Conceptual Projection and

Middle Spaces

Gilles Fauconnier and Mark Turner

April 1994

Report 9401

Department of Cognitive ScienceUniversity of California, San Diego

La Jolla, California 92093-0515

Mark Turner gratefully acknowledges the support of the John Simon Guggenheim Memorial Foundation and the assistanceof the Department of Linguistics, the Department of Cognitive Science, and the Center for Research in Language at UCSD.We are grateful for comments from Adele Goldberg, Todd Oakley, Seana Coulson, and Nili Mandelblit. Copies of this reportare available from the Department of Cognitive Science, UCSD, La Jolla, CA 92093-0515. A Microsoft Word version ofthis report is available by anonymous ftp from hamlet.umd.edu as pub/blend.word.Copyright 1994 by Gilles Fauconnier and Mark Turner.

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Conceptual Projection and Middle Spaces

1994 Gilles Fauconnier and Mark Turner1

(A Microsoft Word version of this report is available by anonymous ftpfrom hamlet.umd.edu as pub/blend.word)

AbstractConceptual projection from one mental space to another always involves projection to "middle"spaces—abstract "generic" middle spaces or richer "blended" middle spaces. Projection to amiddle space is a general cognitive process, operating uniformly at different levels of abstractionand under superficially divergent contextual circumstances. Middle spaces are indispensable sitesfor central mental and linguistic work. The process of blending is in particular a fundamental andgeneral cognitive process, running over many (conceivably all) cognitive phenomena, includingcategorization, the making of hypotheses, inference, the origin and combining of grammaticalconstructions, analogy, metaphor, and narrative. Blending is not secondary to these phenomenabut prerequisite, and its operation is not restricted to any one of these phenomena. We giveevidence for blending from a wide range of data that includes everyday language, idioms, literarymetaphor, non-verbal conceptualization of action, creative thought in mathematics, evolution ofsocio-cultural models, jokes, and advertising. Blending is in general invisible to consciousnessand detectable only on analysis. Blended spaces are routinely necessary for constructing centralmeanings, inferences, and structures, and for motivating emotions. We show that the blending ofhighly schematic spaces yields the fusion of grammatical constructions and functional assembliesstudied in Cognitive Grammar and Construction Grammar. Finally, recognizing the cognitiveimport of middle spaces allows us to propose a generalized four-space model of conceptualprojection that subsumes a variety of previous models. We explore the consequences of this modelfor the theory of concept formation.

ContentsIntroduction 3I. The four space model 4II. The phenomenon of blended spaces 51. Dante's Inferno 52. Regatta 73. The riddle of the Buddhist monk 84. Getting ahead of oneself 95. Tuning in, and other actions 116. Complex numbers 12III. Prototypes of blending and mistaken reductions 14IV. Further evidence for conceptual projection into a blended space 171. President Bush on third base 182. President Nixon in France 193. Personification 21V. Category extension 22VI. Generic spaces 24VII. Parameters and subschemes 25VIII. Blending and grammar 30IX. The concept of a concept 33Notes 35References 38

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Much of the excitement about recent workon language, thought, and action stems fromthe discovery that the same structural cognitiveprinciples are operating in areas that were onceviewed as sharply distinct and technicallyincommensurable. Under the old view, therewere word meanings, syntactic structures,sentence meanings (typically truth-conditional),discourse and pragmatic principles, and then, ata higher level, figures of speech like metaphorand metonymy, scripts and scenarios, rhetoric,forms of inductive and deductive reasoning,argumentation, narrative structure, etc. Arecurrent finding in recent work has been thatkey notions, principles, and instruments ofanalysis cut across all these divisions and infact operate in non-linguistic situations as well.Here are some of them:

Frames structure our conceptual and sociallife. As shown in the work of Fillmore,Langacker, Goldberg, and others, they arealso, in their most generic, and schematicforms, a basis for grammatical constructions.Words are themselves viewed as constructions,and lexical meaning is an intricate web ofconnected frames. Furthermore, althoughcognitive framing is reflected and guided bylanguage, it is not inherently linguistic. Wemanipulate many more frames than we havewords and constructions for.

Analogical mapping, traditionally studied inconnection with reasoning, shows up at alllevels of grammar and meaning construction,such as the interpretation of counterfactuals andhypotheticals (Fauconnier, to appear), categoryformation (Turner 1991), and of coursemetaphor, whether creative or conventional(Lakoff 1993).

Reference points, viewpoints, a n ddominions are key notions not only at higherlevels of narrative structure, but also at theseemingly micro-level of ordinary grammar, asshown convincingly by Langacker 1991, Zribi-Hertz 1989, Van Hoek 1992, Cutrer 1994,among others.

Connected mental spaces account forreference and inference phenomena across widestretches of discourse, but also for sentence-internal multiple readings and tense/mooddistributions. Mappings at all levels operatebetween such spaces, and like frames they arenot specifically linguistic. (Fauconnier 1985,1994, Dinsmore 1990, Cutrer 1994,Fauconnier and Sweetser, to appear).

Connectors and conceptual connectionsalso operate at all levels, linking mental spacesand other domains for coreference, formetonymy (Nunberg 1978), and for analogyand metaphor (Turner 1991, Sweetser 1990).

And there are many other notions that applyuniformly at seemingly different levels (forexample, figure/ground organization, profiling,pragmatic scales, focus and viewpoint, and soon).

This report explores another cognitiveprocess which operates uniformly at differentlevels of abstraction and under superficiallydivergent contextual circumstances. Thegeneral process is the conceptual projection oftwo mental spaces into a third, "middle" spacegiving rise either to a more abstract "generic"space or to a richer "blended" space.

