Comparing conceptual domains

Comparing Conceptual Domains

Jacek Woźny, University of Wrocław

The goal of the chapter is to investigate thelevel of similarity between source and targetdomains of metaphors. The problem of similarityconstitutes the crucial difference between theclassical theory of metaphors and conceptualmetaphor theory of Lakoff and Johnson (1980). Theresearch method is based on statistical comparisonof the features of basic domains, which aregrounded in the pre-conceptual sensory-motorperception. Applying the method to a particulargeneric metaphor indicates that visualsimilarities are much less prominent than thesimilarities based on other experiential domains,such as, for example, EMOTION or TEMPERATURE.Further application of the statistical method to alarger corpus of metaphorical expressions may helpto find a rule-governed, systematic connectionbetween the similarity of domains and conventionalmetaphors.

Keywords: conceptual metaphors, basic domains

1. INTRODUCTIONGeorge Lakoff, referring to the classical theoryof metaphors, states that "the word metaphor wasdefined as a novel or poetic linguistic expressionwhere one or more words for a concept are used

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outside of its normal conventional meaning toexpress a similar concept" (Lakoff 1993:1). One ofthe charges Lakoff and Johnson (1980:114) bringagainst the classical theory is the existence ofsimilarities between the source and target domain:

[…] the claim that such similarities exist ishighly questionable. For example, what possiblesimilarities could there be that are shared by allof the concepts that are oriented up? Whatsimilarity could there be between UP, on the onehand, and HAPPINESS, HEALTH, CONTROL,CONSCIOUSNESS, VIRTUE, RATIONALITY, MORE, etc., onthe other? What similarities (which are notthemselves metaphorical) could there be between aMIND and a BRITTLE OBJECT, or between IDEAS andFOOD?

However, in their theory of conceptual metaphor,Lakoff and Johnson do not deny the existence ofcorrespondences between source and target domains:‘Metaphor is mostly based on correspondences inour experiences, rather than on similarity’(Lakoff 1993:40). The question that should beanswered first is: “what exactly are thecorrespondences (similarities) in our experiencesand how can we measure them”? The aim of thispaper is to create a method of comparingconceptual domains, which will allow us, at leastpartly, to answer the above question. Partly,because the method presented in the next sectionconcerns only the building blocks of a conceptualdomain – the set of basic domains such as SPACE,COLOUR, TEMPERATURE, EMOTIONS, PRESSURE, ODOUR,etc., which 'derive either from subjective

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embodied experiences [...], or from sensory-perceptual experiences which relate toinformation derived from the external world'(Langacker 1987: 150).

At this point it should be stated very clearlythat the analysis of only basic domains cannotpossibly account for the infinitely complicatedand intricate network of cross-domain relationswhich constitute source and target domainmatrices, neither will it help us to account forunidirectionality of metaphors, the concept ofhighlighting and hiding, or the InvariancePrinciple. To use a metaphor, the comparison ofonly basic domains is like analyzing the chemicalcomposition of the bricks – it has only verylimited bearing on the structure of the wholebuilding. However, despite the above-mentionedlimitations, the method of comparing basic domainsmay prove a useful and mathematically rigoroustool, which will shed some light on the degree towhich the similarity of the source and targetbasic domains motivates conventional metaphors. Inother words, it can help to answer the question ofwhy some domains are linked with conventionalmetaphors and others are not. Additionally, thestatistical comparison of source and target basicdomains is interesting in itself because itreveals which basic domains play the dominant rolein accounting for the 'correspondences in ourexperiences' (ibid.) . For example, as we will seein Section 3, the domains of TEMPERATURE andEMOTION are decidedly the most prominent in the

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COMPETITION IS PHYSICAL AGGRESSION metaphor.Section 2 offers an outline of the method of basicdomain comparison and Section 3 contains anexample of its practical application, i.e. thestatistical assessment of source and target domainsimilarity for the COMPETITION IS PHYSICALAGGRESSION metaphor (Conceptual Metaphor Home Page,http://cogsci.berkeley.edu/lakoff/sources/, accessed29.10.2012).

