformulation at on of B & K K'ss un systems. integration ntegrat on leads universals versa s of color co or categor thiss reformu categorization zat on and co color-category or-category deve development. opment In th reformulation, at on fuzzy set theory iss used to mode model the structure of individual nd v dua co color or categor categories es and to relations at ons wh which ch deve between the var various ous un explicate exp cate the re develop op betweenthe universal versa co color or categor categories es which wh ch appear as bas basicc co color or vocabu vocabularies ar es expand expand. ANTHROPOLOGICALRESEARCHINTO BASIC COLOR ANTHROPOLOGICALRESEARCHINTO COLOR-TERM TERMSEMANTICS 22. B & K K'ss exper researchinto nto the systems of co experimental menta and library braryresearch color or categor categorizzation at on in n 98 languages, wide de range of major language anguages represent representing ngaa w anguage stocks stocks, focused on the categor basicc co color or terms of each language. categorization zat on as represented by the bas anguage Basicc co Bas color or terms were def defined ned as those (a) wh which ch are mono monolexemic exem c (un (unlike ke redd reddishshn that of any other term (un nc uded in blue); b ue); (b) whose ssignification gn f cat on iss not included (unlike ke crimson cr msonand and verm which ch are k kinds nds of red); (c) whose app vermilion, on both of wh application cat on iss not restricted restr cted to a narrow cclass ass of objects (un blond ondand (unlike ke b and roan); and (d) wh which ch are salient ent as ev n frequentand evidenced denced in relatively re at ve y sa frequent and genera general use (un (unlike ke puceand puce and mauve) mauve).22 2 For ur her d scuss on o 1975a he concep bas c co or erm see B & K p 5 and Kay LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 613 The exper K'ss research with th twenty languages, research, dea dealing ng w experimental menta port anguages portion on of B & K in n of colored co with w th the absence the stimuli, mu of the eelicitation, c tat on any part particular cu ar ored st began basicc co bas nformant s language. nformant s bas basicc co color or terms in n each informant's colororanguage After an informant's in n the informant nformant term inventory had the elicitation e c tat on been determined determ ned was interview, nterv ew nventory basicc co color or terms to co asked to perform two tasks that involved nvo ved match color or matching ng these bas in n was a informant's nformant s first f rst task to standardized standard zed The stimulus st mu us out chips ch ps pick p ck array.33 array the co color or ch basicc co color or terms which ch he fe feltt were the best examp examples es of each of the bas chips ps wh in n h hiss language. nd cate the boundar boundaries es of each co color or anguage The second task was to indicate i.e. e to in n whose color co or be indicate nd cate ALL the denoted the category, category might m ght by chips ch ps array a ggiven color or term term. ven co Informants se selected ected best examp with th far greater ease ease, speed reliability ab ty examples es w speed, and re than they determ determined ned boundar boundaries. es B & K found that these judgments of best called ed the focus of each co color or category example, examp e indicating nd cat ng what they ca category, were more useful than the judgments of boundar usefu n descr boundaries es in describing b ng and compar comparing ng the mean meanings ngs of bas basicc co color or terms in n the languages n the studied ed exper anguages stud experimentally. menta y As expressed in basicc exper co or categor original or g na report report, the bas experimental menta ffindings nd ngs were that 'color categorization zat on iss not random and the foc foci of bas basicc co color or terms are ssimilar m ar in n aall languages' anguages (10) (10). A total of eeleven tota even foc foci were identified, n the co color or space where Eng ocated in dent f ed located English sh speakers locate ocate the best examp black, ack wh white, te red red, orange brown, green blue, ue examples es of b orange, ye yellow, ow brown green, b foci were interpreted purple, purp e p pink, nk and grey grey. These foc nterpretedas the pr primary marydes designata gnata of a set of un universal versa semant semanticc categor categories. es results ts as a gu considered dered pub Using Us ng these resu guide de to interpretation, nterpretat on B & K cons published shed data from 78 add additional t ona languages, n determined ned that there iss a tempora anguages and determ temporal order in which wh ch languages anguages encode these un universal versa categor categories. es They conc concluded uded as fo follows ows (3-4): different eren languages n their he r vocabu vocabularies ar es d different eren numbers oof bas color or 'Although A hough d anguages encode in basicc co o a un universal versa inventory color or ca even bas basicc co exists s s from rom categories, ca egor es a total nven ory oof exac exactlyy eeleven categories egor es ex which wh ch the he eeleven even or fewer ewer bas basicc co color or terms erms oof any ggiven ven language anguage are aalways ways drawn ... IIf a language ewer than even bas han eeleven basicc co color or ca hen there here are sstrict r c limitam a anguage encodes fewer categories, egor es then tions ons on wh which ch ca encode. The d restrictions r c ons oof co color or terms distributional s r bu ona res categories egor es it may encode erms across languages are: anguages are All languages '1. 1 A contain a n terms erms for or wh whitee and b black. ack anguages con '2. 2 IIf a language contains a ns three hree terms, hen it con contains a ns a term erm for or red red. anguage con erms then ' 33. IIf a language contains a ns four our terms, hen it con contains a ns a term her green or ye erm for or eeither anguage con erms then yellow ow not bo (but bu no both). h '4. 4 IIf a language contains a ns five ve terms, hen it con contains a ns terms erms for or bo anguage con erms then both h green and ye yellow. ow '5. 5 IIf a language contains a ns ssixx terms, hen it con contains a ns a term erm for erms then or b blue. ue anguage con '6. 6 IIf a language contains a ns seven terms, hen it con contains a ns a term erm for or brown brown. anguage con erms then '7. 7 IIf a language contains a ns eeight hen it con anguage con gh or more terms, erms then contains a ns a term erm for or purp purple, e combination na on oof these. pink, p nk orange orange, grey grey, or some comb hese 3 The s stimulus mu us array cons consisted s ed oof 329 Munse Munsell co color or ch chips, ps including nc ud ng (a) a 320 chroma chromaticc ch chips ps uniform orm samp he co colors ors on the he ou skin n oof the representing represen ng a un sampling ng oof the outer er sk he percep perceptual ua co color or so solid, d where the he mos most h saturated ura ed co colors ors oof every hue and br highly gh y sa brightness gh ness are found; ound and (b) b n nine ne achromaticc ch rom b black ack through neutral, neu ra achroma chips ps rang ranging ng from hrough grey too wh white. e For the he reader un unfamiliar am ar with w h the he co color-solid or so d mode model oof the he psycho color or space psychological og ca co space, the he important mpor an po point n here iss that ha the he sstimulus mu us array represen reasonablee samp he es representss a reasonab sampling ng oof the estimated ma ed seven m million on d distinguishs ngu sh ablee co ab colors. ors For further ur her d he sstimuli, discussion scuss on oof the n 33; 162 mu see B & K (5; 5 160 160, fn. 162, fn. n 12 12). Collier Co er 1973 and Co Collier er eet aal. 1976 have exam examined ned the he poss ha res possibility b y that restricting r c ng the he se selection ec on oof chroma chromaticc ch he max saturated ura ed ch chips ps too the maximally ma y sa chips ps aat each hue and br brightness gh ness level eve may have biased b ased B & K K'ss resu but it was found ound that ha no such b results; s bu bias as ex exists. ss 614 LANGUAGE, VOLUME 54, NUMBER 3 (1978) 'These distributionalfacts are summarizedin [Table 1], in which each row corresponds to an actually occurring type of basic color lexicon. The pattern displayed by the actual distribution is a tight one; of the 2,048 (that is, 211)possible combinations of the eleven basic color terms, just twenty-two, about 1 per cent, are found to occur in fact. Perceptual categories encoded in the basic color terms No of basic color Type terms . . 3 v, , v oSu0D . 1 2 3 4 5 6 2 3 4 4 5 6 + + + + + + 7 8 7 8 + + + ++++++++- 9 10 11 12 13 14 8 8 8 9 9 9 + + + + + + + + +------+ +--+ -+----+ + + + + + ++- + + + + ++++ + + ++ + ++ - + +- + + -+--+- + + - + - -+ +++++++++-- + + + + + 15 9 +++++++-++- 16 17 18 19 20 21 22 9 9 10 10 10 10 11 +++++++ -+ + + + ++ + + + + + + ++ + + + + ++ + + + +++ + + + + + + + + + -+ + + + + + + ++ + + ++ + + + + + -+ - - -+ + ++ +- + + + + + + + + Only these twenty-two out of the logically possible 2,048 combinations of the eleven basic color categories are found. NOTE: TABLE1. The twenty-two actually occurring types of basic color lexicon. 'Moreover, the twenty-two types which do occur are not unrelated but may be summarized by (or generated from) a rather simple rule [Figure 1]: [ whitel< blac k] <[red] [re l< <bu1< ellow < le < ~ < < purple pink orange Lgrey FIGURE1. LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 615 or d distinct s nc co color or ca he express ha a iss presen where, for where a b b), the present categories egor es (a, expression on a < b ssignifies gn es that b iss no b iss presen n wh which chb in n every language n some language n wh which chb not presen so in present. anguagein presentand aalso anguagein hus a par he se set oof bas basicc co color or ca he ssixx bracke bracketed edse setss [Fig. F g 11] iss thus partial a order on the categories, egor es the series es oof ssixx equ asses oof this h s order ... [Fig. not on being be ng a ser onlyy a representssno equivalence va ence cclasses F g 11] represen a emen for distributional d s r bu ona sstatement or con but aalso so the he chrono chronological og ca order oof contemporary emporarylanguages anguages bu ex ca encod basiccco color or ca the he lexical n each language. The chronological n encoding ng oof bas categories egor esin og ca orderiss in anguage Thechrono turn urn interpreted n erpre edas a sequence oof evo evolutionary u onarysstages.' ages Thiss d Th distribution str but on of co color or categor n the ethnograph reflect ect a categories es in ethnographicc present must ref which ch each language ts number of sequence through wh anguage has to pass as itt changes its basicc co bas color or terms terms. If th thiss were not the case would d be forced to assume that case, we wou n the past wh existed sted in which ch d did d not conform to the observed d distribution; str but on; languages anguages ex with th words for b black, ack wh red, green white, te and b blue, ue but none for red ee.g., g a language anguage w green, or Thiss wou would d imply yellow. ye ow Th mp y that the pattern d synchronicc displayed sp ayed by the current synchron with th respect to languages fortuitous tous w n genera Thiss iss an samplee of 98 languages samp anguages iss fortu anguages in general. Th which ch no ev exists. sts Moreover evidence dence ex considerable derab e d direct rect Moreover, cons unlikely un ke y conjecture for wh evidence ev dence has been adduced support temporal supporting ng the hypothes hypothesized zed sequence of tempora n bas basicc co color-term or-term systems (B & K Berlin n & Ber Berlin n 1975 1975, K, 36-41; Ber development deve opment in Kuschel & Monberg 1974) 1975, Kusche Dougherty 1975 1974). To cont continue nue our quotat quotation on from B & K (4-5): 'The The logical, hus corresponds og ca par partial a order ordering ng oof [Fig. F g II] thus corresponds, accord according ng too our hypo hypothesis hes s too a temporal-evolutionary o ows [Figure empora evo u onaryorder ordering, ng as follows F gure22]: "purple black iiN N LblackJ [green] r[yellow] ow] r [blue] [b ue]J->> [brown]P [brown] P l J X^ r[ye [yellow] ->> [green] A orange _grey FIGURE2 2. where the he arrow may be read 'iss encoded be nd before' ore ... In sum sum, our two wo ma major or findings nd ngs indicatee that ca ha the he re referents eren sfor or the he bas basiccco color or terms ermsoof a all languages rom a anguagesappear appeartoo be drawnfrom set oof eeleven se even un universal versa percep hese ca n the he perceptual ua ca categories, egor es and these categories egor es become encoded in n a par history h s ory oof a ggiven ven language xed order anguage in partially a yfixed order.' Although A though subsequent research has substant substantiated ated B & K K'ss bas basicc ffindings, nd ngs the theirr 1969 reportconta report contained ned some errorsof errors of fact and a theoret theoretical ca equ equivocation. vocat on The latter atter involved nvo ved the conf conflicting ct ng treatments of category foc foci and category boundar boundaries es in n the exp explanation anat on of the success successive ve stages of bas basicc co color-term or-term deve development. opment B & K interpreted nterpreted the deve developmental opmenta sequence pr primarily mar y as the success successive ve encod encoding ng of new foc foci. Stage I ((i.e. e two-term) systems were descr described bed as cons consisting st ng of the categories gor es BLACKand WHITEwhere WHITE,where these hese ca categories categor egor es included nc uded (on on the he one hand hand) b black ack and aall darkerhues darker hues, and (on the other) wh white te and aall the lighter ghter hues hues, w with th the foc foci of the categor categories es be being ng at pure b black ack and pure wh white te respect respectively. ve y At Stage II II, the warm hues were descr described bed as be being ng accorded the theirr own separate bas basicc co color or term, RED term which ch focused at red RED, wh red. Thus the deve development opment at Stage II was thought essentially essent a y to cons consist st of add adding, ng to the categor categories es focused at b black ack and wh white, te a category focused at red red. But an equ equivocation vocat on enters at th thiss po point nt w with th respect to the mean meanings ngs of the labels abe s BLACK and WHITE WHITE. In Stage II, these labels abe s referred to categories, categor es focused at b black ack and wh white, te whose extens extensions ons (cons (considered dered together) take in n aall other co colors. ors At Stage 11 though, the extens extensions ons of BLACKand WHITE 11, though have retracted retracted, so that the warm co colors ors are not included nc uded in n eeither ther of them them, but \ 616 \ X LANGUAGE, VOLUME 54, NUMBER 3 (1978) instead are included in the extension of the new term RED, focused at red. Thus BLACK and WHITE mean one thing at Stage I, and something else at Stage II. The same equivocation occurs with respect to all B & K's category labels BLACK, WHITE, RED, and GREEN. These labels were used sometimes to refer to a category having a particular focus, and at other times to a category having a particular extension. Moreover, the extensions referredto were not constant across occasions of use of the category label. These equivocations are eliminated in our present analysis of basic color-term semantics, where the non-discrete formalism of fuzzy set theory is shown to provide a unitary mechanism for describing the relationships between color-category foci, extensions, and boundaries. Studies appearing after 1969, testing B & K's hypotheses, produced empirical results which highlighted the equivocation just noted and revealedcertain factual errors in the original report. Heider 1972a,b studied the Stage I system of the Dugum Dani in detail. She found that the Dani's two color categories, mola and mill, were better labeled 'white-warm' and 'dark-cool', rather than simply WHITE and BLACK (as B & K had suggested for all Stage I systems), since mola contains not only white but all the warm colors (reds, oranges, yellows, pinks, and redpurples), while mili contains black and all the cool colors (blues and greens). Diagramatically, the situation may be represented as in Figure 3. brighter 'W\\\\\\HITE' ^\\\\\\\\^ '' ~~~~~~~~~~~~color \ \\ (2) ' \\\\\\\\ (2)\ vXX ^\. darker ////////// brighterv by ~~~~~~~~~~~~hypothesized \ \ TE ' BLACK' ~~~~~'WHITE'/BLACK' system as Berlin and Kay \ (1969) v^/\\\\\'^ LACK' H'( \\\X\\^ / 'XXs ^ \^V 'WHITE'/'BLACK' ^SX^NS^^ >^/////z?