We give evidence for this process from awide range of data that includes everydaylanguage, idioms, literary metaphor, non-verbal conceptualization of action, creativethought in mathematics, evolution of socio-cultural models, jokes, and advertising. Theprocess of blending is in general invisible toconsciousness and detectable only on analysis.Certain spectacular and highly noticeablephenomena of blending are only the tip of theiceberg.

We show how blended spaces areconstructed and how they serve as sites offundamental cognitive work. They areroutinely necessary for constructing centralmeanings, inferences, and structures, and formotivating emotions.

We also show that the blending of highlyschematic spaces yields the fusion ofgrammatical constructions and functionalassemblies studied in Cognitive Grammar andConstruction Grammar.

Finally, recognizing the cognitive import ofmiddle spaces allows us to propose ageneralized four-space model of conceptualprojection that subsumes (among other things)a variety of models of analogical andmetaphorical mapping. We propose that manydisagreements between theorists of analogy andmetaphor are resolved by taking into accountthis more elaborate model, and the parameterswhich define particular configurations.

The thrust of this report is that blending is ageneral instrument of cognition running overmany (conceivably all) cognitive phenomena,including categorization, the making of

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hypotheses, inference, the origin andcombining of grammatical constructions,analogy, metaphor, and narrative. Blending isnot secondary to these phenomena orinessential or elective. It is prerequisite. Itsoperation is not restricted to any one of thesephenomena. Blending is motivatedindependently of metaphor and analogy, and isnot restricted to phenomena of language.

The report is organized as follows:Sections I and II present the model and analyzea broad range of data which motivate thetechnical notion of blended space. Section IIIdiscusses the mapping strategies involved anddistinguishes blending in its general form fromsome of its salient prototypes. Sections IV andV present further relevant evidence, includingthe important phenomenon of categoryextension. Section VI describes generic middlespaces, and section VII shows how the modelyields various subschemes for conceptualprojection when parameters are set in certainways. Section VIII shows the key role ofblending in generating grammaticalconstructions, and Section IX asks what all thismeans for concept formation.

I. The Four Space Model

The projection of conceptual structure is anessential instrument of thought. A metaphorbetween mind and computer, an analogybetween electricity and water, a new socialevent imagined as a version of one we alreadyknow, an assimilation of something novel to anestablished category, a creation of a provisionalcategory for local purposes—all of these andmany other cognitive operations involve theprojection of conceptual structure.

We reconsider the customary view—often reflected in our own work—thatconceptual projection carries structure from oneconceptual domain to another in a manner thatis direct, one-way, and positive. We suggestthat direct, one-way, and positive projectionfrom source to target is only a special aspect ofa more robust, dynamic, variable, and wide-ranging assortment of processes. In addition tothe notions of source and target, all conceptualprojections involve middle spaces that areindispensable sites for central mental andlinguistic work. The existence of these middlespaces entails that conceptual projection is not

Generic

Source Target

Blend

Figure 1

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direct, except perhaps as a limiting case withinthe full range of cognitive possibilities. Wewill show that middle spaces provide keyinferences not derivable in the source or target,and that such inferences can project to sourceor target, demonstrating that conceptualprojection is not in general one-way. We willalso show that blended spaces can pick outnon-correspondence between source and target,demonstrating that conceptual projection .is notin general positive.

Here is an outline of the scheme to beproposed. First, we take it that when aconceptual projection occurs, two mentalspaces are set up, one for the source, and onefor the target—such spaces do not represententire domains, but rather represent relevantpartial structure, as highlighted from a certainpoint of view.2 Like mental spaces in general,they may inherit additional structure by defaultfrom context, culture, and background.

As in standard accounts, there will beprojection from source to target: the mentalspaces will be linked by counterpart functions.But in addition, middle spaces will beconstructed. The most abstract, which we callGENERIC, reflects the roles, frames, andschemas common to the source and targetspaces. This part of the analysis actually hasequivalents in most approaches and should befairly uncontroversial. But a fourth kind ofmiddle space, which we call BLENDED, is alsoavailable: it combines specifics from source andtarget, yielding an impression of richer, andoften counterfactual or "impossible" structure.We shall argue that significant cognitive workis performed relative to such blended spaces.

Aspects of blending, and their cognitiveimportance, have been noticed and discussed inprevious work. Koestler (1964) noted the roleof blended spaces in problem-solving.3 Talmy(1977) comments briefly, but with greatinsight, on the blended nature of certainsyntactic constructions. Moser and Hofstadter(ms.) provide significant examples and deep,extensive, discussion of linguistic and othercognitive blends. Goffman (1974), in hispenetrating analysis of social framing, alludesto frame mixing. Kunda, Miller, and Clare(1990) report experiments on the combining ofsocial concepts that show that although theprocess of blending follows a logic, its outputcannot be predicted, because subjects recruit

from a wide range of knowledge in the processand because the blend routinely containsemergent structure not simply inherited fromeither input concept.4 Turner (1991) analyzessome everyday linguistic constructions thathave conceptual blending as part of theirsemantic and pragmatic interpretation.Fauconnier (1990, to appear) notes theblending involved in the construction ofanalogical counterfactuals.

This report generalizes such observationsempirically and theoretically, and concludesthat space-blending is a central, indispensablecomponent of conceptual projection, and thatcrucial aspects of meaning (inferences,emotions, creativity) cannot be accounted forwithout it.

Finally, we suggest that middle spaces fallon a gradient, with the most abstract generics atone end, and the richest blends at the other. Asmeaning unfolds, there will be shifts in themiddle space configurations.