2. THE METHOD OF COMPARING CONCEPTUALDOMAINS

The basic notions of Langacker’s (1987) theory ofknowledge representation are those of concept (profile)and domain (base). The first is described as thebasic unit of mental representation and the secondas the background knowledge in terms of which aparticular concept is understood. Clausner andCroft (1999:6) explain the nature of theconnection between concepts and domains in thefollowing way:

The nature of the concept-domain relation is suchthat any concept can in turn function as the domainfor other concepts (e.g., arc-CIRCLE and circle-SPACE […] respectively). The embedding of domainsas concepts in other domains eventually “bottomsout”, according to Langacker, in basic domains:domains which are footed in fundamental humanbodily experiences, such as SPACE, TIME, varioussensations, emotions and perceptions.

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http://cogsci.berkeley.edu/lakoff/sources/

As we can see, according to Langacker (1987: 150),all concepts are ultimately grounded in basicdomains, which are directly based on humansensory-motor experience. Evans and Green(2006:234) provide a list of such domains togetherwith their sensory, pre-conceptual sources (Table1).

Basic domain Pre-conceptual basisSPACE Visual system; motion and position

(proprioceptive)sensors in skin, muscles and joints; vestibular system(located in the auditory canal – detects motion and balance)

COLOUR Visual system

PITCH Auditory system

TEMPERATURE Tactile (touch) system

PRESSURE Pressure sensors in the skin, muscles and joints

PAIN Detection of tissue damage by nervesunder the skin

ODOUR Olfactory (smell) systemTIME Temporal awareness

EMOTION Affective (emotion) system

Table 1. The inventory of basic domains

Having established that all conceptual domains canbe finally analyzed in terms of a finite number ofbasic domains, we are now ready to begin to definethe statistical notion of similarity of twodomains. Let us start with an example. Table 2 inthe next section contains the analysis of the

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features of the source and target domains of themetaphorical expression ‘He clobbered me attennis’. The features of both domains are arrangedvertically with respect to the basic domains ofSPACE, COLOUR, SOUND, TEMPERATURE, PRESSURE,ODOUR, EMOTION and TIME. As we can see in Table 2,the spatial features of the source domain (FISTFIGHT) are:

two participants, moving, distance of about 1 meter

The analogous spatial features for the target domain (TENNIS) are:

two participants, moving, distance of about 10-20 meters

The comparison of both sets of three spatialfeatures (number of participants, movement,distance) allows us to conclude that the degree ofsimilarity is 2/3 (77%) because two of the threefeatures (the number of participants and themovement) are equal. To use a mathematicalformula:

(1) S1 = 77% ,

where S1 is the degree of similarity of the spatial features between the two domains. The similarity of the two domains will be calculated as

(2) S = (S1 + S2 + S3 + … + S8) / 8 ,

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which is simply the average of the partialsimilarities for the 8 basic domains. As we cansee from Table 2, the similarity between the twodomains (FIST FIGHT and TENNIS) is finallycalculated as

(3) S=(77%+0%+100%+100%+100%+100%+100%+50%)/8 =78.38%

Tables 3 to 8 contain analogous analyses for sixother metaphorical expressions listed by Lakoff asexamples of COMPETITION IS PHYSICAL AGGRESSION.?Averaging the similarities S calculated fromTables 2 to 8 gives us an estimation of thesimilarity of the source and target domains of thegeneric metaphor COMPETITION IS PHYSICALAGGRESSION (See Table 9):

(4) St = 52 +/– 17 %

The simple arithmetical operations exemplified above by equations (1) to (4) could be expressed by the following general formula, defining the statistical similarity of two domains:(5)

,

where N is the number of metaphorical expressionsanalyzed (or number of texts in the corpus sample,in our case N=7), J is the number of basic domains(in our case J =8), Kj is the number of analyzedfeatures of basic domain j (for example, we

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analyzed 3 features of the domain SPACE – numberof participants, movement and distance, so K1 =3) , and fn,j,k is a two-valued function equal OF ?either 0 (if the specific feature does not match)or 1 (if it does).