///>^ Y^y //////*//////)\ v V"' \^ FIGURE 3. Source: Kay (1975a:259). N reported th fmol 1w P. Ieider 'WHIT, LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 617 Heider der aalso so found that the foc foci of these wh white-warm te-warmand and dark-coo Significantly, S gn f cant y He dark-cool variable ab e across informants. nformants Mo Molaa and m mili were not aalways categories categor es were var ways focused at on white te and b black. ack For examp nformants focused the wh onlyy wh whiteteexample, e 697%of her informants warm category mo molaa at Eng focal red red. B & K K'ss or assumed that English sh foca original g na ana analysis ys s aall bas basicc co color or categor focus. Other recent emp studies es of categories es have a ssingle ng e focus empirical r ca stud basicc co color-term or-term systems nformants were tested early-stage ear y-stage bas systems, where mono monolingual ngua informants in n the theirr nat native ve env Heider's der s ffinding environments, ronments have corroborated He nd ng that a language anguage basicc co color or terms terms.44 may have mu multiply-focused t p y-focused bas Thiss and re Th related ated factua factual emendat emendations ons to B & K show that the theirr treatment of the basicc co bas color-term or-term encod successive ve encod encoding ng sequence as the ssimple mp e success encoding ng of ssingle ng e foci cannot be ma foc maintained. nta ned The rere-interpretation nterpretat onof the encod encoding ng sequencepresented sequence presented here fo follows ows McDan McDaniel e 1974 n treat successive ve stages of bas 1974, MS basicc co MS,in color-term or-term treating ng the success differentiation fferent at onof of co color or categor development deve opment as the progress rather ratherthan than as the progressive ve d categories es successive success ve encod foci. Th Thiss reencoding ng of foc involves nvo ves re-interpretation, nterpretat on as our genera general ana analysis, ys s a mode model of bas basicc co formation on that ut utilizes zes ffindings from recent color-category or-category format nd ngs researches into nto the neurophys color or percept neurophysiological o og ca bases of co perception. on These ffindings nd ngs are reviewed rev ewed in n ?3 ?3. THE NEUROPHYSIOLOGICAL BASES B ASESOF OF COLORPERCEPTION COLORPERCEPTION 33. Research conducted in n the past two decades has ssignificantly ncreased our gn f cant y increased knowledge know edge of the phys physiological o og ca processes wh which ch under underliee the human percept perception on of color. co or Th Thiss research iss concerned concerned, for the most part part, w with th d differfferdiscovering scover ng how d ences in n the wave wavelengths engths of light ght reach reaching ng the eye are transformed into nto response n the vvisual differences d fferences in sua nervous system system. It has been known for some ttime me that co color or perception percept on beg begins, ns neurophys neurophysiologically, o og ca y at the ret retina, na w with th the st stimulation mu at on of color-sensitive co or-sens t ve ce cellss ca called ed cones cones. There are three types of cone cone, and each type iss distinguished d st ngu shed by its ts own un unique que pattern of wave wavelength-dependent ength-dependentresponse response. The light ght of each wave wavelength ength d distinguishes st ngu shes itself tse f neura neurallyy at the ret retinal na level eve by evok evoking ng a un unique que set of neura neural responses from th thiss three-cone system system. Each d distinct st nct co color or iss associated assoc ated w with th a un unique que pattern of responses among the three types of cones cones. The neura neural process processing ng and cod coding ng of co color or cont continues, nues however however, beyond th thiss retinal ret na level. eve Many recent stud studies es of the vvisual sua processes have been concerned w with th the neura neural representat representation on of co color or at some remove from the ret retina, na in n the neura neural pathways between the eye and bra brain. n These stud studies, es wh which ch have used m microeleccroe ectrodes to mon monitor tor ssingle ng e neurons neurons, indicate nd cate that that, by the ttime me wave wavelength-governed ength-governed neural impulses neura mpu ses reach h higher gher po points nts in n the vvisual sua pathway pathway, the tr tripartite part teresponse response of the ret retina's na s three-cone system iss transformed into nto a set of opponent neura neural responses. ses Two propert properties es d distinguish st ngu sh a ce cell as an opponent response ce cell. F First, rst an opponent response ce cell has a spontaneous rate of ffiring-a r ng-a basa basal response rate that itt 4 The sstudies ud es encompass one JJivaroan varoan language, anguage one Mayan Mayan, one Papuan Papuan, one Esk Eskimoan moan and three hree Aus Austronesian rones an (Berlin Ber n & Ber Berlin n 1975 1975, Harkness 1973 1973, Hage & Hawkes MS MS, He Heinrich nr ch 1972, Dougher 1972 Doughertyy 1974 1975, He Heider der 1972a 1972a,b, b and Kusche 1974, 1975 Kuschel & Monberg 1974 1974). These da dataa have been cr critical ca in n the he deve development opmen oof our new unders understanding and ng oof the he encod encoding ng sequence sequence. The resultss oof these resu hese sstudies, ud es as regards the he subs substance ance oof the he encod encoding ng sequence sequence, are summar summarized zed in n Berlin Ber n & Ber Berlin n 1975 1975, Dougher Doughertyy 1975 1975, Kay 1975a 1975a, and McDan McDaniel e 1974 1974, MS MS. 618 3 (1978) VOLUME 54, NUMBER LANGUAGE, maintains without external stimulation. Second, the cell shows an increased rate of firing in the presence of lights whose dominant wavelengths are from certain regions of the visual spectrum, while lights from the complementaryspectral regions will decrease its rate of firing below its basal rate. The opposing effects of complementary regions of the visual spectrum on these cells gives rise to the term 'opponent response.' Cells with opponent response characteristics have been identified by R. De Valois and his co-workers in the lateral geniculate nucleus (LGN) of the macaque (Macaca irus), an Old World monkey with a visual system similar to man's (De Valois et al. 1966, De Valois & Jacobs 1968). These scholars discovered four types of opponent cell. The mean response patterns that distinguish these four types are shown in Figure 4, where horizontal dotted lines indicate the mean spontaneous 25 2 - tR-G CELLS f/, oo , +Y- B CELLS r S"\ | ! , . .. A - .. :o: 400 20 40 60o "3 ......... 500 20 40 60 80 600 20 40 WAVELENGTH (mp.L) 0 0 ui Ul UJ v, Q. (/ u. ,'t 4, / 700 z < UJ: 2 /4 t~I +G-R CELLS / i / // oef ' /1 ..... ,? / *l oo40020 ''. \\ I~~ . i \\ 1 ', -.. \~~ ~~1.~1 , ,,*t '$\T'i /' / A . *i \ ". ' * * .* ' "*. I-04 '-o ' .? *? .. .. ... 40 60 500 80 20 40 60 80 600 20 40 60 eb800 201 w \ w Y 0 ui .- IJ-~~~~~~~~~~~~I d^\ o/ 5? v, LL "? SPONAhEOUSRATE CELLS +B-Y B Y CELL \o *\ *i1Ii zz < 5 O WAVELENGTH mAL F GURE 4 Source \ WAVELENGTH(mj) -- ,.i-'' '\ - -l^r \/ \ .!* X X SPONTANEOUS RATE/ *5! . --- -*----....... ..'..; ... ....... ..........',.. ' i/ /b j//d ' / * n '\lt \ / / / / / %1j4 I' . / '/ ' F i\ \ \ 13 ] rSPONTANEOUS RATE 5 . 5 '1 , 40 \ a\ I 5 - fe ' / 1r-- " w UJ /15- \ \ *. SPONTahlEOUS O O RATE 55..1..... 1 5 ' 01 0O __..' * - 99 s -s i 1- I - WAVEL CENGTH m De Va o s e a 1966 972 73 F gs 9 12 No e Hor zon a nd ca e mean basa response ra e or each ce ype do ed nes f r ng rates of the ce and the curv near dotted dashed and dotted-and-dashed nes nd cate the observed response rates of the ce to ghts of vary ngwave engths at three d fferent eve s of br ghtness The +R-G and +G-R ce s shown n F gs 4A and 4C have responses opposed between the red (far ong) and green LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 619 (near short) regions of the spectrum. These cell types differ fundamentally only in the directions of the response deviations that represent the opposition between the red and green regions of the spectrum. The +Y-B and + B-Y cells illustrated in Figs. 4B and 4D have responses opposed between the yellow (near long) and the blue (far short) regions of the spectrum. These two types again differ primarily only in the response modes (increased vs. decreased firing) in which this opposition is expressed. In their analysis of the translation of these response patterns into perceptual effects, De Valois et al. (976) argue, with respect to the cell types that are opposed between the same regions of the spectrum, that 'it seems reasonable to say the excitation in one type [e.g.] (+R-G) carries the same information as inhibition in the other [e.g.] (-R+G).' Following this argument, they sum the absolute values of the red, yellow, green and blue deviations of the +R-G, -R+G, +Y-B, and -Y+B opponent cells into unitary red, yellow, green, and blue response effects. They then take these response distributions as the neutral bases of color discriminations at the perceptual level. Figure 5 presents these response distributions for human observers as estimated by Wooten 1970 from human psychophysical data. The direction of deviation above or below the X-axis signifies in this figure the chromatic value (i.e. red, yellow, 2 - (I) LLI0, 0 F - ' / 6 z CD o ^\ X Q, _- L L OW Y^E 1 4O O 5O \ J\ >00 / ^ B L UE \ /' 550 \ \ 600 - '''RE , D 6 50 70 0 / \ / \ \. / / GREEN WA V E L ENGTH NM FIGURE5. Note: Values are taken from Wooten 1970, who estimated them using methods outlined in Jameson & Hurvich 1968. green, and blue) of the deviations in the combined RG and YB opponent systems (not the actual direction of response rate changes from a basal rate as in Fig. 4). The plus and minus values are used here simply to represent the opposition of red with green and of yellow with blue in their respective opponent systems. The absolute magnitudes of the red, yellows green, and blue deviations represent the strengths of the response states at different wavelengths (regardless of whether the 620 LANGUAGE, VOLUME 54, NUMBER 3 (1978) ower level eve iss through inhibition nh b t on or neural representat neura representation on of that response at some lower excitation). exc a on Valois o s and h hiss co nd cates that whilee co color or iss In sum that, wh sum, the work of De Va colleagues eagues indicates retinal na level eve in n the d differential fferent a d distributions str but ons of responses from the coded at the ret thiss code iss transformed beyond the ret retina na into nto one of opposed three types of cone cone, th blue ue neura neural response states d red and green and opposed ye distributed str buted by yellow ow and b nF below. ow It iss the re relative at ve strengths of these states states, Figure gure 66, be wavelength wave ength as shown in hue. (In add addition t on to the opponent ce determines nes perce cellss then, that d then directly rect y determ perceived ved hue n the macaque LGN two add so found in Valois o s et aal. aalso additional t ona discussed, scussed De Va just d which ch are non-opponent; i.e., ack the character characteristic st cof of e they lack cells, s both of wh types of ce regions ons that d complementary ementary spectra spectral reg distinguishes st ngu shes opponent opposed response to comp n the def rolee of these ce cellss in definition n t on of the fundamenta cells. ce s The ro fundamental categor black ack categories es b n ?4 discussed scussed in below. ow For the moment and wh white te iss d continue nue to ?4.2, 2 be moment, however however, we cont basicc to co discussion scuss on to the four hue response states bas restrict restr ct our d color or percept perception.) on ) n the support they prov The above ffindings nd ngs are part gn f cant in particularly cu ar yssignificant provide de for an color or percept quality ty of co analysis ana ys s of the phenomena phenomenal qua perception on presented by Her Hering ng color or appears subject ther as a pure 1920, who argued that any co 1920 subjectively ve y eeither pure, un unique que instance nstance of one of four fundamenta fundamental hues-red blue-or ue-or as a hues-red, ye yellow, ow green green, and b All co colors ors other than un mixture m xture of these pr red, un unique que red unique que ye yellow, ow un primaries. mar es A unique que could d be seen (on introspection) consist st a med cou blue, b ue or un unique que green green, Her Hering ng cclaimed, ntrospect on) to cons of the ssimultaneous mu taneous percept Hiss treatment regarded perception on of two of the pr primaries. mar es H oranges, ee.g., oranges g not as un unitary tary percepts percepts, but as hav having ng recogn recognizable zab e red and ye yellow ow are composed of red and b whilee ye components. Purp components Purples esare blue, ue wh yellow-green ow-green(chartreuse) (chartreuse) and b theirr true compos n the theirr descr blue-green ue-green(turquo (turquoise) se) show the composite te character in descriptive pt ve names.55 names blue ue to be the on Whilee cclaiming Wh fundamental hue a m ng red red, ye yellow, ow green green, and b onlyy four fundamenta so noted certa certain n antagon relations at ons between red and green sensations, sensat ons Her Hering ng aalso antagonistic st c re green, and a correspond blue. ue He observed that corresponding ng antagon antagonism sm between ye yellow ow and b blue ue may be perce call green green and b perceived ved ssimultaneously mu taneous y ((in n what we ca greenish-blues sh-b uesor or bluish-greens) b u sh-greens)and ssimilarly m ar y that red and ye yellow ow may be perce perceived ved ssimultaneously mu taneous y ((in n what we ca call, among other th things, ngs orange) orange). Contrast Contrastingly, ng y he po pointed nted out out, there iss no such th mu taneous percept blue ue and thing ng as a ssimultaneous perception on of green and red red, nor of b yellow. ye ow Perceptua Perceptually, y there are no ye yellowish-blues ow sh-b ues or b bluish-yellows. u sh-ye ows From these and other observat n fact two observations, ons Her Hering ng suggested that the four pr primary mary hues are in opposing oppos ng hue pa pairs, rs red-green and ye yellow-blue, ow-b ue whose oppos opposition t on indicates nd cates that these hue sensat sensations ons are the product of antagon neural processes (as yet antagonistic st c neura n Her undiscovered und scovered in Hering's ng s ttime). me) The correspondence between the phenomena phenomenal ana analysis ys s wh which ch Her Hering ng presented 5 A number o of recen recent sstudies ud es have no noted ed that ha a re relation a on ex exists s s be between ween the he B & K seman semanticc he one hand he oother, her (a) he resu resultss oof the he m results, resu s on the hand, and and, on the her eeither a the micro-electrode cro e ec rode sstudies ud es oof De Va Valois o s and h hiss co he abs abstract rac opponen model oof Her co-workers, workers (b) b the opponent-process process mode Hering, ng (c) c oother her n the material ma er a in he phys s on literature, physiological o og ca and psycho psycho-physical phys ca vvision era ure or (d) d some comb combination na on oof these. hese None oof these hese sstudies ud es traces races in n de detail a the he line ne oof argumen argument deve developed oped here and and, in n any m a ons oof space prec summarize ze their he r con contents. en s These sstudies case, limitations case preclude ude any aattempt emp too summar ud es include nc ude Borns Bornstein e n 1973a Cairo ro (MS); Miller er & Johnson 1973a,b, Fariss 1974 b 1975 1975; Ca MS Far 1974; M Johnson-Laird La rd (1976:342-55); 1976 342 55 Ratliff 1976 Ra Sahlins ns 1976 Witkowski kowsk & Brown 1977 1976; Sah 1976; S Stephenson ephenson 1973a 1973a,b; b 1976 1976; W 1977; and Zo Zollinger nger 1976. 1972, 1973 1972 1973, 1976 LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 621 hiss assoc associates ates iss str Valois o s and h and the neurophys striking. k ng nd ngs of De Va neurophysiological o og ca ffindings blue ue to observation on of the phenomena opposition t on of red to green and of b phenomenal oppos Hering's Her ng s observat cellss wh which ch have oppos Valois' os d opposing ng rediscovery scovery of ssingle ng e ce anticipated c pated De Va yellow ye ow ant G, Y Y, and B outputs of the R, G Clearly, ear y the R spectrum. C regions ons of the spectrum sponses to these reg fundamental hues descr described bed by Her Hering. ng The opponent processes are the four fundamenta nd cate the n the RG and YB systems then indicate deviations at ons in relative re at ve magn magnitude tude of the dev associated ated total co color or sensat sensation on assoc n the tota fundamental hue in relative re at ve strength of each fundamenta with w th light ven ght of any ggiven wavelength. ength The phenomena phenomenal appearance of light ven wave ght of a ggiven resultt of (1) the response state (R or G G, Y or B) of each wavelength wave ength iss thus the resu n each state state. Thus relative at ve strengths of the responses in system, and (2) the re opponent system Wooten'ss est estimates mates of the human opponent process funcwhich ch shows Wooten in nF Fig. g 55, wh n the YB system system. ttions, ons light yellow ow response in ght of 520 nm iss shown to produce a ye thiss iss of greatermagn n the RG system It aalso so produces a green response in tude greater magnitude system, and th resultt iss that light than the ye ght of 520 nm iss seen as pr dom domlnantly nant y yellow ow response response. The resu entire re e as ye with th a 'veil' ve of ye yellowish-green. ow sh-green The appearance of tIe ent yellow, ow i.e. green w eacniwaven th thiss manner vvisible s b e spectrum can be accounted for in manner, by eva evaluating uat ng at eacn functions ons relative at ve strengths of the two opponent response funct length ength the states and re nF shown in Fig. g 55. nd cates that observations ons indicates with th Her Valois' o s ffindings articulation cu at on of De Va The art nd ngs w Hering's ng s observat n the human percept nherent in a part color, or a structure perception on of co particular cu ar structure iss inherent one The opponent ght aalone. properties es of light which wh ch iss not deduc physical ca propert deducible b e from the phys neural response: categories es of neura specific f c categor describes bes four spec dent f es and descr process ana analysis ys s identifies As iss shown be states.66As below, ow response states (blue) ue)response the R (red) (yellow), ow) and B (b (green), Y (ye (red), G (green) n aall languages reflect ect the ex color or terms in existence stence of basicc co directly rect y ref the semant semantics cs of bas anguages d universal versa neural response categor Furthermore, when the un categories. es Furthermore these pan-human neura theirr structure and sets, the non-discretely screte y as fuzzy sets basicc co bas color or categor categories es are treated non-d precise se representaven a prec categories es can be ggiven formation format on from these pr prior or perceptua perceptual categor tion. on COLOR CATEGORIESAS FUZZY SETS 44.1. 