In sum, we will argue that the general caseof conceptual projection behind hypotheticals,counterfactuals, analogy, and metaphor has thestructure diagrammed in Figure 1. We call thisthe Four-Space Model. This model will besufficient to guide much of our discussion.But there are good reasons to believe that theFour-Space model itself is only a typical caseof an even more general Many-Spacegenerative scheme.5

II. The Phenomenon of BlendedSpaces

1. Dante's InfernoIn the Inferno, Dante presents the character

of Bertran de Born, who in life had instigatedstrife between the King of England and theking's son, tearing them apart. Spectacularly,Bertran's head is torn apart from his body: hecarries his head in his hand, and must lift hishead manually in order to talk to Dante as hepasses. Bertran cites his punishment asappropriate to his sin:

Perch'io parti' così giunte persone,

partito porto il meo cerebro, lasso!

dal suo principio ch'è in questo toncone.

Così s'osserva in me lo contrapasso.6

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Because I parted people so joined,

I carry my brain, alas, separated

from its root, which is in this trunk.

Thus is to be seen in me the retribution.

This is a blending impossibly in conflictwith our understanding of actual humanbeings. In it, a talking human being has a bodythat is unnaturally divided. This blended spacearises in this way: the sin of setting father andson against each other is understoodmetaphorically as dividing a cohesive andjoined physical object. In this projection,physical division is projected from a space ofphysical objects and actions onto the space ofsocial actions: the joined physical objectcorresponds to the father-son unit; theseparation of the object corresponds to theseparation of the father and the son; the act ofseparating the physical object corresponds tothe act of separating the social unit, and so on.This projection is not at all novel; it relies upona highly conventional metaphor in whichsocial, psychological, and emotional "distance"is understood in terms of physical distance. Inthis highly conventional projection, there is acertain amount of abstract information that isprojected from the source to a generic spaceand then from the generic space to the target.7Such a generic space is available to be projectedto a great range of different target spaces, andin fact we find it in other cases in Dante thatinvolve neither royalty nor family relation, butonly some sort of psychological or social bond.This mental process—projecting skeletalinformation to a generic space, which is thenavailable for infinitely many projections tospecific target domains—is the standardprocedure for interpreting proverbs in theabsence of a pragmatic indication of the target.When we read in a book of proverbs, "He isstrongest who stands alone," we interpret it byprojecting certain kinds of skeletal informationto a generic space, which is then available forprojection to unspecified targets, many ofwhich will not involve any sort of literal"standing." Lakoff and Turner have analyzedprojection to a generic space in their discussionof GENERIC IS SPECIFIC in More than CoolReason.

These generic spaces are one kind ofmiddle space. But in Dante, we can see that

there is another kind of middle space, a"blended" space. This blended space containsthe generic space projected from the source; itadditionally contains specific informationborrowed from both source and target. In theblended space, the sinner and the sin comefrom the target, and the source counterpart ofthe sin is imposed as punishment upon thesinner. The specific information from thesource—physical separation of a joinedphysical object—is applied impossibly to thehuman being from the target in a blended spacewhich contains something impossible for eithersource or target: a talking and reasoning humanbeing who carries his detached head in his handlike a lantern. In the blended space, it isentirely possible and consistent, even expected,that such events will occur; but they areimpossible with respect to the target.8

It is especially to be remarked that thepower and even the existence of the centralinference of this projection come not from thesource space and not from the target space, butonly from the blended space. The centralinference is that Bertran de Born has donesomething not merely wrong, but wrong inspecific ways: unnatural, ghastly, violent,destructive of a worthy whole. In the sourcespace, there may be nothing at all wrong withspatially separating a joined physical object.And of course, a human being, divided at theneck, who thereafter lives and talks in thenormal fashion, is impossible for the source tobegin with. In the target space, there may benothing wrong in advising a son to oppose hisfather—perhaps the father is an evil infidelwarrior, for example. But we all know there issomething bad about having one's headchopped off. Before Bertran de Born evenbegins to tell his story to Dante in hell—whichis to say, before we even learn the relevanthistorical details of the target—we see theamazing spectacle of Bertran carrying histalking detached head, and recognize thatwhatever this division symbolizes, it is meantto be taken as bad and unnatural. The inferenceis established in the blended space and isimported to the target space as Bertran recountshis actions.

Most readers who know this famousportrayal of Bertran de Born have not readDante, and so can derive none of the inferencesfrom context. Although a sophisticated reader

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of Dante may establish from context that theremust be something wrong with Bertran deBorn, given that he is in hell, and that Bertranmust have sinned in a certain way, given hisparticular location in hell, such a reader maynonetheless derive all the central inferencesfrom the spectacular portrayal itself. It ispossible to know an abstract definition of a sinwhile having only the thinnest correspondingconception. Dante is often praised asexplaining sins to readers who otherwisewould have no real understanding of them.Many readers, informed of the relevant history,would not even agree that Bertran de Born'sactions were sinful. But we can all derive theinferences from the spectacular portrayal itself.

Blending is a generative conceptualmechanism of Dante's Inferno. The targetspace of sin and sinner is conceived in terms ofa source space. A blended space is constructedin which the source counterpart of the sin isimposed impossibly upon the sinner.

Dante's blended spaces are explicitlymarked as exotic and literary. They take placein a new conceptual domain: the imaginaryworld of hell. They are alien and fantastic—areality inaccessible to us. But the essence ofour report is that what we see here intechnicolor—blended spaces providing centralinferences—is the routine occurrence ineveryday conceptual projection.

The example with which we began isstriking. But it is literary and metaphorical. Itmight therefore be misunderstood assuggesting that blending is a bizarre event ofstrange literature, which, however clever, isinessential to everyday conceptualization andreasoning. Throughout this report, we willshow that, on the contrary, blending ispervasive in all modes of thinking and talking,and in fact is not even inherently tied tolanguage, but appears more generally in actionand phenomena of cognition. It is useful inthis regard to take a look at cases in whichblending occurs straightforwardly, although noanalogy or metaphor is involved.