To understand Formula (5) better, we may look atthe three summation symbols as three averages.Starting from the right, we calculate an averagenumber of matching features for a particular basicdomain, then we average it over all the basicdomains, and, finally, over all the metaphoricalexpressions in the considered sample. Of course,the statistical error is inversely proportional toN, J and Kj , which means that the larger the numberof metaphorical expressions analyzed and thegreater the number of features of basic domainsconsidered, the more precise the estimation of thesimilarity will be obtained from Formula (5).

As we can see from Formula (5), in order toestablish the value of the fn,j,k function as 1(match) or 0 (no match), we need a list of thebasic domain features and, first of all, aninventory of basic domains. I decided to modifythe list from Table 1 into:

1. SPACE2. COLOUR3. SOUND4. TEMPERATURE5. PRESSURE6. ODOUR7. EMOTION

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8. TIME

I excluded the basic domain of PAIN, because,according to Langacker (2008: 44), a basic domainshould be ‘cognitively irreducible’, and thephysical sensation of pain is always caused by thefactors connected with pressure, temperature,sound, or odour. I also decided to replace PITCHwith a more general domain of SOUND to include thefeature of the sound volume. The list of specificbasic domain features that I decided to use is asfollows:

1. SPACE- number of participants- movement (moving/stationary)- distance

2. COLOUR3. SOUND

- pitch- volume- variability

4. TEMPERATURE- variability (rising, falling)

5. PRESSURE- value - area (localized or not)- variability

6. ODOUR7. EMOTION8. TIME

- duration

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As we can see, the domains of COLOUR, ODOUR andEMOTION were left to an open and, of course,arbitrary and introspective interpretation;however, according to Langacker, a certain levelof arbitrariness when it comes to the choice ofrelevant domains is to be expected:

We should not expect to arrive at anyexhaustive list of the domains in a matrix orany unique way to divide an expression’scontent among them—how many domains werecognize, and which ones, depends on ourpurpose and to some extent is arbitrary.Langacker (2008:44)

As we will see in the next section, the above listof basic domains and their features is sufficientto estimate the similarity of the source andtarget domains of COMPETITION IS PHYSICALAGGRESSION metaphor.

3. APPLYING THE METHODThis section contains outlines the application themethod described in Section 2 to estimate thelevel of similarity of the source and targetdomains of the COMPETITION IS PHYSICALAGGRESSION? metaphor, which is listed as the firstone in the on-line inventory of metaphors preparedby George Lakoff and his students(http://cogsci.berkeley.edu/lakoff/sources/,29.10.2012). The following seven metaphoricalexpressions are given as examples of the abovegeneric metaphor:

1. He clobbered me at tennis.

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http://cogsci.berkeley.edu/lakoff/sources/

2. I beat him at chess.3. She kicked butt at the audition. WHOSE

BUTT? DOES BUTT MEAN ‘BUTTOCKS’ HERE?4. She whipped him at handball.5. They really murdered the other team.6. Losing the contest was a real black eye

for her.7. Those swim teams have been slugging it

out all season.

We will consider each source and target domainconnected with a particular metaphoricalexpression separately because, for example, thepressure and the sounds connected with whipping,kicking, or giving someone a black eye, etc., aredifferent, COMMA as are the colours typicallyassociated with chess and tennis – black and whitein the former and perhaps green and white in thelatter. Tables 2 to 8 contain the analysis of thechosen SELECTED? features of the basic domains foreach of the seven metaphorical expressions.

basic domain

source domain:fist fight

target domain: tennis

source and target domain match[%]

space two participants, moving, distance of about 1 meter

two participants,moving, distance of about 10-20 meters

77

colour red (of blood),mauve and black(of the bruises)

green (of thegrass), white (of thecostume)