1 UNIVERSALSOF COLOR COLOR-CATEGORY CATEGORYSTRUCTURE STRUCTURE. FUZZY SET MEMBERSHIPAND UNIVERSALSOF several re straightforward ghtforwardmod modificaf carelatively at ve y stra developed oped from severa Fuzzy set theory has deve standard The basic bas c of set the of the differences d fferences between ttions ons theory.7 theory 7 concepts n standard set theory iss categor categorically ca y two stem from the fact that membersh membership p in ISN'T Ta member of a ggiven IS or ISN ement ssimply set), wh whilee degrees of defined def ned (an eelement ven set) mp y ISor n fuzzy set theory theory. recognized zed in membership membersh p are recogn 6 The words red n an n bo a es oof LGN ce cellss in refer er too response sstates blue ue in boldface d ace re green, and b red, ye yellow, ow green ha need no not have co color or words aat aall. Tha That is, which ch are s they hey label abe neura neural responses wh organism organ sm that hey have no NECESSARY shared by macaques higher gher pr primates. ma es As such they humans, and probab probablyy aall h macaques, humans he r mean will see that, ha emp empirically, r ca y he correspond meanings; ngs bu but we w relation re a on too the English sh words or their corresponding ng Eng hese response sstates r c re relation a on be between ween these a es and the he mean Later, er color or words words. La there here iss a sstrict meanings ngs oof co he identity certain a n un neural categories egor es w with h neura established ab shed the universal versa seman semanticc ca when we have es den y oof cer will no not aalways desirable rab e too ma n maintain nan a d distinction s nc on in ways be necessary or des categories, egor es it w response ca notation. no a on 7 Th sections ons presen or the he conven convenience ence oof the reader, Thiss and subsequen he non non-mathematical ma hema ca reader present, for subsequent sec he bas basicc eelements emen s oof fuzzy set theory. mathematical hema ca reader a non uzzy se heory The ma description p on oof the non-rigorous r gorous descr 1971. iss re referred erred too Zadeh 1965 1965, 1971 622 LANGUAGE, VOLUME 54, NUMBER 3 (1978) asses denoted by the words Congressman and gourmet Consider Cons der the cclasses gourmet. The former seems to denote a set in n the accepted sense; in n part ther particular, cu ar someone iss eeither a Congressman or he iss not-the Congress does not adm admitt of degrees of memberThiss iss the on theories. es However ship. sh p Th onlyy sort of set countenanced by standard set theor However, ke a set gourmet (like gourmet( ke many other words) seems to denote someth set, except something ng very like that individuals nd v dua s appear to have d different fferent degrees of membersh Charles es may be membership. p Char more of a gourmet than Harry ess of a gourmet than Anne Anne. Zadeh 1965 Harry, and less 1965, 1971 has constructed the not notion on of fuzzy set to forma formalize ze th thiss sort of intuition. ntu t on A fuzzy set A iss def defined ned by a character characteristic st c funct function on fA wh which ch ass assigns, gns to every individual nd v dua x in n the doma domain n under cons consideration, derat on a number fA(x) between 0 and 1 which ch iss the degree of membersh nA A.88 For examp inclusively, nc us ve y wh membership p of x in example, e letting ett ng fG symbo characteristic st c funct function on of the fuzzy set 'gourmet,' symbolize ze the character gourmet perhaps 9 If so 4 ff,(Charles) 7 and fG(Anne) = .9. so, the inequalities nequa t es ggiven ven ff,(Harry) (Harry) = .4, (Char es) = .7, n words are sat above in satisfied: sf ed: fG(Char fG(Charles) es)> fG(Harry) fG(Harry),and fG(Char fG(Charles) es)< fG(Anne) fG(Anne). That co matter of degree in n Eng color-category or-categorymembersh membership piss a matterof English sh iss apparent from even casua casual cons consideration derat on of some of the ways that co color or iss ta talked ked about about. We can examplee of red speak of someth something ng as (a) a good red red, (c) the best examp red, (b) an off red red, red, (e) sslightly red, (f) ye (d) sort of red ght y red yellowish-red, ow sh-red (g) b blue-green, ue-green (h) light ght p pink, nk or dark blue. ue A All these construct constructions ons indicate nd cate the degree to wh which ch the co color or referred ((i)) darkb to approx dea examp color or term term. A good red has a h approximates mates an ideal examplee of the root co high gh degree of ssimilarity m ar ty to some norm for red red. Someth Something ng that iss eeither ther sort of red or sslightly ght y red is, n a lesser degree, an approx approximation mat on to th thiss norm norm. Lakoff has preesser degree s in sented a genera general treatment of hedges like ke those found in (a)-(e), wheresuch n (a)-(e) where such expresssions ons are ana analysed ysed as mod modifying fy ng or qua qualifying fy ng the degree to wh which ch someth something ng iss a member of a part particular cu arcategory category. In (a)-(e) (a)-(e), a co color or iss denoted (1) by referenceto reference to some bas basicc co color or category category, and (2) by the use of a hedge wh which ch indicates nd cates how much the co color or actua actuallyy named dev deviates ates from the norm for th thiss bas basicc category category. Constructions Construct ons (f)-( (f)-(i)) aalso so indicate nd cate degree of approx approximation mat on to a norm norm, but they indicate nd cate the d direction rect on of var variation at on from the norm as we well. A ye yellowish-red ow sh-redfa failss to be a good examp examplee of red by vvirtue rtue of hav having ng some degree of ye yellow. ow B Blue-greens ue-greens are ne neither ther good b blues ues nor good greens; and they d differ ffer from good greens g greens, ee.g., by be being ng b blue ue to a ssignificant gn f cant degree degree. Wh Whilee (f)-(g) indicate nd cate var variation at on in n hue from a norm norm, construct constructions ons such as (h)-( (h)-(i)) indicate nd cate var variation at on in brightness ghtness and n br and/or or saturation saturat on from a norm norm. L Light ghtp pinks nks are p pinks nks wh which ch are to some degree lighter ghter or whiter wh ter than the p pink nk norm norm. Dark b blues uesare are b black ack to a greaterdegree greater degree than b blues ues that are just b arejust blue. ue A phrase such as sslightly ght y purp blue ue comb combines nes spec specification f cat on of both purplish shb degree and d direction rect on of dev deviation at on from a norm norm, to denote a sensat sensation on that iss on onlyy marginally marg na y a member of the cclass ass of purp things, ngs but iss a near nearlyy perfect member purplee th of the cclass ass of b blue ue th things.9 ngs 9 Constructions Construct ons of these sorts are found in n aall languages, showing ng that aall speakeranguages show hearers recognize hearersrecogn ze and ta talk k about degrees of co color-category or-categorymembersh membership. pS Since nce co color or categorization categor zat on iss in n genera general a matter of degree degree, co color or categor categories es are best regarded 8 Ac Actually, ua y the he range oof the he function unc on may be expressed more genera generally, y bu but we need no not be concerned with concernedw h such ma mathematical hema ca n niceties ce es here here. 9 Rosch (1973, 1973 MS MS) hasa has also so ex extended, ended into n oseman semanticcdoma domains nsoother her than hanco color, or the heno notion on that ha semanticcca seman categories egor escan can be de defined ned in n terms erms oof approx approximation ma ontoo pro prototypes. o ypes LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 623 color or basicc co sets. The members of the fuzzy set correspond as fuzzy sets corresponding ng to each bas which ch color or percepts percepts. The degree to wh possible b e co category are chosen from the set of aall poss value ue between each percept iss a member of a part specified f ed as a va particular cu ar category iss spec function on that ass characterized zed by the funct zero and un assigns, gns unity; ty; each category iss thus character n that category color or percept to each co category. membership p in percept, a degree of membersh nformants to thiss framework framework, itt can be seen that when B & K asked informants Adopting Adopt ng th n effect ask nformants to X, they were in asking ng informants examplee of X pick p ck the best X or the best examp X. It n the category X which ch co colors ors had the h indicate nd cate wh membership p in highest ghest degree of membersh universal versa agreement colors ors that B & K found un focal co n these judgments of foca was in agreement. The foci are basicc co universal versa bas n the co color or space where these un color-category or-category foc regions reg ons in universal versa bas basicc co found can thus be understood as reg color-category or-category regions ons where un e un theirr max functions ons reach the maxima, ma i.e. unity. ty membership membersh p funct basicc co color or n the extens extension on of any ggiven nc uded in colors ors included non-focal co ven bas Similarly, S m ar y the non-foca non-maximal ma degrees of category membersh with th pos colors ors w term are co membership. p positive t ve but non-max basicc n these non-foca non-focal reg K'ss study and subsequent ones show that B &K that, in regions, ons the bas which ch are membersof members of more than Colors ors are found here wh color co or categor ntergrade Co categories es intergrade. basicc co thiss over one bas basicc category memberships ps color-category or-category membersh overlap ap of bas English, sh th category. In Eng etc. colors ors such as ye iss obv obvious ous for co reddish-purple sh-purp eetc yellow-green, ow-green redd n more with th pos colors ors w existence stence of these co It iss the ex membership p in positive t ve degrees of membersh n boundary color or categor basicc co than one of the bas variability ab ty in categories es that produced the var K. They co collected ected boundary data by ssimply asking ng mp y ask judgments reported by B & K n each bas basicc co Thiss nc uded in color or term term. Th colors ors included a the co nd cate 'all' informants nformants to indicate ass membersh membership p categor categorically. ca y Informants instruction nstruct on requ required red subjects to judge cclass membersh p An membership, p on onlyy 'membership'. nd cate degrees of membersh owed to indicate were not aallowed nd cate 'all a the reds reds' cou could d reasonab reasonablyy p pick ck nformant asked to indicate English-speaking Eng sh-speak ng informant colororwhich ch are red to a greaterdegree greater degree than they are any other co out aall the st stimuli mu wh nformant cou stimuli mu could d indicate nd cate aall the st red-oranges. Or the informant excluding, ud ng ee.g., g red-oranges thereby exc would d be reddish sh wou nce an express nc ud ng red or redd expression on including red, ssince with w th even a trace of red stimuli. mu Th Thiss amb n the ambiguity gu ty in description pt on of any of these st precise se descr appropriate appropr ate to a prec boundaries es left eft each informant nformant free to determ determine ne eelicitation c tat on frame for category boundar sufficient c entto to perm color or in na he fe feltt was suff nc us on of a co permitt inclusion what degree of membersh membership phe n boundaryjudgments resulted. ted variation at on in Wide de var boundary judgments resu category. W category n the B & K data into thiss amb nto ambiguity gu ty in McDaniel McDan e 1972 has attempted to take th absolute ute un universal versa boundar boundaries es ex exist st (as do un universal versa that, iff abso account-arguing account-argu ng that collected ected for each category foci), foc ) then aall the boundary judgments that B & K co ts focus and some spec Examinnt Exam fall between its absolute ute bounds for it. specifiable f ab e abso should shou d fa K'ss informants anguages for aall languages, color or term across aall B & K nformantsfor extensions ons of each co ing ng the extens universal versa category has we m ts in n the well-defined -def ned limits McDaniel McDan e has shown that (1) each un which ch the category iss never extended absolute ute extended, and (2) these abso color co or space beyond wh foci of the adjacent fundamenta fundamental co color or categor categories. es In the fuzzy boundaries boundar es are the foc universal versa boundar boundaries es are po n the co color or space beyond points nts in framework, these un set framework values ues for a ggiven nd v dua ways zero zero. Once individual which wh ch membersh ven category are aalways membership p va n boundary p attributed butedto to individual nd v dua K, are attr variations var at ons in placement, acement as found by B & K n the se selection ect on of cr criteria ter a for categor nc us on itt can be differences d fferences in categorical ca category inclusion, basicc co color or categor universal versa bas n add addition t on to un foci, universal versa foc have, in categories es have seen that the un boundaries. es absolute ute boundar universal un versa abso 624 LANGUAGE, VOLUME 54, NUMBER 3 (1978) color or category can be regarded as a fuzzy set where the basicc co In sum sum, each bas color or percepts n each set are chosen from the set of aall co eelements ements in percepts. The degree to basicc category iss spec which wh ch each percept iss a member of a part specified f ed as a particular cu ar bas color or value va ue between zero and un distinguished st ngu shed by the set of co unity. ty Each category iss thus d n it. t The genera which ch are ass general membership p in positive t ve degree of membersh assigned gned some pos percepts wh n the theirr pattern of membersh structure of these categor structureof assignments, gnments membership pass categories, es as shown in color or space from the focus of a iss such that that, as one moves through the perceptua perceptual co continuous nuous and gradua decline ne from ts boundar boundaries, es there iss a cont gradual dec category toward its color or percepts successive ve co values ues of success n the membersh addition, t on percepts. In add membership p va unity un ty to zero in theirr abso absolute ute boundar boundaries es are un uniververfoci and the basicc category foc the locations ocat ons of the bas n the co color or space xed in space. sallyy ffixed sa ear the inadebasicc co color or categor nadeThiss formu Th formulation at on of bas categories es as fuzzy sets makes cclear n the 'focus' embodied ed in focus and 'bouncolor or categor bounmodel of co categorization zat on embod quacies quac es of the mode talk k ssimply foci and boundar works. To ta boundaries es enta entailss (or earlier er works mp y of foc dary' language dary anguage of ear admitt of on color or categor nv tes the inference) at least east invites onlyy three degrees of nference) that co categories es adm thiss respect non-focal member non-member. In th focal member member, and non-member member, non-foca membership: membersh p: foca minor nor var variation at on of the two-degrees-of-membermodel iss but a m the focus focus/boundary boundary mode above. The arguments that can be made model quest discrete-feature screte-feature mode questioned oned above ship, sh p d model implicit model aalso so app three-degrees-of-membership pmode applyy to the three-degrees-of-membersh mp c t against aga nst that mode discussed scussed above and be in n the language focus and 'boundary'. below ow boundary The data d anguage of 'focus' indicate nd cate that co color or categor categories es need to be mode modeled ed w with th cont continuously nuous y gradeddegrees graded degrees of membersh membership, p not a sma small ffinite n te number such as two or three three. The forma formalism smof of fuzzy set theory iss a natura natural dev device ce for express expressing ngthe the cont continuity nu ty of bas basicc co color-category or-category membersh membership, p aallowing ow ng accurate descr description pt on of the fu full range of membersh memberships ps adm admitted. tted The spec special a status former formerlyy sought for foc foci and boundaries boundar es iss neverthe nevertheless esspreserved preservedin n the fuzzy set representat representation, on as these become characteristic character st cpo points nts (max (maxima ma and m minima) n ma) of the fuzzy membersh membership pfunct functions ons that represent the bas basicc categor categories. es The resu resultt iss a more accurate descr description pt on of bas basicc color co or categor categories. es In add addition, t on when bas basicc co color or categor categories esare are ggiven ven th thiss non-d non-discrete screte characterization, character zat on the membersh membership p funct functions ons that then represent the semant semanticc structures of these categor categories es can be der derived ved d directly rect y from the neura neural response functions funct ons (d (discussed scussed in n ?3 ?3, above) that make up the phys physiological o og ca code for co color. or 44.2. 2 FUNDAMENTAL NEURAL RESPONSES RESPONSES, FUZZY IDENTITY IDENTITY, AND THE PRIMARY BASICCOLORCATEGORIES BASICCOLOR CATEGORIES. set represen representations a ons oof the he un universal versa bas basicc co color or Fuzzy F uzzy se categories categor es red red, ye yellow, ow green green, and b blue ue can be deve developed oped d directly rect y from neura neural response funct functions ons inherent nherent in n the neura neural code for co color. or Th Thiss code cons consists sts in n the wave wavelength-dependent ength-dependent behav behaviors ors of the opponent neura neural states red red, ye yellow, ow green, and b green blue ue (see ?3) ?3). As shown in nF Fig. g 55, at a ggiven ven wave wavelength, ength at least east one and usuallyy two of these states are evoked usua evoked. Cons Consider, der ee.g., g po point nt YG in nF Fig. g 55, wh which ch represents a (ye representsa (yellowish-green) ow sh-green) light ght of 520 nm nm. At th thiss wave wavelength, ength ne neither ther red nor blue b ue iss evoked evoked. The abso absolute ute va value ue of the green response iss 11.8, 8 and the abso absolute ute value va ue of the ye yellow ow response iss 00.9. 9 These ssimultaneously mu taneous y evoked states compete in n perceptual effect perceptua effect, and the net effect at th thiss wave wavelength ength iss the percept perception on of a co color or zero per cent red red, zero per cent b blue, ue 67% green((l88 8 yellow ow )), and 33% ye 9+ -) From computat calculate cu ate for each response ((l8. 