2. RegattaConsider the following excerpt from a

report in the sailing magazine Latitude 38:

As we went to press, Rich Wilson and Bill

Biewenga were barely maintaining a 4.5 day lead over

the ghost of the clipper Northern Light, whose record

run from San Francisco to Boston they're trying to

beat. In 1853, the clipper made the passage in 76

days, 8 hours. —"Great America II," Latitude 38,

volume 190, April 1993, page 100.

Three situations, two real and oneimaginary, are available to the reader: the actualpassage of the clipper back in 1853, the currentrun by Great America II in 1993, and theimaginary race between Great America II andthe ghost of Northern Light. The excerpt refersonly to the third: the imaginary situation. Andyet there is of course no confusion about whatis said: readers do not assume that the writersbelieve in ghost ships, or that if Great AmericaII should capsize, Northern Light's ghost willcome along and rescue the crew. Tounderstand the excerpt and to draw the properinferences, we construct three spaces: one forthe 1853 passage, one for the current 1993 run,and a blended space into which both ships areprojected, yielding the additional conceptualstructure of a race.

By giving the relative positions of the shipsin the blended space, the writer providesinformation which can be exported to thetarget, the 1993 space: whether Great AmericaII is doing well, is going fast enough, isaccomplishing its goal, and so forth. Althoughpositions in the 1853 and 1993 spaces could becompared to each other in an abstract way, theblended space does more, by fitting thecomparison into a preexisting cultural frame,the RACE, which not only has the requiredstructure, but brings with it emotions andintentions of the sailors, which can then betransferred globally to the target, with reducedcognitive effort and increased efficiency andcontent. Notice how the blend works: it doesnot merely superpose the two initial spaces; itprojects structure from each one into a largerstructure adapted to a preexisting cultural frame(racing), which appears in neither of the initialspaces. Notice also that the blend is perfectlyconsistent and straightforward—two boats in arace. Its "impossibility" is purely pragmatic,9and of no consequence to the efficient exportedinferences and emotions. In the example fromthe Inferno , pragmatic clashes in the blend(carrying one's detached head while movingand talking) were exploited inferentially. In theboat race example, this is not the case.10

NL GA

NL' GA'

1853 1993

Figure 2

Nevertheless11, the blend has produced itsown new, fantastic, conceptual domain withghost ships and imaginary races. But equallyoften, the blended space is set up without acorresponding conceptual domain. So, in thesame context as before (Great America II'sattempt to break the record), it would beperfectly natural to write:

At this point, Great America II is 4.5 days ahead of

Northern Light.

The blend is constructed just as before. Itis in the blend, not in the 1853 space or in the1993 space, that one boat is ahead of the other.But this time, no conceptual domain ofphantom boats and races is invoked. As aresult, the blend does not stand out consciouslyas it might have in the original text. In fact, ourguess is that the sentence would be perceivedby users and analysts alike as verystraightforward. And yet, the sameconsiderations as before motivate theconstruction and cognitive exploitation of theblended space.12

The boat race blend allows journeys that are

distant in time to be construed locally assimultaneous, and part of a fictitious scenario.Great America II could of course be trying tobeat its own previously set record, and then itwould be compared to itself. In the blend, itwould be ahead of itself.

3. The riddle of the Buddhist monkConsider the following riddle mentioned by

Arthur Koestler:

Riddle of the Buddhist monk and the mountain: A

Buddhist monk begins at dawn one day walking up a

mountain, reaches the top at sunset, meditates at the

top for several days until one dawn when he begins to

walk back to the foot of the mountain, which he

reaches at sunset. Making no assumptions about his

starting or stopping or about his pace during the

trips, prove that there is a place on the path which he

occupies at the same hour of the day on the two

separate journeys.13

We need to find a place on the path,occupied at exactly the same time going up andgoing down. An elegant solution to the riddle

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is to imagine the Buddhist monk walking bothup and down the path on the same day. Then,"the place" is where he meets himself. As inthe boat race, the two journeys which reallyoccurred on different days have been projectedinto a blended space where they occursimultaneously. In that space, the Buddhistmonk descending must encounter the Buddhistmonk ascending (himself). This provides theinference that there is a place on the path whichthe Buddhist monk must inhabit at the sametime of the day during his two trips. Thisinference is projected to the target, where nosuch encounter occurs.

Blends can be constructed if there isabstract structure shared by the two inputspaces. This abstract structure is found in thefourth space, the generic space. In the exampleof the Buddhist monk, the generic space isstructured by a single journey from dawn tosunset, over a single distance (that separatingthe foot and the top of the mountain). It is notspecified in the generic space whether thatjourney is up, down, or level. Nor is itspecified on what day it takes place. Nor isthe internal structure of the journey (e. g.,starting and stopping, moving slower or faster)specified. This allows the generic structure tobe projected equally well onto the space of theascent the first day, the space of descent thenext day, and the blended space where bothoccur on an unspecified day.

The example of the Buddhist monk hassome interesting features. In the blend, thesame individual can be at two different places atthe same time. This is not inherentlycontradictory. It is merely pragmaticallyatypical, but still widespread in Marcel Aymé'sstories, many religions, and moderntechnological situations involving state-of-the-art telecommunications.14 In the example of theBuddhist monk, the pragmatic anomaly doesn'thappen to yield any exportable consequence:we disregard it in order to focus on the problemat hand, the search for the meeting point, whichwill be exported back as a point attained at thesame time on two different journeys. But ofcourse, in principle the anomaly could yieldconsequences, as we shall now see with astructurally similar example.4. Getting ahead of oneself

Consider, in contrast to Dante's literaryacrobatics, the everyday, idiomatic, but still

metaphorical expression, "I am getting ahead ofmyself."