0

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sound high volume varying in pitch, shouts, screams, grunts

the same (forexample: Sharapova, Azarenka, Nadal)

100

temperature

rising, fighters getting hot

the same 100

pressure high, localised

the same (high and localised pressure caused by theball moving at high speed)

100

odour odour of sweat the same 100emotion hatred,

triumph, elation of winning, fear and humiliationof losing

the same 100

time between a couple of minutes and a couple of hours

up to a couple of hours

50

average match (similarity) [%] 78.38standard deviation [%] 36.43

Table 2. He clobbered me at tennis.

basic domain

source domain:fist fight

target domain: chess

source and target domain match [%]

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space two participants,moving, about1 meter from one another (arm-length, the distance from which a blow can reach the target)

two participants,almost stationary, about 1 meterfrom one another

77

colour red (of blood), yellow and mauve (of the bruises)

black and white (of thechess pieces)

0

sound high volume, varying in pitch, shouts, screams, grunts

silence 0

temperature

rising due tophysical and emotional exertion

stable, can be rising dueto emotional exertion of the players

50

pressure high, localised

no pressure 0

odour odour of sweat

no odour 0

emotion hatred, triumph and elation of winning, fearand humiliation of losing

similar (perhaps lessintense)

100

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time between a couple of minutes and acouple of hours

the same 100


Table 3. I beat him at chess.

basic domain

source domain: kicking a specific area of the body

target domain:auditioning for a role in film or theatre


space two stationaryparticipants, distance of about 1 metre

more participants, stationary or moving, distance of a couple of meters

0

colour mauve and black of the bruises

no specific colour

0

sound high volume, varying in pitch, shouts,screams, grunts, the thud of kicking

the sound of music or reciting

0

temperature

temperature rising due to physical and emotional exertion

Also rising, due to emotional (stress-related) and, to a lesser degree, physical exertion

100

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pressure high, varying, localised pressure

normal, constant pressure, not localised

0

odour odour of sweatdue to physical exertion

no specific odour

0

emotion satisfaction of landing a blow successfully, humiliation and pain of being kicked

similar emotions connected witheither securing the role or failing to do so

100

time from a couple of minutes to about an hour

the same 100


Table 4. She kicked butt at the audition.

basic domain

source domain: whipping

target domain:handball


space two participants, stationary, a meter or twofrom one another (depending on the length of the whip)

many participants, moving, spaced within about 20-30 meters

0

colour mauve and black of the bruises, red of blood

no specific colour

0

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sound high volume and varying inpitch, shouts,screams and grunts, the sound of the whip hitting the target;

similar high volume and varying inpitch, shouts,screams, grunts of the players, the sound of the ball being hitwith great force

100

temperature

temperature rising due to physical and emotional exertion

the same 100

pressure high and localised pressure exerted by thewhip

the same (exerted by the ball)

100

odour the odour of sweat due to physical exertion

the same 100

emotion fear and humiliation ofthe victim, triumph and elation of thewhip wielder

Similar emotions experienced bythe winners and the losers

100

time half an hour to a couple ofhours

similar 100


Table 5. She whipped him at handball.

basic domain

source domain: murder

target domain:team game


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space two or more participants spaced withinabout 10 -20 meters (depending on the weapon) moving or stationary

similar, depending on the game

100

colour red (of blood) no specific colour

0

sound high volume and varying inpitch, shouts,screams and grunts, various other sounds depending on the weapon

high volume and varying inpitch, shouts,screams and grunts, various other sounds depending on the kind of the game

50

temperature

temperature rising due to physical and emotional exertion, of the victim’s body getting cold

temperature varying, raising and falling duringthe game due to physical and emotional exertion

50

pressure high, varying, localised pressure

can be high, varying, localised as well (as in football or handball)

50

odour odour of sweatand blood

odour of sweat 50

emotion hatred, fear, humiliation, elation

similar 100

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time a couple of minutes (depending on the type of murder)

An hour, a couple of hours (depending on the type of the game)

0


Table 6. They really murdered the other team.

basic domain

source domain: hitting a specified area of the body with a fist

target domain:sport contest


space two participants, stationary, less than a metre from oneanother

two or more participants, moving or stationary from a metre to a couple oftens of metres.