8 this, s we can ca computations ons such as th LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 625 ts proport state its contribution but on to the tota total chromat chromaticc response at each waveproportional ona contr results ts of these ca calculations cu at ons are represented by the four curves in n length. ength The resu which ch indicate nd ca e for or each wave Figure F gure 66, wh wavelength eng h THE PROPORTION OF THE TOTAL CHROMATICRESPONSECONTRIBUTEDBY EACH OPPONENTSTATE CHROMATICRESPONSECONTRIBUTEDBY OPPONENT STATE. (These These propor proportionon functions ons are a standardmeans standard means of express of-total-chromatic-response of-tota -chromat c-responsefunct expressing ngperce perceived ved color co or qua n the vvision s on literature, referredto as 'hue hue coeff terature where they are referredto quality ty in coefficients'.) c ents ) + A , 5 400 oQ Q a ^ B 450 500 550 WAVELENGTH FIGURE6. FIGURE6 600 650 700 NM Each oof the he four our functions unc ons shown in n F he ma mathematical hema ca proper Fig. g 6 has the properties es oof a set. Every individual nd v dua in n the he doma e light fuzzy uzzy se domain, n i.e. gh oof each wave wavelength, eng h iss ass assigned gned a number be between ween zero and un unc on These ne net neura neural unity, y inclusively, nc us ve y by each function. hus formally he graphs oof four our fuzzy response curves are thus sets, s and subs orma y the uzzy se substantively an ve y the he graphs oof the he four our fundamental undamen a neura neural response ca categories egor es fred, red fyeiiow? fgreen? ye ow?green? and fi,iue. hese four our neura neural response ca ha are encoded as the he un universal versa categories egor es that ue lt iss these semanticc ca seman a er fuzzy he red fyeiowr categories egor es fred, b ue The latter green fb,ue. uzzy ca categories egor es are the ye owr fgreen, designata des gnata of the Eng red, ye English sh words red blue, ue and of the words that yellow, ow green green, and b are exac exact translations rans a ons oof these hese in n languages VII. A After er pre V, VI VI, and VII anguages oof S Stages ages V prehe ev evidence dence for or this h s cclaim, will argue further ur her that ha the he seman semanticc ca senting sen ng the catee a m we w he bas basicc co color or terms erms occurr n the he wor world's d s languages gories gor es correspond corresponding ng too aall the occurring ng in anguages are eeither her (a) hese four our fundamental undamen a response ca wo a one oof these categories; egor es (b) b one oof two additional add ona fundamental undamen a response ca n roduced categories, egor es fbiack wh e too be introduced b ack and fwhite, unions ons among these hese ssixx fuzzy below; be ow (c) unc ons c fuzzy uzzy un uzzy ca d ssimple categories; egor es or (d) mp e functions oof fuzzy n ersec ons among these hese ssixx fuzzy neural response ca uzzy intersections uzzy neura categories. egor es The ev evidence dence for or the he identity he fundamental undamen a neura neural response ca den y oof the categories egor es with h the he seman semanticc ca reen and fbiUe categories egor es fred, red fyeilow, green and frcd, rcd fyeii0^, ye ow fgreen, ye 0^ freen. b Uew with h the he observa observation on just ha the he neura neural response ca begins ns w us made that categories egor es and fbiue b uebeg the he seman semanticc ca both h man non-discrete d scre e and na categories egor es are bo manifestly es y non naturally ura y represen representablee as fuzzy ab sets. s uzzy se he neura neural response ca Second, each oof the Second maximal ma categories egor es has a ssingle ng e po point n oof max he membersh unc ons charac he correspond membership, membersh p as do the membership p functions characterizing er z ng the corresponding ng semanticc ca seman categories. egor es he par which ch the he neura neural response functions Third, Th rd the unc ons reach particular cu ar wave wavelengths eng hs aat wh their he r max maxima-in ma n opponen he r un with w h erms their opponent process terms, unique que hue po points-coincide n s co nc de the he wave at wh which ch the he seman semanticc ca he r max e have their he r wavelengths eng hs a categories egor es reach their maxima, ma i.e. foci (McDan foc e 1972) ( McDaniel maximum mum 1972). The po points nts where fred, red fe feiiowv owvfgren, gren and fbiue b ue reach max B and in n are referred re erred as un to o R, Y Y, G G, (points po n s R hese 6 Figs. F gs 55-6) unique que hue po points: n s aat these he opponen channelss iss aat itss basa basal response ra ratee and makes no points, po n s one oof the opponent channe 626 LANGUAGE, VOLUME 54, NUMBER 3 (1978) chromaticc contr chromat chromaticc response iss determ determined ned exc contribution, but on so that the net chromat excluuchannel. In a rep of ssively ve y (and un uniquely) que y) by the response state of the other channe replication cat on B &K K'ss or McDaniel e has shown exper original g na exper experiment, ment McDan experimentally menta ythat wave wavelength ength measures of these un focal unique que hue po points nts correspond to wave wavelength ength measures of foca blues ues chosen by Eng yellows, ye ows greens greens, and b English-speaking sh-speak ngsubjects subjects.10 10The wave wavelengths engths which ch these aat wh hese un or frd rd and fred,11 red 11 575 nm unique que hue points n s occur are 695 nm for hue/focal oca po for or fyeuow or fgreen or fbiue yeuowand fyejiow, green and 475 nm for ye ow 510 nm for greenand fgreen, b ue and fb1ue. b1ue A fourth item tem of ev evidence dence for the identity neural and semant semanticc categor dent ty of these neura categories es iss that both show a gradua n membersh decline ne in values ues as one cons considers ders wavegradual dec membership p va n eeither ther d theirr membersh maxima. ma distances, stances in lengths engths at increasing ncreas ngd direction, rect on from the membership pmax neural response and semant semanticc categor Finally, F na y for each pa pairr of matched neura categories, es the values ues become zero at the same po n the co color or space declining dec n ng membersh membership p va points nts in values ues for both the neura neural and the semant semanticc cate(see ?4 ?4.1, 1 above) above). Membersh Membership p va decline ne cont gories gor es dec continuously, nuous y though rema remaining n ng pos positive, t ve as one moves away from the un until the un unique que hue po point/focus nt focus of each category category, unt unique que po point/focus nt focus of an reached. At these po values ues become zero adjoining adjo n ng category iss reached points nts membersh zero, membership p va and they rema remain n zero across the rema remainder nder of the spectrum spectrum. For examp example, e both the neural response category fgreen neura semanticc green (as psychophys psychophysically ca y determ determined) ned) and the semant nferred from B & K semanticc investigations) K, and from other semant category fgreen(as inferred nvest gat ons) have pos values ues in n the interval nterva between 575 nm (un positive t ve va (unique que ye yellow) ow) and 480 nm values ues eelsewhere. sewhere (unique (un que b blue), ue) but zero va In sum distinctive st nct ve propert semanticc categor sum, the d properties es of the semant categories es red red, ye yellow, ow green green, and b blue ue as d discovered scovered in n semant semanticc investigations to the propnvest gat ons correspond prec precisely se yto erties ert es of fuzzy response funct functions ons der derivable vab e from the opponent process mode model of the neura neural mechan mechanisms sms that under underlieeco color or vvision. s on Each of these semant semanticc categor categories es thus bears the identity relation at on to one of the four fuzzy fundamenta fundamental neura neural redent ty re termed these identity-based semanticc categor sponse categor categories. es We have termedthese dent ty-basedsemant categories es PRIMARY basicc co bas color or categor categories. es The ana full roster of un universal versa semant semanticc co color or categor analysis ys s of the fu categories es to be presented be below ow requ fundamental neura neural response categor b ack requires res two further fundamenta categories, es fbjack and fwhite. neural level eve of response wh e The ex existence, stence at some neura response, of categor categories es corresensations ons of b black ack and wh white te iss supportednot sponding spond ng to the sensat supported not on onlyy by the ev evidence dence so by a w wide de range of psychophys evidence. dence At the neuropresented here but aalso psychophysical ca ev Valois o s et aal. found that the LGN of the macaque has two eve De Va physiological phys o og ca level, 10 McDan McDaniel e d did d no not investigate he re relation a on oof un oca red because oof limitations nves ga e the unique que too focal m a ons in n the he equ available ab e too h him m (see n 10 equipment pmen ava see fn. 10). There iss no reason too suspec ha a test suspect, however however, that es oof that ha re relation a on wou would d have yyielded result d different eren from rom that ha found ound for or ye e ded a resu yellow, ow green green, and blue. b ue 11Thiss iss an overs 11Th he pures sensation on oof red occurs w oversimplification: mp ca on ac with h presen actually, ua y the purest sensa presentation a on too the he vvisual sua sys monochromaticc light, but ra rather her oof a m system em oof no monochroma mixture x ure oof mos gh bu mostlyy long-waveong wave length eng h and a littlee shor That is, short-wavelength wave eng h light D mm ck & Hubbard 1939 he sub gh (Dimmick 1939). Tha s the subjecec n phys erms a k kind nd oof 'purple', tively ve y pures purest red iss in mixture x ure oof lights physical ca terms purp e a m gh s oof long ong and shor short could d no not sstudy nh hiss exper McDan e cou wavelengths. wave eng hs (McDaniel udy red in experiment, men because on onlyy one source oof ssingle ng e Thiss comp wavelength wave eng h light not vvitiate gh was ava a e the he presen available.) ab e Th complication ca on does no present argumen argument, because the he phenomenon in n ques ec s the he neura neural response ca question on equa equallyy aaffects category egory fre(I re and the he semanticc ca seman without hou loss oss oof genera red We may thus, category egory fred. rea un hus w generality, y treat unique que red as if it corre correhe long he vvisual sponded too a ssingle ng e wave sua spec wavelength eng h near the ong end oof the spectrum. rum LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 627 further types of cells beyond those playing a role in the opponent processes. Both of these were non-opponent, in the sense that each cell was either excited or inhibited relative to its basal rate by light of every wavelength. These were called excitatory non-opponent cells and inhibitory non-opponent cells, respectively. By further experimentation and analysis that we will not report here, De Valois et al. concluded that 'the non-opponent excitatory cells carry luminosity information' (974), while the opponent cells do NOT carry luminosity information (975). (For technical reasons, the investigators were unable to make a comparable test on the non-opponent inhibitory cells.) De Valois et al. concluded: 'The brightness of a light is almost certainly encoded in the firing rate of the non-opponent cells; we have presented an analysis only of the non-opponent excitatory cells, but nonopponent inhibitors appear to give comparable information (this is clearly so for the squirrel monkey as shown by Jacobs [1964]).' That is, at the level of the LGN, beside the two opponent-process systems of cells that determine the four fundand a separate channe so ffind mental hue sensat menta channel, cons consisting st ng of br brightnessghtnesssensations, ons we aalso whiteness teness or nform us regard cellss that inform darkness-sensitive t ve ce sensitive sens t ve and darkness-sens regarding ng the wh fundamental additional t ona fundamenta basiss we pos thiss bas stimulus. mu us On th blackness b ackness of a st positt the two add color or ca neura response co neural wh e back and fwhite categories egor es fback n F or fb1ack wh e are g unc ons for b1ack and fwhite us Figure gure 77. As we have just given ven in Membership Membersh p functions charnot have the he opponen wh e do no b ack and fwhite he neura neural ca opponent char categories egor es fblack suggested, sugges ed the e d at the same sua ffield n the same part of the vvisual acteristic. acter st c They may be perce perceived ved in C 11. 0 - 0LU LU WHITE WH TE \ 0 - BLACK 20 -- 40 60 80 100 PERCENT REFLECTANCE 1943. Newhall eet aal. 1943 FIGURE7. Source FIGURE7 Source: Newha n Thiss iss indicated nd cated in unlike ke the opponent pa t me un time, yellow-blue. ow-b ue Th pairs rs red-green and ye values ues throughout the doma domain. n positive t ve va Fig. F g 7 by the fact that both curves have pos sensation on is, white te are perce black ack and wh When b s of course course, resulting t ng sensat together, the resu perceived ved together contribution but on of proportional ona contr reflecting ect ngthe proport grey, the lightness grey ghtness (darkness) of the grey ref n fwh the fwh fwhite teiss taken as the fwhite te(f membership p in Fig. g 77, degree of membersh (f,,a.k) a k) response response. In F n fb divided v ded by ten value ue (br Munsell va Munse ten, and degree of membersh fbiack ackas membership p in (brightness) ghtness) d value ue sca scalee runs from one to ten Munsell va thiss quant minus nus th quantity. ty (The Munse ten.)) The unity un ty m nc dent light reflects. ects abscissa absc ssa represents the proport ght that a surface ref proportion on of incident dent ca to those of the functions ons of fb The membersh and ftwhueare identical fbiack ackand membership p funct with th the semanticc categor semant fwhite teencoded by Stage V systems aalong fbiack ackand fwh ong w categories es fb white te are of course br Black ack and wh chromaticc categor fundamental chromat four fundamenta categories. es B brightness ghtness chromatics cs we have been cons n contrast to the chromat now. considering der ng up to now categories, categor es in dimension d mens on brief ef d discussion scuss on of the fact Introduction Introduct on of the br brightness ghtness requires requ res a br nteract w with th the dimensions mens ons of hue and br that the d nteract and that both interact brightness ghtness interact, 628 LANGUAGE, VOLUME 54, NUMBER 3 (1978) dimension of saturation (to be discussed below) in determining perceptual color categories. These interactions are illustrated in the representation of the full color space of Figure 8. In this standard schematization of the color space, the dimensions BLACK FIGURE 8. Note: Density of stippling indicates degree of membershipin green. of hue and brightness are orthogonal. The black/white (brightness) dimension is a polar axis marking the achromatic core of the color space, a line of greys that varies from black to white. Around this central axis the continuous dimension of hue circles in perpendicular planes. A color's distance out from the central axis toward the surface in a particular brightness-defined hue plane determines its chromatic purity or saturation. Chromatic purity is a measure of a color's vividness or chromaticity, an indication of how free a hue is from dilution by achromatic blacks, greys, or whites. Chromatic purity, i.e. saturation, is thus a function of the relative strengths of the chromatic (opponent) and achromatic (non-opponent) LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 629 ew of the co color or sphere with th the neural responses neura sphere, w responses. (F (Fig. g 8 represents a cut-away vview well as both upper and lower ower green-ye removed, as we upper b blue-green ue-green quadrant removed green-yellow ow quadrants.)) quadrants which ch the Because hue saturation on are aall d dimensions mens ons aalong hue, br brightness, ghtness and saturat ong wh neural responses that code co neura color or vary membership pspec specifications f cat ons for the vary, comp complete ete membersh neural response categor fundamental neura fundamenta semanticc categor defined ned categories es (and hence the semant categories es def in n terms of them) wou would d requ n each of these categor require re that membersh categories es be membership p in function on of aall threed three dimensions. mens ons F ustratesth thiss ssituation tuat on for the expressed as a funct Fig. g 8 illustrates n fgreen with h move n F movegreendec declines, nes as was shown in category ca egory fgreen. green Membersh Membership p in Fig. g 66, w ment away from foca focal green on the hue ccircuit. rcu t Membersh n fgreenaalso so dec declines nes Membership p in with w th movement from foca focal green toward the achromat achromaticc ax nce the greensa axis, s ssince greens along ong thiss path are becom th ess saturated saturated. Perce Perceived ved hue rema remains ns conbecoming ng progress progressively ve y less Thiss dec n green membersh chromaticness cness decreases decline ne in decreases. Th stant, but chromat stant membership p iss matched n the membersh ncrease in achromaticc category by a correspond corresponding ng increase membership p of some achromat category. As the sphero color or space indicates, maximal ma saturat saturation on nd cates the max spheroidal da shape of the co that green can have decreases focal green are decreases, as greens darker and lighter ghter than foca considered. cons dered Thus membersh n fgreens so a funct function on of br fgreenis aalso membership p in brightness. ghtness In def defining n ng the fundamenta fundamental chromat chromaticc categor formal descr three-dimenmencategories, es forma description pt on of these three-d ssional ona membersh functions ons iss poss thiss paper are not membership p funct possible, b e but the arguments of th n the beg affected thereby; and expos facilitated tated iff (as in thiss sect section on exposition t on iss fac beginning nn ng of th and in nF saturation on are tac held d constant constant. Fig. g 6) br brightness ghtness and saturat tacitly t y he 44.3. 