One evident inference of "I am gettingahead of myself" is that the speaker feelshimself to be engaged in an event in advance ofits scheduled moment. Another stronginference is that this is not a good thing. Thissecond inference is not available from thesource of this projection. The source concernsself-locomotion along an intended spatial track.In the logic of this space, it is simplyimpossible for someone to be ahead of himself.It is quite possible for two different people tobe at two different spots on a track, and even tobe in a kind of race with each other. But thereis no inference in the source that there isanything wrong with two different people'sbeing at different spots on the track, and nopossibility of a single person's being at twodifferent spots on the track. So the inferencethat something is wrong is not constructed inthe source space. Nor is it required or evencommon in the target space. The targetconcerns the scheduling of events, and it maybe a very good thing to be engaged in an eventin advance of its scheduled moment: "He madelieutenant a year ahead of schedule," "He'szipping through the schedule faster thanexpected," and "She finished ahead ofschedule" can all be read as positive.

The inference that something is wrongarises when we recognize that it is undesirablefor a single person to be at two different placesat the same time. It is only in a blended space,where it is "possible" for someone to be at twodifferent places at the same time, that thisinference can arise.

There are two metaphoric mappings thatconnect the source of self-locomotion along anintended track to the target of the organizationof events. In the first, the person at a locationin the source is projected to the person engagedin the actual event in the target, as in theexchange, "I'd like to talk to John." "Youcan't, he's in the middle of an exam" said in acase when John is actually in the middle of anexam at the time of speaking. In the second,the person at a location in the source isprojected to the person associated with thescheduled event in the target, as in theexchange, "Can I see you at three?" "Sorry, atthree I am in the middle of an exam."

In both mappings, the locations in thesource are mapped onto the same sequence of

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events in the target. In any one mapping, twodifferent events must correspond to twodifferent locations in the source. Normally, wecannot use both of these mappingssimultaneously. "I am ahead of John" does notmean that the event I am actually engaged in isearlier than the event John is expected to beengaged in, nor does it mean that the event I amexpected to be engaged in is earlier than theevent John is actually engaged in. It onlymeans that the event I am actually engaged in isearlier in the sequence of events than the eventJohn is actually engaged in, or that on theschedule of events, my event comes beforeJohn's, as when my tennis match is at 7pm andJohn's is at 8pm.

But consider what happens if source andtarget are blended. Recall that in the source,the essential information is that two differentpeople are racing along one track, while in thetarget, one person is associated with twodifferent "tracks"—the actual sequence ofevents versus the scheduled sequence ofevents. In the blended space, the two peoplefrom the source are blended into the one person

from the target; and the one spatial sequencefrom the source is blended into the two eventsequences in the target. So, when the actualevent is not the scheduled event, the one personfrom the target corresponds to two locations inthe source, and thus, since two locationsrequire two different people in the source, theone person from the target is equal to twopeople from the source. One person in twodifferent places is of course impossible for thesource and irrelevant in the target. But thisimpossible clash is possible in the blendedspace and occurs there to yield the evidentinference that something is wrong. We projectfrom the blended space to the target this centralinference. We cannot project from the blendedspace to the target the impossibility of oneperson's being in two different locations: thefact that one person is in two locations in theblended space corresponds in the target spaceto the situation of one person not being onschedule. The central inference that somethingis wrong is available only in the blended space;this inference, but not the impossible clash, isprojected to the target.15

I'm getting ahead of myself. [Contrast: I am ahead of schedule.]

b a

a a

a

cscheduled events

actual eventsspatial track

1 track2 people2 locations

2 sequences of events1 person2 events

1 track1 person2 locations

Figure 3

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In the view we are developing, the exoticand highly structured example of Bertran deBorn in Dante's Inferno, the boat race with orwithout the ghost, the ubiquitous Buddhistmonk puzzle, and everyday locutions like "I amgetting ahead of myself" and "I forgot myself"all require for their central inferences theconstruction of a blended space. On the basisof examples such as these, we are claiming thatprevious models of conceptual projection areinadequate and partial, since they neitherrecognize nor provide instruments foranalyzing the cognitive and linguisticphenomena involved. It might be argued thatsuch examples are mere marginal curiositiesthat do not warrant a radical theoretical shift toa many-space model such as we propose. "I'mgetting ahead of myself," for example,although neither exotic nor literary, might seemto offer no fundamental problem, since it is anidiom. So, let us look at other examples withdifferent characteristics, each of whichprovides a different kind of evidence for thenecessity of a many-space model of conceptualprojection.

5. Tuning in, and other actionsFirst, are we just dealing with language

games, strange ways found in language toexpress otherwise unproblematic situations andconceptions? Consider the following, reportedwith some embarrassment by one of theauthors of the present paper:

I'm driving, and someone is sitting in the front

passenger seat, talking to me, but I have trouble

hearing what they say. I turn the volume knob on

the car radio (which is off, of course). I've blended

the frames for listening to the radio and for

conversing with a passenger. I can't appeal to simple

error: I am in no way under the misapprehension that

the voice is coming from the radio, or that turning

knobs will make people speak more loudly. What I

have done, irrelevant, inefficient, and absurd as it may

be, is EXTEND my category of controlled sound

amplification within a blended space.