33

colour Black no specific colour

0

sound high volume, varying in pitch, shouts,screams, grunts, the thud of the punch hitting the target

silence (as inchess) or highvolume, varying in pitch, shouts,screams and grunts, other sounds depending on the kind of game

50

temperature

rising due to physical and emotional exertion

the same 100

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pressure high, varying and localised

can also be high, varying and localised,depending on the type of the contest

50

odour no specific odour

the odour of sweat, depending on the nature of the contest

0

emotion hatred, triumph, elation of theattacker (the winner), Fear, shame and humiliation ofthe attacked (the loser)

the same 100

time very short, a couple of seconds

half an hour to a couple ofhours

0


Table 7. Losing the contest was a real black eyefor her.

basic domain

source domain: fist fight

target domain: swimming competition


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space two participants, moving, less than 1 meter

two or more participants, moving within the distance of a couple ofmeters

25

colour red (of blood),mauve and black(of bruises)

blue (of the water)

0

sound high volume andvarying in pitch, shouts, screams and grunts

participants are silent (onaccount of being in water), cheersand shouts from the spectators at the swimming pool

0

temperature

rising due to the physical exertion

the same 100

pressure high, varying and localised

moderate pressure of water on the whole body of the swimmer, not localised

0

odour odour of sweat chlorine smellof the swimming pool

0

emotion hatred, triumphand elation of the attacker (the winner), fear and humiliation of the attacked (the loser)

the same 100

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Time between a couple of minutes and a couple of hours

the same (depending on the swimming distance and the duration of the whole competition)

100


Table 8. Those swim teams have been slugging itout all season.

The numerical results of Tables 2 to 8 aregathered in Table 9. The so called average verticalmatch means the degree of similarity for the sevenmetaphorical expressions analyzed. The averagehorizontal match indicates the degree of similarityfor each of the eight basic domains. The totalaverage similarity St calculated from Formula (5)(it is simply an average of the seven average verticalmatch values) is indicated in Table 9 as 52%. Thetable also contains standard deviations calculatedfor all vertical and horizontal average values.

basic domain 1 2 3 4 5 6 7

averagehorizontal match

standarddeviation

space 77 77 0 0 100 33 25 44,57 40,14colour 0 0 0 0 0 0 0 0 0sound 100 0 0 100 50 50 0 42,86 44,99temperature

100 50 100 100 50 100 100

85,71 24,39pressure

100 0 0 100 50 50 042,85 44,99

odour 100 0 0 100 50 0 0 35,71 47,56

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emotion 100 100 100 100 100 100 100 100 0time 50 100 100 100 0 0 100 64,29 47,56averagevertical match[%]

78,38

40,88

37,50

75.00

50.00

41,63

40,63

averagematch St

(similarity):

52.00

standarddeviation of theaverage match St:

17,32standard deviation [%]

36,43

46,39

51,75

46,29

37,80

41,80

49,89

Table 9. The results of source and target domaincomparison.

Graph 1 shows the degree of source and targetdomain similarity for the 7 metaphoricalexpressions (the average vertical match):

1. He clobbered me at tennis. (78%)2. I beat him at chess. (41%)3. She kicked butt at the audition. (38%)4. She whipped him at handball. (75%)5. They really murdered the other team.

(50%)6. Losing the contest was a real black eye

for her. (42%)7. Those swim teams have been slugging it

out all season. (41%)

As we can see, expressions 1 and 4 arecharacterised by the largest degree of similaritybetween their source and target domains.

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0

20

40

60

80

100

1 2 3 4 5 6 7

Graph 1. The average source/target domain match(similarity)

for the 7 metaphorical expressions.