3 FUZZYUNIONS EARLYSTAGEBASIC COLOR-TERM TERM UNIONS, COMPOSITECATEGORIES CATEGORIES,AND EARLYSTAGEBASICCOLOR standard set theory union on of two sets A contains ns theory, the un A,B B iss the set that conta nB n both nA both. Thus everything everyth ng that iss in A, or in B, or in Thus, iff the set of peop peoplee eeligible g b e for ckets iss the un union on of the set of reg cheap ttickets registered stered students and the set of peop peoplee under twe twelve ve years oold, ther reg students or under twe twelve ve d peop peoplee who are eeither registered steredstudents or both are eeligible. union on of the fuzzy sets A which ch we w will denote as 'A g b e The un A,B, B wh A OR B' iss def B defined ned by a funct which ch ass function on wh nd v dua x the larger assigns gns to each individual argerof of the two values va ues fA(x) define ne the un union on of two fuzzy sets A fA(x), fB(x) fB(x). In symbo symbols, s we def A,B B by th thiss SYSTEMS.In SYSTEMS equation: equa on (1) 1 fAORB AORB = Max [fA, A fB] B Let us suppose that we are interested n form nterested in union on of the fuzzy sets forming ng the un basketball p 'competent competent basketba player', ayer B B, and 'competent competent landscape andscape pa painter', nter P P. (Perhaps we are compos st for a potentate whose pr composing ng a guest list principal nc pa avocat avocations ons are basketball and landscape basketba andscape pa painting.) nt ng ) Let us further suppose that Kareem Abdu Abdul-Jabbar has a degree of membersh n B and .02 99 in n P; wh 02 in membership p of .99 whilee Joe Furge Furge, who has p basketball and so sold d a few waterco played ayed sem semi-pro -pro basketba watercolors, ors has degrees of membern these fuzzy sets of .55 and .6, ship sh p in 6 respect respectively. ve y Intu Intuitively, t ve y our potentate w will be more interested n meet nterested in Abdul-Jabbar -Jabbarthan n meet than in meeting ng Abdu meeting ng Furge; and so we are definition n t on of(B OR P) ggives gglad ad to note that our def ves a h higher gher degree of membersh membership pto to Abdul-Jabbar Abdu -Jabbar ((.99) 99) than to Furge ((.6), 6) desp despite te the fact that the sum and product of Furge'ss degrees of membersh Furge membership p both exceed those of Abdu Abdul-Jabbar. -Jabbar In standard set theory n the un nd v dua iss in union on of two sets iff itt iss in theory, an individual n eeither ther set; in n fuzzy set nd v dua iss in n the un union on of two sets to the greatest degree that itt iss in theory, an individual theory n eeither ther set (not to the degree that itt iss in n both both, whatever that m might ght mean) mean). 630 LANGUAGE, VOLUME 54, NUMBER 3 (1978) east one term that encodes color-term or-term systems pr All bas A basicc co prior or to Stage V have at least fundamental neura neural response categor a fuzzy un union on of two or more of the ssixx fundamenta categories. es union on w will be referredto referredto as COMPOSITE in n the sense of A category formed by such a un COMPOSITE, n colors ors that have any degree of pos positive t ve membersh membership p in being be ng composed of aall the co which ch itt iss formed formed. The compos fundamental response categor composite te categories es from wh any of the fundamenta he fuzzy union on fgreenoRblue; most ooften en iss GRUE ound mos GRUE, equ greenoRb ueccf. uzzy un equivalent va en too the category ca egory found characteristic st c of many described bed a grue category as character Figure F gure 99. Gatschet 1879 descr world d surveys by B & K and by BornIndian an languages; American Amer can Ind anguages; and the recent wor world's d s languages basicc co color or stein ste n 1973a 1973a,b b have shown that many of the wor anguages have a bas term that means grue grue. 11.00 E OELLOW / BLUE \ / GREEN \ / \ /RED RED 01 400 475 492 505 WAVELENGTH 545 575 593 700 NM FIGURE F GURE 9 9. No Note: e heavy line ne indicates nd ca es fgreonoRblue. greonoRb ue The heavy line ne in n F values ues that resu resultt from membership p va Fig. g 9 represents the membersh scalee in nF transformed from fgreenoRblueue(The wave Fig. g 9 has been transformedfrom wavelength ength sca evaluating eva uat ng fgreenoRb unc ons oof the he fundaunda normalize ze the he membersh uniform orm sca scalee oof F the he un Fig. g 66, too norma membership p functions h s membersh unc on iss ea ure oof this mental men a response ca n eres ng feature membership p function categories.) egor es An interesting mu us oof, say ower degree oof that ha a b say, 492 nm iss ass assigned gned a lower blue-green-appearing ue green appear ng sstimulus n grue than han a sstimulus mu us near eeither oca po her the he b blue ue or green focal membership membersh p in points, n s 475 nm and 510 nm Thiss corresponds too the n languages ha he cclaim a m that, ha in nm, respec respectively. ve y Th anguages that he co colors ors intermediate n ermed a e be encode grue between ween focal oca b oca green are re relaa blue ue and focal grue, the han eeither her focal oca b blue ue or focal oca green hough tively ve y poorer members oof grue than green, even though colors ors are nearer the these hese intermediate n ermed a e co he ma mathematical hema ca cen center er oof the he ca category. egory Thiss somewha Th somewhat coun counter-intuitive er n u ve pred direct rec produc he treatment rea men oof prediction, c on a d product oof the evidence dence on the he d distribution s r bu on oof grue focal oca union, on iss suppor grue as a fuzzy uzzy un supported ed by ev rom an e d sstudies ud es (Kay he exper choices cho ces from ud es anthropological hropo og ca field Kay 1975a 1975a). In the experimental men a sstudies that ha have been conduc K'ss work conducted ed subsequen work, it has been frequently subsequent too B & K requen y or Tze observed (as ound for ha ear as B & K found Tzeltal) a that early-stage y s age ca categories, egor es including nc ud ng grue grue, hese sstudies, are ooften en mu oca grue se selections ec ons have ooften en proved ud es focal multiply-focused. p y ocused In these too be b rom bo both h the he focal oca b blue ue and focal oca green reg But bimodal, moda be being ng chosen from regions. ons Bu n the ound too be focused ocused in he intermediate n ermed a e b grue has never been found blue-green ue green reg region. on The oca cho choices ces from rom this h s intermediate n ermed a e reg absence oof focal evidence dence that ha these hese region on iss sstrong rong ev colors co ors have lower ower grue membersh ha grue has the he membersh values, ues and that membership p va membership p sstructure ruc ure sstipulated he fuzzy union on ana uzzy un analysis. ys s pu a ed by the ormed by taking unions ons oof Fifty-seven F y seven compos compositee ca categories egor es can be formed ak ng aall poss possible b e un two wo or more oof the he ssixx fundamental undamen a neura neural response ca but bu hree categories; egor es onlyy three on in n add addition on too grue (cool) have been observed as basic bas c color co or coo actually ac ua y categories. ca egor es These observed compos warm ' (red ORye composites tes are 'warm yellow), ow) 'light-warm ght-warm' (wh (white te ORred LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 631 McDaniel e dark-coo (b (black ack OR green OR b yellow), ye ow) and 'dark-cool' blue) ue) (Kay 1975a; McDan ke that of the Dan 1974 MS 1974, Dani, are made up ent MS). On Onlyy Stage I systems systems, like entirely re y of neural response categor fundamental neura composite compos te categor categories. es At Stage II, aall the fundamenta categories es are jo nto the two compos dark-cool. Systems joined ned into categories es light-warm ght-warm and dark-coo composite te categor at Stages II contain n both pr II, III primary mary and compos composite te categor categories. es The III, and IV conta transitions trans t ons between these stages take p total decompos decomposi-place ace through the part partial a or tota ttion on of compos with th the separate encod composite te categor encoding ng of the pr categories, es w primary marycategor categories es of wh which ch they were composed ast of the compos composed. Grue iss the last composite te categor categories es that ts frequency transition t on to Stage V basicc co where all bas color or ose; hence its V, wherea languages anguages lose; frequency. The trans ts component pr categories categor es are pr primary, mary occurs when grue iss rep primaries mar es replaced aced by its blue b ue and green green. follows ows a basicc co color-term or-term vocabu vocabularies ar es fo V, the deve Beyond Stage V development opment of bas different d fferent pattern addition t on of pr transitions t ons no longer pattern. Stage trans onger occur through the add primary mary oss of compos basicc co color-term or-term lexicons ex cons expand by Instead, bas categories categor es and the loss composites. tes Instead the add addition t on of terms that referto color or space where the fundamenta refer to reg fundamental regions ons of the co neural response categor neura der ved categor ater 'derived' overlap. ap These later, categories-brown, es-brown categories es over related ated to the fuzzy intersections ntersect ons of the fundaorange, p orange pink, nk purp purple, e and grey-are re mental response categor menta categories. es OR DERIVED D ERIVEDCATEGORIES AND LATERSTAGEBASICCOLOR COLOR44.4. 4 FUZZY INTERSECTION INTERSECTION, CATEGORIES, TERMSYSTEMS.In standardset TERMSYSTEMS ntersect on of standard set theory theory, the intersection two sets A A,B B iss the set that so members oof B B. The contains con a ns just us those hose individuals nd v dua s that ha are members oof A and aalso A AND B '-is - s def intersection ntersect on of fuzzy sets A A,B-denoted B-denoted here as 'A defined ned by a funct function on of the two va that ass assigns gns to each individual nd v dua x the sma smaller erof values ues fA(x), A x fB(x). B x In symbo symbols, s thiss equat the intersection ntersect on of the fuzzy sets A A,B B iss def defined ned by th equation: on: Min n [fA, (2) 2 fAANDB AANDB = M A fs] s If the category correspond called ed charcorresponding ng to the fuzzy set 'green green AND ye yellow' ow iss ca treuse (as itt iss by some speakers of Eng chartreuse encodes a category English), sh) then chartreuseencodes whose membersh membership pfunct values ues indicated nF function on has the va nd cated by the heavy line ne in Figure gure 10 0 LE too oo t7s 7 O^ O ,,,|1 492 ,RE RE w /^E E ............................... sos o s4s 4 575 ....... ss33 700 WAV EL E NGTH NMlU NM U FIGURE10. Note: FIGURE10 No e heavy line ne indicates nd ca es fgreenA;NDyeiiowgreenA NDye ow monotone one function unc on thereof, which ch we re return urn be (or or perhaps some mono hereo a po below). ow point n too wh Colors Co ors be n this below ow 505 nm and above 575 nm have zero degree oof membersh hs membership p in As to o the he one advances from rom and to o the he left e (505 505 rright gh nm) nm category. ca egory unique un que green from rom un nds qu of o nm), one initially 575 nm chartreuse; char reuse unique que ye yellow ow (575 n a y finds quitee poor examp examples es but as one con bu her end continues nues from rom eeither he sstimuli mu exemp chartreuse reuse increasingly end, the exemplifyy char ncreas ng y with h membersh values ues reach maximum mum somewhere around 545 nm nm. well, w we membership p va reaching ng a max LANGUAGE, VOLUME 54, NUMBER 3 (1978) 632 n Eng color or term in non-basicc co Chartreuse iss a non-bas English; sh; yet the category itt encodes n the color or categor basicc co with th the bas shares an important categories es that are added in mportant property w e brown color-term or-term deve basicc co later ater stages of bas brown, orange orange, p pink, nk purp purple, e and development, opment i.e. basicc co color or categor Like ke chartreuse membership p chartreuse, these later-stage categories es have membersh ater-stage bas grey. L grey color or restricted cted to reg functions funct ons whose pos regions ons of the co positive t ve (non-zero) ranges are restr e to reg fundamental response states co-occur co-occur, i.e. regions ons where space where two of the fundamenta n the fundamental response categor two adjacent fundamenta overlap. ap Brown iss found in categories es over white te over black ack over purplee overlap, ap purp overlap, ap p pink nk where red and wh yellow ow and b region reg on where ye blue ue over where red and b yellow ow over overlap, ap and gray where overlap, ap orange where red and ye with th chartreuse which ch lateraterwhite te over black b ack and wh Thus, as w chartreuse, the reg regions ons over wh overlap. ap Thus ntersect ons of values ues are reg basicc categor regions ons where fuzzy intersections positive t ve va categories es have pos stage bas fundamental response categor certain certa n fundamenta positive. t ve categories es are pos basicc ntersect ons can thus be used to spec specify fy the reg regions ons where later-stage ater-stagebas Fuzzy intersections actual membersh color co or categor values; ues; but the actua membership p va membership p positive t ve membersh categories es have pos n these reg values ues that which ch these categor values va ues wh regions ons are not prec precisely se y the va categories es have in nF Consider der orange: in thiss category ntersect ons yyield. the ssimple 11A, th Figure gure 11A e d Cons mp e fuzzy intersections A C)~ C ~ 575 tI- ^ ~~~ ~ 700 O B O P~ 5S75 700 WAV EL E NGTH Nh1 ex he text. n the or reasons ggiven ormu a on for ven in he pre Note: e B iss the FIGURE11. No FIGURE11 preferred erred formulation a ms wo cclaims model makes two Thiss mode Th set fyeiiowANDredhe fuzzy den ca too the iss mode modeled ed as identical uzzy se ye owANDred he observations. ons F First, rs the casual and exper both h casua contradicted rad c ed by bo experimental men a observa that ha are con maximum mum oof orange. The max here are no rea ha there examples es oof orange a ms that reallyy good examp model cclaims mode he below ow the well be h s way modeled ed this or orange way, iss we unc on for orange, when mode the he membersh membership p function iss it fact ac in n and red; red encoded yellow ye ow he prev or the categories ca egor es maxima max ma for primary pr mary previously ous y are that ha evidence ev dence essentially essen a y contradicts con rad c s subjects sub ec s This Th s 0.5. 0 5 experimental exper men a precisely prec se y about hey are abou about ass examples es oof orange too orange as they as con confident den abou assigning gn ng good examp other o her of o or to o primary pr mary of o red any examples examp es red, red good examples examp es assigning ass gn ng good as is s them hem for or that ha declare dec are just us orange that ha to o subjects sub ec s Many category. ca egory category ca egory he ssixx sensation-as on as color or sensa distinctive s nc ve a co as d any oof the fundamental undamen a a ca category-just egory us ha not on model implies, h s mode onlyy that mp es no Second, this 1966). Second 1966) Boynton on 1966 S ernhe m & Boyn primaries pr mar es (Sternheim but he pr n compar primaries, mar es bu comparison son too the there here are no rea examples es oof orange in reallyy good examp n orange with h a h membership p in sensation on w here iss no hue sensa ha there higher gher degree oof membersh aalso so that he orange half oof the e ha he left her red or ye n eeither point n under the than han in yellow. ow Every hue po n ye yellow ow membership p in n F unc on in higher gher degree oof membersh Figure gure I11A has a h membership membersh p function memberhalf has a h he rright higher gher degree oof member n orange gh ha than han in point n under the orange, and every po existence s ence he ex about the confidence dence abou n orange han in n red than subjects' ec s con orange. As iss shown by sub ship sh p in LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 633 of good oranges oranges, there iss unquest unquestionably onab y a range of hues that speakers of Eng English sh more read abe orange than eeither ther ye n both exper readilyy label yellow ow or red in experimental menta and natural contexts natura contexts. These observat observations ons requ ntersect on mode model require re that we abandon the ssimple mp e fuzzy intersection of orange nF n favor of a mode ustrated in model wh which ch aallows ows some co colors ors A, in orange, illustrated Fig. g 11A to have a h n orange than in n eeither ther ye red, and higher gher degree of membersh membership p in yellow ow or red which wh ch aalso so has a membersh function on whose max maximum mum iss un Since nce orange membership p funct unity. ty S encodes the ssimultaneous mu taneous occurrence of ye red, the best examp yellow ow and red examples es of with th the h colors ors w n orange) w will be e the co orange ((i.e. highest ghest degrees of membersh membership p in those that are most near n the theirr ye redness. In other words words, nearlyy equa equal in yellowness owness and redness as the abso absolute ute d difference fference between a co color's or s degree of ye yellowness owness and degree of redness decreases ts orangeness approaches un decreases, its unity. ty The fuzzy set 'orange' orange iss therefore ore de he reg he spec defined, ned over the redANDye ow > O region on oof the spectrum rum where fredANDyellow O, by (3) 3 forange(x) o ang x = 1 - |fyellow(x) y ow x - fred(x) dx | The membersh function on for orange that th thiss equat membership p funct e ds iss shown by the equation on yyields nF ne in 11B. Th ts max Thiss funct function on reaches its maximum mum of un heavy line Figure gure 11B unity ty at the po point nt where the he functions unc ons fyeiiow n ersec A he ye red intersect. ye ow and fred Also, so aat the yellow ow and red un unique que hue value ue of the abso absolute ute d difference fference term iss un points, po nts the va unity; ty; hence the degree of zero, as des desired, red at these boundary po membership membersh p iss zero points. nts Equat Equations ons of the same derive ve membersh functions ons for aall of the general form can be constructed to der genera membership p funct basicc categor later-stage ater-stage categor categories. es The bas functions ons are categories es whose membersh membership p funct formed in n th thiss fash fashion on are thus referredto referred to as DERIVED bas basicc co color or categor categories. es Whilee Equa Wh not the he ssimple n ersec on fyellowANDred, Equation on 3 iss no mp e fuzzy uzzy intersection ye owANDred it can be rewritten rewr en in n a form orm that ha re relates a es forange orange d directly rec y too the he fuzzy n ersec on uzzy intersection will be reca recalled ed that ha each oof the he four our fundamental undamen a chroma chromaticc fyellowANDredye owANDred IIt w reflects ects the PROPORTIONof tota response categor categories es ref total chromat chromaticc response resu resulting t ng from part particular cu ar response state at each wave wavelength. ength Consequent Consequently, y at each wavehe sum oof the he four our fuzzy set functions unc ons fred, length, eng h the uzzy se b ue iss un unity. y red fyeiiow, green and fblue ye ow fgreen, within th n the interval nterva in n wh which ch orange iss def Furthermore, w Furthermore defined, ned the funct functions ons fblue b ue and fgreenboth have the va value ue zero; hence n th thiss interval, hence, in nterva the funct functions ons fredand o un ha Equa defines nes fredANDyelow he m minimum n mum unity. y Reca Recalling ng that fyeiiow ye ow sum to Equation on 2 de redANDye ow as the he functions oof the unc ons fred n this o ows that, h s interval, redand fyeiiow' he sma smaller er oof the ha in n erva (a) a the he ye ow it follows two wo functions unc ons fred, will aalways red fyeiiow ways be equ equivalent va en too fredANDye1jow; b the he redANDye1 ow and (b) ye oww he two wo w will aalways larger arger oof the ways be equ equivalent va en too 1 - fredANDyeliow. Equation on 3 redANDye ow Thus Equa rewritten tten may be rewr (33 ) (4) 4 forange(x) o ang x forange(x) o ang x = 1 - (11 = 1 - 1 + - = 2fredANDyellow(x) AND w fredANDyellow(x) dANDy ow x - fredANDyellow(x)) dANDy ow x 22fred d AND yyellow(X) ow X That is, n a der derived ved category such as orange s membersh membership p in orange, though not equ equivalent va ent to the fuzzy intersection ntersect on of the membersh membership p funct functions ons of its ts two const constituent tuent catethiss intersection.12 twice ce th ntersect on 12 gories, gor es iss equ equivalent va ent to tw Whilee Equat Wh 3-4 Equations ons assign ass gn the same membersh membership pfunct function on to orange orange, they may distinct st nct cogn n the format represent two d cognitive t ve processes in formation on of der derived ved categor categories. es 12 We are indebted ndeb ed too John R R. A Atkins k ns for or po out too us the pointing n ng ou he equ equivalence va ence oof Equa Equations ons 3 and 44. 