This blend is not produced by languageuse; it is a case of conceptual projection applieddirectly to action. Notice that it is inefficient in

this particular case: the inferences that thedriver of the car hopes will transfer to the realworld in fact do not—the sound is notamplified, he does not hear his friend moreclearly. Nature proves him wrong, the blend issuppressed, and the action is called a mistake.The other author of the present paper reportssitting down late at night to a dimmed computerscreen at a desk illuminated by an architect'slamp and attempting to brighten the screen byturning the knob on the lamp instead of on thecomputer: another mistake, we say.

But in other circumstances, the blend mayproduce very rewarding inferences. Forexample, many people do not know how to coila cord of neutral lay in a way that makes it easyto deal with afterward. But say to a sailor,"Pretend it is a braided dock line," and thesailor will coil it perfectly, not by goingthrough some elaborate analogy, but simply bytreating, for the moment, for local purposes,the cord as a dock line. In the frame of sailing,the person with the cord knows what to do; thesailing frame just has to be called up andblended with the frame of the cord.

We bring up such cases because they arenon-verbal, and therefore clearly don't dependon special literary effects, metaphoric language,or idiomatic construals. Nor are these casesjust abstract analogy—transfer of abstractschemas from one domain to another. In theblended space fleetingly revealed by a strangeaction, human and radio voices are not justsimilar; they are the same, under the control ofthe same knobs and switches. The cord is notjust "like" a dock line; it is conceived of as adock line in the blend. The successful actionpattern is exported to the reality target, but theextended "dock line" category is not.

These examples and several others that weshall come across show that blended spaces docognitive work in the strongest sense. Theymake available not just inferences, but alsoemotions and novel action patterns. And sothey leave their mark on the real world. In theboat race example, the sailors were able,through the blend, to live their action as a race.They could wonder whether they were catchingup with Northern Light, or how far ahead theywere, and they could (through projection fromthe other spaces) actually find out: the blendedspace of the race comes with very precise,quantifiable truth conditions. By living as arace what is not a race, they could feel, react,

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and reason differently, and perhaps moreefficiently, and with more pleasure or pain, asthe case may be.16

Our informal characterization of theconstruction of blended spaces has thefollowing characteristics:—Mental spaces in general have only very

partial explicit structure, that typicallyincludes roles, values, and relations.

—To blend two spaces is to project them onto athird space, also partially structured, in sucha way that the first two partial structures mapcoherently onto the third. The word"coherently" here is a place-holder for a vastresearch program. We return to the issue inlater sections.

—A blend in this sense is neither a union nor ablur. It is a space structured in its ownright, onto which the two initial spaces areprojected. The blended space typically hasstructure absent from the input and genericspaces, as we saw in the boat raceexample.17

—A blended space may give rise to a newconceptual domain (Dante's Hell, the raceagainst ghost ships), but it doesn't have to,and in fact usually won't.

—A blended space may be used for localcognitive purposes only, or it may lead tomore permanent reconceptualization andcategory extension, as we discuss below insection V.

6. Complex numbersConceptual projection enables us to extend

categories to cover new provisional members.The blended space that develops during suchsuch a projection merges the original categorywith its new extension. When categories areextended permanently, it is the structure of thisblend that defines the new category structure,thus carving out a novel conceptual domain.The history of science, and of mathematics andphysics in particular, is rich in such conceptualshifts.18 It is customary to speak of modelseither replacing or extending previous models,but the pervasiveness and importance ofmerging may have been underestimated.

Consider as an example the stage ofmathematical conceptual development at whichcomplex numbers became endowed with angles(arguments) and magnitudes.19 Square rootsof negative numbers had shown up in formulas

of sixteenth-century mathematicians andoperations on these numbers had been correctlyformulated. But the very mathematicians whoformulated such operations, Cardan andespecially Bombelli, were also of the opinionthat they were "useless," "sophistic," and"impossible" or "imaginary". Such was alsothe opinion of Descartes a century later.Leibniz said no harm came of using them, andEuler thought them impossible but neverthelessuseful. The square roots of negative numbershad the strange property of lending themselvesto formal manipulations without fitting into amathematical conceptual system. A genuineconcept of complex number took time todevelop, and the development proceeded inseveral steps along the lines explained abovefor analogical connections and blending.

The first step exploited the preexistinganalogical mapping from numbers to one-dimensional space. Wallis is credited20 withhaving observed—in his Algebra (1685)—thatif negative numbers could be mapped onto adirected line, complex numbers could bemapped onto points in a two-dimensionalplane, and he provided geometricalconstructions for the counterparts of the real orcomplex roots of ax2 + bx + c = 0. In effect,Wallis provided a model for the mysteriousnumbers, thereby showing their consistency,and giving some substance to their formalmanipulation. This is of course a standard caseof extending analogical connections; geometricspace is a source domain partially mapped ontothe target domain of numbers. The mappingfrom a single axis is extended to mapping fromthe whole plane; some geometric constructionsare mapped onto operations on numbers.Notice that neither the original mapping nor itsextension requires more than two domains.We do not need a generic space, since there isno assumption in work like Wallis's thatnumbers and points in a plane share propertiesat some higher level of abstraction. Thenecessary structure is already present in theconceptual source domain of two-dimensionalspace because it already contains the notion ofdistance which is expressed directly by meansof numbers.21 Nor does it involve a blend;numbers and points remain totally distinctcategories at all levels. Although the mappingproposed by Wallis showed the formalconsistency of a system including complex

13

numbers, it did not provide a new extendedconcept of number. As Morris Kline reports,Wallis's work was ignored: it did not makemathematicians receptive to the use of suchnumbers. In itself, this is an interesting point.It shows that mapping a coherent source onto aconceptually incoherent target is not enough togive the target new conceptual structure. It alsofollows that coherent abstract structure is notenough, even in mathematics, to producesatisfactory conceptual structure: In Wallis'srepresentation, the source metric geometryprovided abstract schemas for a unifiedinterpretation of real and imaginary numbers,but this was insufficient cognitively formathematicians to revise their target domainaccordingly .