Graph 2 shows the average similarity of source andtarget domains for the 8 basic domains (averagehorizontal match values). The domains of EMOTION andTEMPERATURE display the greatest degree ofsimilarity. Rather surprisingly for a visualdomain, the average similarity value for thedomain of COLOUR is zero, which means that thesource and target domains for the sevenmetaphorical expressions analyzed have no commonfeatures in the domain of COLOUR. The other visualdomain, SPACE, also shows a rather low degree ofsimilarity of 45%. The average similarity(arithmetical mean value) for the two visualdomains, (0 + 45%)/2 equals 22.5%, which is 4times lower than the value for the domain ofTEMPERATURE and almost 5 times lower than theaverage similarity in the domain of EMOTION, whichcan indicate that the metaphor COMPETITION ISPHYSICAL AGGRESSION? is not motivated by visualsimilarity

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0102030405060708090100

space

colour

sound

temperature

pressure

odour

emotion

time

Graph 2. The average source/target domain match(similarity)

for the 8 basic domains.

4. SUMMARY AND CONCLUSIONIn Section 2 we presented a statistical method ofcalculating similarity of two conceptual domains.The method is based on dividing each of thedomains into 8 basic domains and establishing howmany singular features of the basic domains match.Formula (5) allows us to calculate source andtarget domain similarity for generic metaphorswhich comprise a given number of metaphoricalexpressions. Section 3 contains a practicalapplication of the method described in Section 2.The results of source and target domainscomparison for COMPETITION IS PHYSICAL AGGRESSIONmetaphor are presented in Graphs 1 and 2. Graph 2indicates that the greatest similarity between thesource and target domains for the sevenmetaphorical expressions considered occurs in thedomains of EMOTION and TEMPERATURE. We can alsosee that the source and target domains have no- 24 -

common features at all in the domain of COLOUR. Aswe have already observed in Section 3, the secondvisual domain, SPACE, also displays a rather lowdegree of similarity of 45%. The averagesimilarity for both visual domains equals 22.5%,which is 4 times lower than the value for thedomain of TEMPERATURE and almost 5 times lowerthan the average similarity in the domain ofEMOTION. This can lead to a conclusion that themetaphor COMPETITION IS PHYSICAL AGGRESSION isnot motivated by visual similarity, which allowsus to see Lakoff’s statement (1993: 40), alreadyquoted in the introduction, in a new light.Metaphor is mostly based on correspondences in ourexperiences, rather than on similarity’ can now beparaphrased as ‘Metaphor is not based on visualsimilarity but rather on similarities grounded inother domains of experience, such as, for example,EMOTION or TEMPERATURE’.

REFERENCESClausner, T.C. and W. Croft. 1999. ‘Domains and

image-schemas’. Cognitive Linguistics 10, 1-31Evans, Vyvyan and Melanie Green. 2006. Cognitive

Linguistics: An Introduction. Mahwah, NJ: LawrenceErlbaum Associates

Fillmore, C.J. 1982. ‘Frame semantics’. InLinguistic Society of Korea (ed.), Linguistics inthe Morning Calm: Seoul: Hanshin, 111-138

Lakoff, George and Mark Johnson. 1980. Metaphors WeLive By. Chicago: University of Chicago Press

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Lakoff, George. 1987. Women, Fire and Dangerous Things.What Categories Rreveal about the Mind. Chicago:Chicago University Press

Lakoff, George. 1993. ‘The contemporary theory ofmetaphor’. In A. Ortony (ed.), Metaphor andThought (2nd ed). Cambridge: CambridgeUniversity Press, 202-251

Langacker, R. W. 1987. Foundations of Cognitive GrammarI: Theoretical Prerequisite. Stanford: StanfordUniversity Press

Langacker, R. W. 2008. Cognitive Grammar: A BasicIntroduction. Oxford: Oxford University Press

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Comparing conceptual domains