634 LANGUAGE, VOLUME 54, NUMBER 3 (1978) referredto in n these equat n equations ons correspond in operations ons referredto Assuming Assum ng that the fuzzy set operat different fferentcclaims a ms about actual neura neural and cogn some way to actua events, 3 and 4 make d cognitive t ve events derived ved co formation. on Equat available ab e for der the cogn Equation on color-category or-category format cognitive t ve processes ava formation on of a der derived ved category 4 suggests that the on onlyy operat operations ons needed for the format scalar ar mu are fuzzy intersection ntersect on and sca however, suggests Equation on 33, however multiplication. t p cat on Equat different fferentcogn n orange the ex existence stence of three ent cognitive t ve operat operations. ons Membersh Membership pin entirely re y d orange, determined ned by tak absolute ute of, (b) the abso taking ng (a) the comp complement ement of according accord ng to 33, iss determ functions ons represent n difference fference between two funct value va ue of of, (c) the d representing ng membersh membership p in choice ce between 3 and 4 can thus have fundamental response categor fundamenta categories. es Mak Making ng a cho example, e iff 3 iss taken as the proper representamp cat ons For examp general cogn genera cognitive t ve implications. which ch comp rolee wh thiss encourages cons consideration derat on of the ro ttion on of orange complement ement orange, th n fuzzy doma domains. ns Accept motive. ve In add addi-Accepting ng 4 prov provides des no such mot play ay in operations operat ons p distinctive st nct ve cogn ttion, on the ssimple processuallyy d cognitive t ve paths by mp e fact that there may be processua structure can be formed suggests that semant semanticc processes which wh ch the same semant semanticc structurecan sometimes mes be independent. and semant semanticc structuresmay somet example, e one m ndependent For examp might ght be different fferent individuals-or nd v dua s-or a ablee to exam ab examine ne exper hypothesiss that d experimentally menta y the hypothes conditions-would t ons-wou d process the semant semanticc category nd v dua under vary varying ng cond ggiven ven individual n ways that somet sometimes mes suggested 33, and somet sometimes mes 44. orange in n There iss indirect nd rect ev evidence dence indicating nd cat ng that these and the other equat equations ons used in n fact representat neural structuresare structures are in thiss paper to re th relate ate semant semanticc to neura real representative ve of rea be t at a grosser level. eve Tak neural and cogn neura cognitive t ve events events, aalbeit Taking ng the equat equations ons presented actual cogn in n th thiss paper as mode modelss of actua ther 3 or 4 as a mode model cognitive t ve processes processes, us using ng eeither which ch under of the cogn underlies es der derived ved categor would d be to assert that cognitive t ve process wh categories es wou these categor categories es have more comp complex ex cogn cognitive t ve bases than do the pr primary mary caterelation. at on A likely observablee effect of th thiss greater gories gor es based on the identity dent ty re ke y observab n the ttime would d be an increase ncrease in me needed by subjects to detercognitive cogn t ve comp complexity ex ty wou mine m ne der derived ved category membersh me needed to determ memberships, ps over the ttime determine ne pr primary mary thiss effect in Heider der found just th n a study of Eng category membersh memberships. ps He English sh foca focal color co or nam foca co n the study were probab colors ors used in naming, ng even though the 'focal' probablyy not thiss hypothes optimal opt ma for a proper test of th hypothesis. s Her ffinding nd ng was that the 'primary pr mary focal co foca colors ors b black, ack wh white, te b blue, ue green green, ye yellow, ow red were named ssignificantly gn f cant y more focal co colors ors p rapidly rap d y than the non-pr non-primary mary foca pink, nk brown brown, orange orange, purp purple; e; t(22) = 01 (for corre correlated ated measures) 22.86, 86 p< .01 measures)' (1972b: 15) 15).13 13 13 The abso absolute u e order oof reac reaction on times mes was no not in n exac exact agreemen agreement w with h the he hypo hypothesis. hes s Whereas orange should d have had the he four our longest orange, purp purple, e p pink, nk and brown shou onges response latencies, a enc es the he ac actual ua rank order oof latencies a enc es was (from shortest es too longest) rom shor onges b black, ack ye yellow, ow wh white, e PURPLE PURPLE, 1972b: 15 But there here are aat least blue, b ue red red, p pink, nk brown brown, GREEN GREEN, orange (Heider He der 1972b 15). Bu eas two wo d difficulties cu es with w h He Heider's der s me which ch sugges caution on in n interpreting methodology hodo ogy wh suggest cau n erpre ng these hese resu results. s F First, rs she determined de erm ned 'focal' oca co colors ors by taking he 'geometric ak ng the geome r c cen centers' ers oof the he areas enc enclosing os ng aall the he focal oca cho choices ces in n the he B & K da dataa (p. Heider der 1972b 1972b: 12 p 99; He 12). Un Unfortunately, or una e y focal oca greens in n B&K were over over-extended ex ended toward oward b blue ue because V Vietnamese e namese xanh 'grue', grue wh which ch has a near near-unique un que blue b ue focus, misclassified sc ass ed as green he 'focal' oca green wh ocus was m green. Thus the which ch He Heider der used used, Munse Munsell 77.5G 5G 55/10, rather her d n bo distant s an in both h hue and sa saturation ura on from rom the 10 iss ra he lOGY OGY and 22.5G, Munsell 5G Munse colors co ors typically oca greens Thiss par yp ca y chosen as focal greens. Th particular cu ar d difficulty cu y m might gh he help p exp explain a n the he espe espeow pos n the he response latency ccially a y low position on oof green in a ency rank rankings. ngs obtained a ned their he r focal oca co Second, and more important, Second mpor an B & K ob color or judgments, udgmen s wh which ch He Heider der used too se select ec her sstimulus mu us ma materials, er a s under a sstandard andard illuminant um nan A A, wh whilee He Heider der conduc conducted ed her tests es s w with h day uorescen illumination. daylight gh fluorescent um na on The d difficulty difficu cu y here iss that ha ob object ec co colors ors can LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 635 Apart from the details of their formal (or cognitive) representation, another question raised by the emergence of derived categories in post-Stage V systems is the possible effect of the emergence of these categories on the primary categories from which they are derived. It was noted above that the encoding of a primary category is accompanied by decomposition of some previously existing composite category. What might seem a comparable effect of the encoding of a derived category would be contraction of the membership functions of the primary categories from which it is derived. This possibility is illustrated for orange, yellow, and red in Figure 12B. A o BG X LLJ 57 s7s 70 57 700 575 WAIELENGTH 0 700 NM FIGURE12. Note: Formulation A, in which there is no change in the primary categories, is preferred for reasons given in the text. There are data, however, which indicate that the non-contracted membership functions for yellow and red shown in Figure 12A are retained by yellow and red even after orange is encoded. In an experiment conducted by Sternheim & Boynton, subjects were asked to name ten long-wavelength (530-620 nm) stimuli under a variety of naming conditions. One condition allowed subjects to use the names yellow, red, and orange. ln this condition, the yellow and red naming-functions were like the retracted functions shown in Fig. 12B. A second condition required that subjects use only the terms yellow and red, although a null response was accepted if a subject felt that neither yellow nor red was appropriate. In this condition, the naming functions for yellow and red expanded to approximate the non-contracted functions shown in Fig. 12A. These results suggest that, as derived categories are encoded, the underlying membership functions of the primary categories remain unchanged, while competition between the memberships which colors have in the old primary categories and the newly encoded derived categories alters surface naming behavior in many (but not all) contexts. Our intuitions about the use of primary basic color terms in comparative constructions also support the model of orange, yellow, and red depicted in Fig. 12A. An English speaker discussing the two oranges denoted by x and y in Figures 12A and 12B might distinguish them by saying that y is redder than x, since in shift rad sh with h changes in n illuminant conditions. ons Thus He radically ca y w well-defined de ned um nan cond relatively a ve y we Heider's der s re oca s mnayhave been poor approx he focal oca co colors ors when vviewed ewed under illuminant um nan A focals approximations ma ons too the her day uorescen il conditions. ons A less ess than han ideally constituted u ed se set oof sstimuli daylight gh fluorescent mu for or illuminant um nan cond dea y cons the he ggiven conditions ons may therefore here ore be par or the he somewha ven exper experimental men a cond somewhat equ partlyy respons responsible b e for equivocal na voca nature ure oof these hese resu results. s 636 LANGUAGE, VOLUME 54, NUMBER 3 (1978) he mode model represen n F both bo h figures he speaker 12A, the red x By the represented ed in gures fred(y) Fig. g 12A red y > fred(x). han yy, ssince could cou d as we ha x iss ye nce fyeiiow(x) well say that if ye ow x > fyeiiow(y). However, However yellower ower than ye ow y = = is s as in n then hen and our fyellow ye ow con contracted, rac ed 12B, 00, fyeiowv(x) ye owv x Fig. F g 12B speaker fyeiiow(y) ye ow y won'tt be ab won ablee to use re relative at ve ye model Thus, by the mode yellowness owness to d distinguish st ngu sh x and yy. Thus in nF describe be a ffirst rst 12B, there iss a reg Fig. g 12B region on of the spectrum where a speaker can descr rst An second, but not the second as ye yellower ower than the ffirst. orange as redder than a second thiss to be the case; but our intuition ntu t on iss that any orange experiment exper ment m might ght show th that iss redderthan redder than another iss aalso so less ess ye will aalways yellow, ow and therefore the second w ways Thiss intuition rst Th ntu t on iss taken as further argument as ye be descr describable bab eas yellower ower than the ffirst. in n support of the ana nF derived ved categor 12A. analysis ys s of der categories es shown in Figures gures 11B and 12A ntersect on mode model of orange and the other der Whilee a ssimple Wh derived ved bas basicc catemp e intersection ntersect on iss the appropr model rejected, itt may be that ssimple gories gor es has been rejected mp e intersection appropriate ate mode for secondary co color or categor non-basicc terms such as chartreuse chartreuse. corresponding ng to non-bas categories es correspond Like L ke der derived ved categor mixtures xtures of the categories es are psychophys psychophysically ca y m categories, es these categor or examp fundamental undamen a response ca chartreuse, reuse for Treating ng char ye owAND ggreenn categories. egor es Trea example, e as fyeiiow in n the he appropr oca e fchartreuse char reuse of the would wou d locate he co color or space w with h an intuitively appropriate a e reg region on o n u ve y function. on In add thiss forma formal move wou would d enta entail the addition, t on th acceptablee membersh acceptab membership p funct with th chartreusein a m that n the theirr act active ve vocabu that, for speakers w empirical emp r ca cclaim vocabulary, ary any would d judge as chartreusewou which ch they wou chartreuse would d be judged as an equa stimulus st mu us wh equallyy good or better representat Thiss specu representative ve of ye yellow ow or of green green. Th speculation at on iss not immediately mmed ate y rejected by introspection; rejectedby ntrospect on; however however, we know of no systemat systematicc data that support it. t If some subjects were found to react to appropr appropriate ate st stimuli mu w with th the labels abe s chartreuse, ye treuse yellow, ow and green in n the mannerjust manner just suggested suggested, wh whilee others were found to use chartreuse in n the way they genera generallyy use labels abe s for bas basicc (der (derived) ved) categor categories es such as orange orange, th thiss cou could d be taken as ev evidence dence for the assert assertion on that chartreuse has ach achieved eved bas basicc co color-term or-term status for the latter atter group group, but not the former former. Fuzzy set-theoret set-theoreticc representat representations ons of co color or categor categories es m might ght thus prove usefu useful in n yet another way way, th thiss ttime me in n the theirr ab ability ty to aaid d in n the somet sometimes mes d difficult ff cu t task of distinguishing d st ngu sh ng bas basicc and non-bas non-basicc categor categories. es (Severa (Several contro controlled ed ffield e d stud studies es have shown order orderlyy var variation at on among speakers in n a ggiven ven commun community ty w with th regard to the number of bas basicc co color or categor categories es they have; see Kay 1975 for a summary summary.)) The use of character characteristics st csof of co color-category or-category membersh membership pfunct functions ons to d distinguish st ngu sh between bas basicc and non-bas non-basicc categor categories es suggests a natura natural way to enr enrich ch the not notion on of bas basicness cness itself. tse f The bas basicness cness of a co color or category cou could d be taken as the degree to wh which ch its membership pfunct ts membersh function on approx approximates matesaa character characteristic st c(prototyp (prototypic) c) membership bersh p funct function on of one of the three types of bas basicc category descr described bedabove above. We are not aware of any extant emp empirical r ca ev evidence dence bear bearing ng on th thiss specu speculation. at on 44.5. 