In the analysis developed here, the novelconceptual structure in the mathematical case of

numbers is first established within a middleblended space. In the blend, but not in theoriginal source and target, it is possible for anelement to be simultaneously a number and ageometric point, with cartesian coordinates(a,b) and polar coordinates (r,q). In the blend,we find interesting general formal properties ofsuch numbers, such as

(a, b) + (a', b') = (a+a', b+b')(ρ, θ) × (ρ', θ') = (ρρ', θ + θ')Every number in this extended sense has a

real part, an imaginary one, an argument, and amagnitude. By virtue of the link of the blend tothe source (two dimensional plane), thenumbers can be manipulated geometrically; byvirtue of the link of the blend to the target (realnumbers), the new numbers in the blend areimmediately conceptualized as an extension of

Generic Space[commutative ringoperations on pairs ofelements]

������Target Space�����[positive and�� negative numbers,������� addition, �������� multiplication]

Source Space�����[points in oriented ����plane; vector transfor-���� mations] �������

Blended Space[complex numbers,real, imaginary partsargument, magnitude,addition and multiplicationof complex numbers]

Figure 4

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the old numbers (which they include by way ofthe mapping). As in Wallis's scheme, themapping from points on a line to numbers hasbeen extended to a mapping from points in aplane to numbers. This mapping is partialfrom source to target—only one line of theplane is mapped onto the numbers of the targetdomain—but it is total from source to blend: allthe points of the plane have counterpartcomplex numbers. And this in turn allows theblend to incorporate the full geometric structureof the source.

Interestingly, when a rich blended space ofthis sort is built, an abstract generic space willcome along with it. Having the three spacescontaining respectively points (source),numbers (target), complex point/numbers(blend) entails a fourth space with abstractelements having the properties "common" topoints and numbers. The relevant abstractnotions in this case are those of "operations" onpairs of elements. For numbers, the specificoperations (in the target domain) are additionand multiplication. For points in the plane, theoperations can be viewed as vectortransformations—vector addition, and vectorcomposition by adding angles and multiplyingmagnitudes. In the blended space of complexnumbers, vector addition and number additionare the same operation, because they invariablyyield the same result; similarly, vectortransformation and number multiplication areconceptually one single operation. But such anoperation can be instantiated algorithmicly indifferent ways depending on which geometricand algebraic properties of the blend areexploited.22

In the generic space, specific geometric ornumber properties are absent. All that is left isthe more abstract notion of two operations onpairs of elements, such that each operation isassociative, commutative, and has an identityelement; each element has under each operationan inverse element; and one of the twooperations is distributive with respect to theother. Something with this structure is calledby mathematicians a "commutative ring."

Under our account, then, the evolution andextension of the concept of number includes afour-space stage at which the concept ofcomplex number is logically and coherentlyconstructed in a blended middle space, on thebasis of a (presumably non-conscious23)

generic middle space structured as acommutative ring. The abstract andmathematical example of complex numbers issuperficially different from other phenomenawe consider in this report, such as jokes,idioms, literary metaphors, action slips, orsocial category extensions. And yet, like theothers, it illustrates and supports thefunctioning of four-space conceptualprojection, with its blended and generic middlespaces.24 Like the car radio and dock lineexamples, it confirms that we are dealing withan aspect of thought that is not purely linguisticor verbal. It highlights the deep differencebetween naming and conceptualizing; addingexpressions like √-1 to the target domain ofnumbers, and calling them numbers, is notenough to make them numbers conceptually,even when they fit a consistent source model.This is true of category extension in general.Calling a tail a leg doesn't make it one, asAbraham Lincoln insightfully and supposedlyobserved.25 But blending our conceptions oflife and computation may well decide not justwhat counts as a virus, but what a virus is.

III: Prototypes of blending andmistaken reductions

Although one central process that we treatin this report is the functioning of blendedmiddle spaces in analogical and metaphoricalmappings, the phenomenon of blending ismore general, applying to non-analogical caseslike the boat race, and, as we shall discuss insection VIII, to highly schematic grammaticalframes and functional assemblies.

To see the kinds of formal problems thatwill have to be faced, consider once again thesimple example of the boat race, analyzed nowin terms of its precise frame and role structure.

Some of the relevant partial structure isdistributed in the spaces as follows:

1853 space: a1 , the clipper NorthernLight; t1, the trajectory San Francisco toBoston; the clipper's positions on t1, the daysof the passage from start to finish in 1853.

1993 space: a2 , the catamaran GreatAmerica II; t2, the trajectory San Francisco toBoston, the catamaran's positions and thecorresponding days of the 1993 voyage.

generic space G : b , the boat; t , the

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trajectory San Francisco to Boston, p1, ... pi,... pf, the positions of b on the trajectory t;the initial day d1 and the final day df of thevoyage; a generic day of the voyage, d, and itsposition p.

This generic space frames the other two in acertain way: b, d1, df, d, p, are roles filled bythe more specific values for the boat, departure,and arrival dates and positions, in the 1853 and1993 spaces. The trajectory t, on the otherhand, is essentially the same as t1 and t2. Theinitial position is San Francisco in all spacesAt the same time however, this generic spaceitself is framed by a more general schema ofboat, trajectory, and positions, which itself isframed by an even more general oriented pathschema, with a moving trajector, an origin,goal, and intermediate times and positions.

Notice that G is built for local purposes to fitthe spaces at hand and to fit the more generalbackground knowledge frame-schemas.