5 SUMMARY OF THE FUZZY SET FORMULATIONFOR FORMULATIONFOR BASIC COLOR CATEGORIES CATEGORIES. Basicc co Bas color or terms are un universally versa yassoc associated ated w with th a sma small set of non-d non-discrete screte though well-defined we -def ned semant semanticc categor categories. es The forma formalism sm of fuzzy set theory prov provides des a natural framework for the descr natura description pt on of these un universal versa and non-d non-discrete screte categories. gor es It aalso so aallows ows a forma formal set-theoret set-theoreticc character characterization zat onof of the re relations at ons wh which ch these fuzzy categor categories es bear to neura neural categor categories es inherent nherent in n the percept perception on of co color. or All bas A basicc co color or categor categories es are formed from the human vvisual sua system system'ss ssixx fundamental response categor menta categories es by one of three fuzzyfuzzy-logical og ca operat operations: ons: identity, dent ty LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 637 fuzzy union, or fuzzy intersection, sometimes along with one or more non-fuzzy operations. Identity with the six fundamental response functions is the basis of the primary basic color categories black, white, red, yellow, green, and blue. Fuzzy unions of fundamental response categories are the basis of the four composite basic-color categories light-warm, dark-cool, warm, and cool (grue). Fuzzy intersections of fundamental response categories are the basis of at least five derived basic color categories-brown, pink, purple, orange, and grey.14Thus where B & K described eleven universal basic color categories of a single logical type, there are in fact at least fifteen basic color categories of three types (McDaniel 1974, MS), distinguished by the relations which their semantic structures bear to the visual system's fundamental neural response categories for color. Table 2 is a summary listing of these categories, showing the three types of fuzzy set operations that relate them to the fundamental neural response categories. NEURALRESPONSE CATEGORIES BASEDON IDENTITY CATEGORIES SEMANTIC fblack fred fblack fwhite fred fyellow fyellow = = = = fgreen fgreen = fblue fblue = blue fblack OR green OR blue fblack OR green OR blue = red OR yellow fwhite OR red OR yellow = f\hhite black white red yellow green SEMANTIC CATEGORIES BASED ON FUZZY UNION fwhite OR fred OR yellow fgreen OR blue fred OR yellow fgreen OR blue dark-cool light-Warm = warm = cool; grue SEMANTIC CATEGORIES BASED ON FUZZY INTERSECTION fblack + yellow fblack fred + blue fred + blue + yellow = = brown purple fred + white fred + white = pink fred + yellow fred + yellow = orange grey fwhite + hlack fwhlte + black = TABLE 2. color or categor basicc co The bas categories es formed by each fuzzy logical og ca operat operation on share a semanticc proper unc ons oof the he ssixx pr number oof seman properties. es The fuzzy uzzy membersh membership p functions primary mary with h the he fundamental undamen a response ca basicc ca bas being ng based on identity den y w categories, egor es be categories, egor es he fundamental undamen a ca he proper share aall the properties es common too the categories. egor es Each ca category egory has e a ssingle a ssingle defined ned maximum, mum i.e. ocus aat a phys membership p max ng e focus, ng e membersh physiologically o og ca y de n these hese ca declines nes con colors ors Membership p in point. n Membersh categories egor es dec unique un que hue po continuously nuous y as co 14 The formulation or orange genera ormu a on we have ggiven wo ven for generalizes zes d directly rec y too purp purple, e whose two both h hue ca constituent cons uen pr rue for or grey both h oof categories egor es are bo categories. egor es The same may be true primary mary ca grey, bo achromatic. c The aalgebraic constituent uen pr whose cons ormu a on ggiven n Equa primaries mar es are achroma gebra c formulation ven in Equation on 3 so too the he ca which ch iss based on one categories egor es p pink nk and brown brown, each oof wh generalize ze aalso may perhaps genera achromaticc cons but the he spec hue cons constituent uen and one achroma relations a ons ob constituent; uen bu between ween the he special a re obtaining a n ng be he der derivation va on oof 4 from rom 3 do no not app ha perm n the he case oof p brown. permit the applyy in primary pr mary hues that pink nk and brown he symbo will use the denotee wha + too deno whatever ever function, Henceforth, Hence or h we w symbol '+' unc on known or unknown unknown, derived ved ca wo pr relates re a es two will wr writee 'forange orange = categories egor es too produce a der primary mary ca category. egory Thus we w eetc. c The symbo not deno denotee a ssingle, wellsymbol '+' 'fpink p nk = fred+hlte', + so used does no ng e we fred+yellow', d+y ow d+h defined de ned fuzzy uzzy opera operation. on 638 LANGUAGE, VOLUME 54, NUMBER 3 (1978) maxima ma are cons distant stant from these max considered, dered reach reaching ng zero at the perceptuallyy more d perceptua characteristics st csof of focal un unique que hue po points. nts These character unique un que hue po points nts adjacent to the foca nF 6-7. functions ons are illustrated ustrated in basicc co Figs. gs 6-7 membership p funct color-category or-category membersh primary pr mary bas In contrast union, on have mu contrast, compos multiple t p e membercategories, es based on fuzzy un composite te categor colors ors increasingly distant stant from a focus do not necessar maxima ma (foc necessarilyy (foci); ); and co ncreas ng y d ship sh p max ower degrees of membersh have lower unique que hue po points nts of the two or three membership. p The un fundamental response categor fundamenta composite te category are the categories es encompassed by a compos n the category does dec decline ne to zero for foci of the category Membership p in (multiple) (mu t p e) foc category. Membersh non-included nc uded un focal un colors co ors between one of the foca unique que hue points nts and a nonunique que hue po values ues define ne foc colors ors between un foci, membersh membership pva points nts that def unique que hue po point. po nt For the co zero. Instead minimal n ma decline dec ne away from each focus Instead, a pos focus, but do not reach zero positive t ve m foci. F value ue iss reached somewhere between the two foc Fig. g 9 shows a membership membersh p va characteristics. st cs with th these character function on w membership membersh p funct ntersect ons produced memmodified f ed fuzzy intersections formation on from mod Derived Der ved category format characteristics st cs ana structural character functions ons w with th structura analogous ogous to those of the pr primary mary bership bersh p funct derived ved category membersh with th the pr color or categor basicc co bas primaries, mar es der membership p categories. es As w n the co color or space maxima ma at ssingle functions funct ons reach max declining n ng cont continuously nuous y space, dec ng e po points nts in them. But wh whilee the from these foc foci to zero at the un unique que hue po points nts adjacent to them structural character derived ved categor differ ffer characteristics, st cs they d categories es share these structura primary pr mary and der association. at on In part whilee the foc foci n the neural assoc theirr patterns of neura particular, cu ar wh ssignificantly gn f cant y in (and compos composite) te) categor categories es are assoc associated ated w with th phys physiological o og ca un unique que primary mary(and of the pr foci of the der derived ved categor categories es are not not. Der Derived ved category foc foci are points, nts the foc hue po points nts in n the co color or space perceptua perceptuallyyequ equidistant d stant between the two with th po associated assoc ated w points nts that def define ne the category category'ss boundar boundaries. es S Simple mp e fuzzy intersections ntersect ons unique un que hue po assign gn the correct co colors ors pos positive t ve degrees of membersh membership p in n the functions ons that ass yyield e d funct scalar ar mu multiplication t p cat on of these funct functions ons iss necessary to categories, es but a sca derived der ved categor membership p va values ues appropr appropriate ate for these categor categories. es F Figs. gs 11B actual membersh produce the actua membership p funct function on of th thiss type type. ustrate a membersh and 12A illustrate basicc co color or categor categories es as fuzzy sets sets, ratherthan rather than in n terms formulating at ng bas general, formu In genera foci and boundar boundaries, es aallows ows us to construct mode discrete screte features or of foc modelss eeither ther of d n accord w with th our emp empirical r ca know knowledge edge of the theirr semant semanticc categories es more in of these categor so prov provides des descr descriptions pt ons of bas basicc co color or categor categories es that can be der derived ved structure. It aalso structure neural response patterns that under underliee the percept perception on of co color. or directly d rect y from the neura below, ow the fuzzy set forma formalism sm aalso so aallows ows a succ succinct nct forma formal restatediscussed scussed be As d K'ss mode model of bas basicc co color-term or-term evo evolution. ut on ment of B & K THE EVOLUTIONOF EVOLUTIONOF BASIC COLORCATEGORIES COLOR CATEGORIES PRIMARY, AND DERIVED BASIC COLOR CATEGORIESAND CATEGORIESAND THEIR COMPOSITE, PRIMARY 55.1. 1 COMPOSITE PROCESSESAND PATTERN OF BASIC COLOR COLOR-TERM TERMEVOLUTION EVOLUTION. AS RELATIONS TO THE PROCESSESAND discussions scuss ons above above, pr primary, mary compos composite, te and der derived ved bas basicc co color or n the d noted in onlyy in n the theirr character characteristic st c semant semanticc structures structures, and in n the differ ffer not on categories categor es d fundamental neura neural response categor categories, es but aalso so in n the relations re at ons they bear to the fundamenta color-term or-term deve development opment w with th wh which ch they are assoc associated. ated Compos Composite te basicc co stages of bas onlyy pr prior or to Stage V V. No pr primary mary categor categories es ex exist st at Stage categories categor es are found on primaries mar es encoded encoded. The der onlyy at Stage V and beyond are aall the pr derived ved II, and on begin n appear appearing ng on onlyy after Stage V V. F Figure gure 13 illustrates ustratesthese these re relations, at ons categories categor es beg R or YW 1 [WorRorY [ Bk or G or Bui _^ F ]/ jRorY [ DoB] G or Bu j-WR Bk J-RY Bk I BkRB Y-Bk_ -Bk or G or Bu Stages: I II lila IV IIIb FIGURE 13. v 640 LANGUAGE, VOLUME 54, NUMBER 3 (1978) n terms of the fuzzy setevolutionary ut onary sequence in original g na B & K evo recasting recast ng the or above.15 15 described bed above color or categor basicc co theoreticc bas theoret categories es descr ews the embodies es a reevolutionary ut onary sequence that vviews re-interpretation nterpretat onof the evo Fig. F g 13 embod successive ve encod ex con not as the success color-term or-term lexicon basicc co encoding ng of foc foci, but development deve opment of bas basicc co color or categor differentiation fferent at on of prev successive ve d as the success existing st ng bas previously ous y ex categories es with th the compos 1974, MS composite te categor categories es lightMS). Beg Beginning nn ng at Stage I w (McDaniel (McDan e 1974 ghtmolaa and m Dani mo Heider der 1972a) ustrated by Dan dark-cool (as illustrated warm and dark-coo 1972a), Stages mill;; He nvo ve the decompos n the evo nto II-V in decomposition t on of compos composites tes into evolutionary ut onary sequence involve white te component of the light-warm First rst the wh constituent tuent pr theirr const the ght-warm category primaries. mar es F dark-cool conf iss lexically white, te warm warm, dark-coo configuration gurat on of producing ng the wh distinguished, st ngu shed produc ex ca y d described bed by Kusche color or system descr Kuschel & Monberg Bellonese onese co systems. The Be Stage II systems nto b black ack and coo dark-cool iss decomposed into ther dark-coo thiss type iss of th cool, or warm Next, eeither type. Next rst aalternative ternat ve resu results ts in n a Stage constituents. tuents The ffirst ts red and ye iss sp nto its yellow ow const splitt into Berlin n & Ber Berlin n and for West described bed for Aguaruna by Ber IIla a conf configuration, gurat on as descr eads to a stage IIIb system 1975. The second leads Futunese by Dougherty 1974 1974, 1975 system, as Binumarien. numar en Wh Whichever chever of these decompos describe be for B decompositions t ons Hage & Harkes descr n the trans transition t on to Stage IV achieved eved in iss not accomp IV, produc accomplished shed at Stage III iss ach producing ng well as the ex ca zes the pr a system that lexicalizes red, and ye white, te red black, ack wh yellow, ow as we primaries mar es b most endur (cool). ) Such Stage IV systems have been composites, tes grue (coo enduring ng of the compos acculturated turated speakers of Aguaruna (Ber (Berlin n experimentally exper menta y observed among more accu 1975), and among the Mam (Harkness); & Ber Berlin) n) and Futunese (Dougherty 1975) ngu st c sources general ethnograph ethnographicc and linguistic from the investigation nvest gat on of genera sources, Stage IV anguages(Bornste of New Wor World d languages majority tyof appear to include nc ude the major systems appearto (Bornstein n 1973a 973a,b; b; of coo cool into with th the d differentiation fferent at onof achieved eved w 1972). Stage V iss ach nto its Hays et aal. 1972) ts green decomposition t on of the compos completing et ng the decompos primary mary const constituents, tuents comp and b blue ue pr composites. tes system. examplee of such a system Mam Span Spanish sh (Harkness) iss an examp beyond, d At Stage VI and beyond differentiation fferent at on proceeds through the encod encoding ng of VI, brown encodes the intersection primaries. mar es At Stage VI intersections ntersect ons of the pr ntersect on of privilege v ege of name to wh white te+ black. ack Stage VII extends the pr + red (p yellow ye ow and b (pink), nk) usuallyy to b (purple), e) and usua (orange), red+b red+blue ue (purp red+yellow red+ye ow (orange) black+white ack+wh te (grey) (grey).16 16 categories es suggests that iff no language derived ved categor Thiss vview Th ew of the later-stage, ater-stage der anguage investinvest terms, w with th the poss even bas basicc co color or terms gated so far has more than eeleven possible b e except exception on accident dent of the present moment in K, 35-36) 35-36), th thiss iss more an acc of Russ Russian an (see B & K n goluboy uboy 'light ght b Russian an go theoretical ca inevitability. nev tab ty Russ history story than a theoret world wor dh blue' ue (wh (white te+ + basicc co color or term; itt iss sure twelfth fth bas potential a instance nstance of a twe surelyy a bas blue) b ue) iss a potent basicc term 17 There iss no certa probablyy not for aall.17 Russian an speakers speakers, though probab for some Russ certainty nty basicc term status for aall future, ach achieve eve bas point nt in n the future will not not, at some po that go goluboy uboy w 15 The emp he encod encoding ng sequence represen he res restatement a emen oof the ac s re relevant evan too the empirical r ca facts represented ed in n above. n fn. n 44, above he works ccited ed in n the Fig. F g 13 are presen presented ed in dotted ed arrow in 16 The do n F Fig. g 13 indicates nd ca es that ha grey may occur (albeit a be infrequently) n requen y 'as as a B &K K, 45 45). Whereas B & K or n the he sequence sequence' (B various ous po points n s in wild w d card aat var originally g na y guessed that ha IV', more recen recent information point n aafter er S Stage age IV n orma on shows that say aat any po grey m might gh occur occur, 'say ha it may earlier er (Barry Barry A Alpher, pher p possibly b y even ear age from rom lilaa onward onward, or poss occur aat any sstage p.c.; c MacLaury 1975a 261 ur her d discussion, scuss on see Kay (1975a:261). MS). For further MS 17 C erms for or 'light monolexemic exem c terms Slavic av c languages anguages have mono Cf. Da Dalyy MS MS. O Other her S gh b blue', ue bu but these hese any. ew speakers speakers, if any erms for or very few appear too be bas basicc terms LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 641 Russian. an S several now non-bas non-basicc co color or terms speakers of Russ Similarly, m ar y itt iss poss possible b e that severa in n Eng ntersect ons of fundamenta fundamental response categor will English, sh used to name intersections categories, es w n the future become bas basicc in future, ee.g. g aqua aqua/turquoise turquo se(green (green+ b blue), ue) maroon maroon/burgundy burgundy chartreuse/lime me(ye (black (b ack + red) red), and chartreuse (yellow ow + green) green). Some of these may aalready ready be basicc terms for some speakers bas characterizes zes der derived ved category speakers. The process that character formation format on has not been logically og ca y exhausted by any known language; anguage; so there iss no believe eve that the process w will not cont basicc apparent reason to be continue, nue extend extending ng bas color-term co or-term lexicons ex cons beyond the theirr present eeleven even terms terms. 55.2. 2 FUZZY PARTITIONS PARTITIONS: A FORMAL CHARACTERIZATIONOF CHARACTERIZATIONOF THE ENCODING SE SEdiscussion scuss on of the evo QUENCE.In forma QUENCE desirable rab e formalizing z ng the d evolutionary ut onary sequence sequence, itt iss des to extend fuzzy set theory in nam minor nor way by deve developing op ng the concept of fuzzy part parti-ttion. on In standard set theory collection ect on of sets part theory, a co partitions t ons a set S just iff (a) each set in n the co collection ect on iss a subset of S n S iss a member of one of these S, (b) everyth everything ng in n S be subsets.18 18Such Such subsets, and (c) noth subsets nothing ng in belongs ongs to more than one of these subsets subsets are often ca called ed the ce cellss or b blocks ocks of the part partition. t on There iss an intuitive ntu t ve use of the word 'partition' n wh which ch itt iss obv obvious ous that every part t on in color co or term universe verse of co color or percepts n wh which ch the terminology no ogy 'partitions' part t ons the un percepts, and in transition trans t on from stage to stage in n the evo (until Stage V iss reached) evolutionary ut onary sequence (unt involves nvo ves mov ner part Thiss intuitive ntu t ve usage can be moving ng from a coarser to a ffiner partition. t on Th follows. ows We note ffirst rst that each co color or category iss a fuzzy subset of ((iss explicated exp cated as fo contained ned in) color or percepts fuzzilyy conta fuzz Thiss fo follows ows from the fact that n) the set of aall co percepts. Th that, for each individual n the doma nd v dua in ts degree of membersh n the fuzzy set 'color co or domain, n its membership p in ts degree of membersh n any percept' (wh percept (which ch iss un unity) ty) iss greaterthan greater than or equa equal to its membership p in color or term ggiven ven co term.19 19Hence Hence any co color or category iss forma formallyy a fuzzy subset of the set of co color or percepts n speak percepts. Thus Thus, in speaking ng of fuzzy part partitions, t ons we can d directly rect y take over condition cond t on (a) of standardset standard set theory that the ce cellss of the part partition t on be subsets of the set be Condition t on (b) being ng part partitioned. t oned Cond (b), the exhaust exhaustiveness veness cond so be condition, t on can aalso nto the def definition n t on of fuzzy part directly d rect y taken over into translate' ate be partition, t on iff we trans to' belongs ongs to as 'having hav ng a non-zero degree of membersh n 20 membership p in'.20 18 For he ce cellss oof a jail example, examp e the a norma normallyy prov provide de a par partition on oof the he se set oof pr prisoners, soners ssince nce every pr prisoner soner iss ass assigned gned too a ce cell, and no pr prisoner soner iss ass assigned gned too more than han one ce cell. 19 The se set oof co color or percep perceptss is, s oof course course, a sstandard andard se set and iss therefore here ore a fuzzy uzzy se set, ssince nce andard se every sstandard set iss aalso so a fuzzy uzzy se set-in n par particular, cu ar the he spec special a case oof a fuzzy uzzy se set in n wh which ch aall values va ues oof the he charac characteristic er s c function unc on are eeither her zero or un unity. y A fuzzy set A iss con contained a ned in n (iss a subse uzzy se subset oof) a fuzzy uzzy se set B if, for or aall x in n the he doma domain n oof d diss course, fB(x) course B x > fA(x). Ax 20 Zadeh cautions: cau ons 'the he no notion on oof "be "belonging" ong ng" [membership], membersh p wh which ch p plays ays a fundamental undamen a rolee in ro he case oof ord n the ordinary nary se sets, s does no not have the he same ro rolee in n the he case oof fuzzy uzzy se sets. s Thus Thus, it iss not mean no meaningful ng u too speak oof a po point n x "be "belonging" ong ng" too a fuzzy uzzy se set A excep except in n the he trivial r v a sense oof fA(x) A x be being ng pos positive' ve (1965:342). 1965 342 We w will hence henceforth or h use 'belong' be ong in n just us this h s sense sense, ssince nce w with h color or the he no notion on iss no respect too co respec not trivial. r v a Zadeh appears too have in nm mind nd app applications ca ons in n wh which ch n the nd v dua s in he re relevant evan doma few, ew if any any, individuals domain n w will have zero membersh membership p in n any oof the he fuzzy uzzy setss under d se discussion. scuss on Such iss no not the he case in n co color. or For examp example, e no co color or percep percept be belongs ongs bo both h too red and too green holds ds for or b green. The same ho blue ue and ye yellow. ow In d discussing scuss ng co color or percep perceptss and ca catee en oof interest n eres too know if a ggiven gories, gor es it iss ooften ven percep percept be belongs ongs (too ANY POS degree) too a POSITIVE T VE degree certain cer a n ca en oof interest category. egory S Similarly, m ar y it iss ooften n eres too know whe whether her two wo ca categories egor es have members in n common ke green and ye common, like yellow, ow or are d disjoint, s o n like ke green and red red. 642 LANGUAGE, VOLUME 54, NUMBER 3 (1978) condi-conditions t ons (a) and (b) can be taken over from standard set theory Whilee cond Wh theory, cond distinct st nct but adjacent bas basicc categor nce d ttion on (c) must be mod modified, f ed ssince categories es have conssiderable derab e over (unique que Fig. g 6) 6), every green above 505 nm (un overlap. ap As shown above (see F below ow 505 nm iss to so to some pos yellow, ow and every green be positive t ve degree ye green) iss aalso blue. ue Thus aall greens except the un some degree b unique que green at 505 nm are to some blue. ue These are not suppos so ye formalism, sm but facts suppositions t ons of the forma yellow ow or b degree aalso which ch the forma formalism sm must account account. for wh mutual exc exclusion us on cond condition t on (c) with th by rep dealtt w These facts can be dea replacing ac ng the mutua cell of a fuzzy part standard set theory by a statement to the effect that each ce of standardset partition t on cell. Thus member that be east one memberthat has at least Thus, ggiven belongs ongs to no other ce ven a fuzzy set S and collection ect on of fuzzy sets F = {F1 a co {F1, F2 F2,..., Fn} Fn}, if f of S F is s a fuzzy part just partition t on (5) n F iss a subset of S; Fi in ((i)) each F n S has a degree of membersh n at membership p greater than zero in ((ii)) each x in n F; and least east one F Fi in n F conta contains ns at least east one member xxi such that the degree Fi in ((iii)) Each F n every other member Fj of F (Fj = F of membersh membership p of xxi in Fi)) iss zero. zero follows ows that the set of fundamenta definition n t on of fuzzy part fundamental thiss def From th partition, t on itt fo red, ye white, te red blue) ue) iss a part (black, ack wh yellow, ow green green, and b partition t on of categories es (b response categor color or percepts percepts. S Since nce every co color or category iss a subset of the set of universe verse of co the un condition t on ((i)) iss sat satisfied. sf ed As ev evidence dence for the sat satisfaction sfact on of ((ii), ) we percepts, cond color co or percepts subjects given ven labels abe s for b black, ack wh white, te red red, ye yellow, ow green green, and b blue ue note the fact that subjectsg ass fy any co color or st stimulus mu us (Her (Hering; ng; Sternhe Sternheim m & Boynton) Boynton). successfullyy cclassify can successfu condition t on ((iii)) iss met iss that that, for each of these categor categories, es co color or evidence dence that cond The ev ass f ab e in n that category and not in n any of the other ffive. ve exist st that are cclassifiable stimuli st mu ex fundamental response categor categories es are a part partition t on of the Having Hav ng shown that the fundamenta percepts, we can show that every bas basicc co color-term or-term lexicon ex con iss a color or percepts universe un verse of co partition, t on of the un universe verse of co color or percepts percepts. To see how th contains ns a part thiss partition, part t on or conta n turn Stage V systems systems, systems later ater than Stage V V, and ffinally na y consider der in so, we cons iss so V. prior or to Stage V systems pr consist st of just the ssixx pr primary mary co color or categor categories es whose identity dent ty Stage V systems cons categories es makes them ipso pso facto a part fundamental response categor partition t on with w th the ssixx fundamenta color or percepts percepts. of the set of co contain n aall the Stage V pr primary mary categor categories. es If we ater than Stage V conta Systems later n sect section on ?4 ?4.4, 4 that the membersh membership p funct functions ons of the pr primary mary assume, as argued in assume with th the encod encoding ng of der derived ved categor categories, es these systems cstegories cstegor es do not contract w partition t on of the co color or space space. contain n a part therefore conta primary maryand and compos composite te categor categories es earlier er than Stage V are made up of pr Systems ear st of fundamenta fundamental response categor categories. es It iss easy to show that together exhaust the list with th a set F of subsets of a set S S, where F iss a fuzzy part partition t on of S S, that, iff we start w that taking ng fuzzy un unions ons of the members of F in n and create a new set of subsets of S by tak n exact exactlyy one of the un unions, ons then the such a way that every member of F occurs in so a fuzzy part partition t on of S S.21 21S Since nce the ear earlyycollection ect on of subsets of S iss aalso resulting resu t ng co 21 We wan o prove ha a S s a uzzy se b F s a uzzy par on o S and c F s a se whose members are un ons o he ce s o F hen F s a uzzy par on o S Obv ous y he LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 643 fundamental response category ewed as formed from the fundamenta stage systems can be vviewed so const constitute tute fuzzy color co or basic bas c in n this th s manner, manner Stages category I-IV aalso partition part t on just basic bas c co at the color or of color co or of the domain doma n Thus, Thus any stage, stage percepts. percepts partitions part t ons entire re co color or contain n a set of categor partitions t ons the ent categories es that part comprise se or conta categories categor es compr basicc co color-term or-term vocabu vocabularies ar es follows ows that thiss itt fo that, at every stage stage, bas space. From th space colors. ors provide prov de terms for aall co continuous nuous Given G ven the fuzzy part perspective, ve Stages I-V can be seen as a cont partition t on perspect ref nement of a part color or doma domain-where n-where 'refinement refinement ref nement of part partition' t on partitions t ons of the co ass f es separate which ch cclassifies creation on of a new part refers to the creat everything ng separatelyy everyth partition t on wh n add ass f es separate addition t on cclassifies d part n the oold cclassified ass f ed separate separatelyy at partition, t on and in separatelyy in addition t on of n the oold d part ass f ed the same in nd v dua s cclassified least east two individuals partition. t on The add n th thiss sense ref refine ne basicc co color or categor derived der ved bas categories es subsequent to Stage V does not in condition t on ((iii)) of fuzzy derived ved categor nce the der the part satisfy sfy cond categories es do not sat partition, t on ssince basicc catefollows ows from the argument made above that pr Thiss fo primary mary bas partition. part t on Th derived ved categor with th the emergence of der categories, es and the resu resulting t ng gories gor es do not contract w so be derived ved category iff itt does not aalso sensation on be color or sensat fact that no co belong ong belongs ongs to a der n a der derived ved category be stimulus mu us in to a pr fact, every st belongs ongs to category. In fact primary mary category which ch itt iss der derived ved categor derived. ved That der both of the categor categories es do not categories es from wh n the sense ggiven color or space refine ref ne the part above, supports the observen above space, in partition t on of the co ess important derived ved categor vation vat on that der mportant than pr fundamentallyy less primary mary categories es are fundamenta n two senses: (a) any co gratuitous tous in color or categories es are thus gratu Derived ved categor categories. categor es Der using ng any of them them, and (b) no co color or sensat without thout us referredto w sensation on sensation sensat on can be referredto can be referredto them.22 22 referred to exc exclusively us ve y by any one of them condition on percepts. s So cond color or percep he se set oof co subset oof the F' are subse g grue iss a subse members oof F subsetss oof S S; ee.g., F' whatever ever member oof F belongs ongs too wha nS or each x in condition on (ii), for With h respec respect too cond S, x be satisfied. s ed W (i) iss sa condition on grue. So cond belongs ongs too grue hen it be green, then belongs ongs too green n S be g if some x in subset; ee.g., contains con a ns F Fi as a subse which ch iss subset F F' con contains a ns a subse With h respec condition on (iii), each member oof F respect too cond satisfied. s ed W (ii) iss sa Fi wh ha F sa satisfies s es he fact ac that r ue oof the with h the he des desired red proper property, y by vvirtue guaranteed guaran eed too have a member w he point n oof green has the unique que hue po he un subset, and the condition cond on (iii); ee.g., contains a ns green as a subse g grue con complete. ee he proo proof iss comp satisfied, s ed and the condition on (iii) iss sa desired des red proper property. y Thus cond 22 rom be being ng categories egor es from derived ved ca excludes udes der partition on exc uzzy par As no he way we have de defined ned fuzzy noted, ed the mutual ua exc exclusion us on cond condition on (iii). he mu not mee meet the hey do no cellss oof a par partition, on because they possible poss b e ce which ch condition on wh exclusion us on cond mutual ua exc with h a weakened mu defined ned w erna ve y de Fuzzy par partition on may be aalternatively he pr primaries. mar es well as by the derived ved co categories egor es as we color or ca iss me met by der uzzy collection ec on oof fuzzy exclusion us on (iii), a co mutual ua exc uzzy mu n the he or original g na sstatement a emen oof fuzzy Recall that, Reca ha in mempositive ve mem ha has pos nd v dua that set, there here iss an individual setss mee se uzzy se or each fuzzy meetss this h s cond condition on just us if, for Thiss may he co collection. ec on Th set in n the n this her se n each oother h s se set and zero degree oof membersh membership p in bership bersh p in uzzy or each fuzzy us if, for exclusive us ve just mutually ua y exc setss as mu be weakened by de uzzy se defining n ng a co collection ec on oof fuzzy her han in n any oother h s se set than n this membership p in here iss an individual higher gher degree oof membersh nd v dua that ha has a h set, there se nd v dua s he doma domain n oof individuals, B, C par partition on the setss A A, B set in se n the he co uzzy se below, ow fuzzy collection. ec on In F Figure gure (i) be partition. on here iss no par n F Figures gures (ii) and (iii) there he absc but in abscissa; ssa bu represented represen ed by the (i) An a erna e de n on o (ii) uzzy mu ua exc us on and uzzy par (iii) on 644 LANGUAGE, VOLUME 54, NUMBER 3 (1978) considered dered should d be cons derived ved categor In th thiss context context, itt may be asked whether der categories es shou n color or categor bas c co color or term basicc co bas term', B & K had tac tacitly t y in defining n ng 'basic categories es at aall. In def A bas basicc co color or term term'ss ssignifimodel when they wrote: 'A mind m nd a standard set-theory mode gn f whether a n that of any other co color or term term' (p nc uded in cance iss not included 6). We can ask whethera (p. 6) criterion ter on ke orange sat satisfies sf es the trans translation at on of th thiss cr basicc but non-pr bas category like non-primary marycategory does. Orange into nto fuzzy set theory fuzzilyy conOrange, ee.g., g iss not fuzz theory. The answer iss that itt does color or category) n eeither ther red or ye tained ta ned in set, say that category). A fuzzy set yellow ow (or any other co ha de defined ned by forange(x), contains a ns ano defined de ned by fred(x), us in n case fred(x) another, her say that red x con orange x just red x defined ned (Equat derived ved orange has been def exceeds forange(x) x. But 3-4), But, as der (Equations ons 3-4) orange x for any x thiss ho th holds ds ne neither ther for red and orange nor for ye Figs. gs 11B yellow ow and orange (see F nonetheless ess derived ved categor notion on that non-pr and 12A categories es are nonethe non-primary, mary der 12A.)) Thus the not model. translation at on into nto the fuzzy set mode survives ves the trans basicc co bas color or categor categories es surv CONCLUSIONS substantial a color or d semantics cs of co reviewed ewed ev evidence dence that the semant 66. We have rev display sp ay substant which wh ch a considercons derthat these semantic semant c and universals, un versa s universals; versa s; explain exp an linguistic ngu st c un diachronic achron c linguistic ablee range of both synchron ab fact, are based on panngu st c fact synchronicc and d n the percept color. or We interpret human neurophys perception on of co nterpret neurophysiological o og ca processes in of the Sap limits m ts on the strict str ct as these ffindings Sapir-Whorf r-Whorf applicability app cab ty nd ngs placing p ac ng related ated hypotheses of extreme linguistic/cultural relativity. at v ty ngu st c cu tura re hypothesiss and re hypothes color or semant semantics cs are mode modeled ed fe further that the facts of co We have found furtherthat felicitously c tous y n the trad traditional t ona theory of d dissmodeled ed in in n fuzzy set theory theory, and are not read readilyy mode Thiss ffinding features. Th semanticc features cretelyy contrast crete contrasting ng semant nd ng casts doubt on the genera general usefulness usefu ness of the feature mode model, and suggests that more powerfu powerful forma formalisms, sms restricted ctedBoo Boolean ean aalgebra structures much broader than the restr employing emp oy ng a range of structuresmuch gebra implicit mp c t in n the d discrete screte semant semantic-feature c-feature approach approach, are probab probablyy necessary to provide prov de rea realistic st c accounts of the mean meanings ngs of words (F (Fillmore more 1975 1975, Kay 1975b 1975b, Lakoff 1972) 1972). REFERENCES E. A BERLIN.1975. Aguaruna co color or ca A. BERLIN1975 American can E BERLIN,B., and E BERLINB categories. egor es Amer Ethnologist hno og s 22.61-87. 61 87 P. KAY KAY. 1969 1969. Bas Basicc co color or terms: erms their he r un universality versa y and evo evolution. u on Berke Berkeley ey , and P & Los Ange California orn a Press Press. 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Science ence No 41 101 susceptibility. b y Behav ha none oof the he ssituations Notee that No ua ons dep n these hese figures depicted c ed in gures con conforms orms too the he de definition n on oof fuzzy uzzy exclusion us on (and n cond mutual mu ua exc condition on S nce no se set has a member and hence fuzzy uzzy par partition) on ggiven ven in Siii, ssince with w h zero membersh n each oof the he oother her se sets. s In par membership p in particular, cu ar B has no such member member. IIf this hs weakened vers version on o of fuzzy mutual ua exc exclusion us on and fuzzy uzzy mu uzzy par partition on iss adop adopted, ed then hen add addition on oof derived der ved ca er S ur her re refine ne the he par categories egor es aafter Stage age V does further partition on oof the he co color or doma domain. n Th Thiss would d appear too charac characterize er ze the he sys formulation ormu a on wou systems ems oof those hose individuals nd v dua s for or whom der derived ved categories ca egor es such as brown brown, p pink, nk orange orange, and grey are on a percep perceptual/conceptual ua concep ua par w with h the he n the Notee that, he aalternate erna e de definition n on oof fuzzy primaries. pr mar es No ha in uzzy par partition, on ca categories egor es such as cr crimson mson chartreuse reuse (cf. not par (cf. c F Fig. g B B) and char c F Fig. g C C) sstill do no participate c pa e in n a re refinement nemen oof the he par partition. on LINGUISTIC SIGNIFICANCE OF MEANINGS OF BASIC COLOR TERMS 645 culture. ure Amer American can An n uence oof vvisual sua percep 1975. 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The Linguistic Significance of the Meanings of Basic Color Terms

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The Linguistic Significance of the Meanings of Basic Color Terms

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