G has the "same" trajectory as the othertwo spaces (San Francisco to Boston), andtherefore conceptually it has the same availablepositions on that trajectory. However, the daysfor those positions are different in the inputspaces, and so we have no specific dayassociated with a position in G. What we dohave is the more abstract notion that eachposition p is reached on some day d, where p,d is a pair of roles without specified values inG .

Space G induces a mapping between thetwo input spaces, by correlating elements withthe same G-projection:

a1 → b → a2 (Northern Light → Great America)

t1 → t → t2 (SF - Boston → SF - Boston)

pi' → pi → pi" (same points on the path)

di' → d → di" (days in 1853 and 1993 onwhich a particular position was—initial and final dayswill be correctly mapped)

Relational structure in G, projected onto theother spaces includes:

b sails from p1 to pf on t .b is at position p on day d, where the roles

p and d define a function from positions todays, unspecified in G, but specified in theinput spaces. This function meets theconditions d(p1) = d1, d(pf) = df.

The blended space B is obtained through adifferent projection scheme from the inputspaces, that preserves the mapping to thegeneric space:

The trajectories t1 and t2 are projected tothe same trajectory t'. The moving boats a1and a2 are projected to distinct moving boatsa'1 and a'2 on t'. The blended space inheritsthe dates of 1993. The 1853 days are mappedonto corresponding 1993 days by using the d1role for the first: i.e. in the blend, the two boatsare assumed to start together on the first day ofthe 1993 passage. The boats in the blend retain

their characteristics (clipper, catamaran).Positions and days for each boat are thenmapped in the obvious way: identity for thecatamaran, sequence from day 1 for the clipper.

We see that while the two boats werecounterparts with respect to the genericframing, they no longer are with respect to theblend, where a1 and a2 project onto distinctelements. At the same time, the blend fits thegeneric in a many-to-one map. New relationalstructure is automatically created in the blendby this projection: there are now relativepositions of the moving boats, distancebetween them at any time, difference in time toreach the same position, and so on. Noticecrucially that this additional structure is notspecified in the blended projection itself. It justfollows topologically from that projection.

The next step, of great importance in ouranalysis, is to fit the blended structure thusobtained into a preexisting cognitive model. In

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the case at hand, the blended structure in itselfdoes not contain any notion of "race," but it fitsthe richer "race" model which we areindependently familiar with: two movingvehicles driven by human beings, moving onthe same path, with the same goal, and startingat the same time. The conceptual leap inbuilding the blend is to automatically give it thismore highly organized structure.

We take the mapping strategies outlined forthe simple boat race example to berepresentative of space blending in general.While the Generic space is a structuralintersection of the input spaces, the Blendcreates new structure by allowing counterpartsto be mapped to distinct elements, with distinctattributes, and by allowing importation ofspecific structures in the inputs. The keyconstraint is that we don't just have a union ofthe input spaces: only selected structure in theinputs is exported to the blend, but the overallprojection will contain more structure than isavailable from the inputs. So for example, wesaw that the days of 1853 were mapped ontothe blend without their actual 1853 dates(selected structure), but that the resulting "race"structure in the blend went beyond what wasprojected from the input spaces.

The "whole" that we find in the blend isthus both greater and smaller than the sum ofthe "parts." Through projection of partialstructures, and embedding into backgroundframes, we get a truly novel structure, notcompositionally derivable from the inputs.Therein lies the creative force of such blends.New actions (as in the dockline example), newconcepts (as in the complex numbers case),new emotions and understandings (as inmetaphor) emerge.

As we shall see in section VIII, the formalmerging operations outlined above show up inthe same form in grammar at the moreschematic level of blended grammaticalconstructions and functional assemblies. Adeep generalization is that the full interpretationof any sentence in a particular context is asequence of successive blends meeting moreand more specific local constraints. Meaningconstruction consists in solving successiveconstraint satisfactions on blends.

There is no way that all such mechanismsand constraints can be specified a priori. Thedetailed examples in this report point to achallenging research program. We believe that

considerable empirical work must still be doneto understand the precise functioning of theprojections.

The general phenomenon of blending is notto be confused with any one of its easy,striking, or memorable special uses. In thehope of laying down for the reader a permanentbarrier against the all too easy covertassumption that blending in general reduces tothe features we see in one or another instanceof its operation, we will survey some instancesof blending and their central differences. Noone of these instances provides a prototype towhich other instances can be assimilated.

The most obvious special instance is thecartoon presentation of impossibly literalizedmetaphor made strikingly manifest throughvisual blending.26 Consider the cartoon of theangry character: his skin grows red from histoes to his head in the manner of a boiledthermometer; he flips his lid and steam shootsfrom his ears. This is certainly a blend, basedon the metaphoric projection from heatedobjects to angry human beings. It is alsohighly visible at a conscious level, because thecartoon world allows its explicit conceptualrepresentation. It is therefore not representativeof the general nature of blends. We stress thepoint, because it is tempting to reduce thephenomenon to its salient manifestations, andmiss the deeper issue. Visual cartoonliteralization of metaphor is a peripheral, not aprototypical case of blending.

A second tempting reduction is to theprototype of the fantastic, as in the Infernoexample. A third tempting reduction is to theprototype of impossibility. "I'm getting aheadof myself" involves a structure that isimpossible in Euclidean space for humanbeings. A fourth tempting reduction is to theprototype of "literary deviance," as we mightsuppose applies to Dante's Bertran de Born.This reduction compounds two errors: first, itassumes that blending belongs only to languageexplicitly marked as literary, and second, itassumes that the cognitive mechanisms ofliterature differ in kind from cognitivemechanisms of everyday thought.

All of these reductions, and others as well,obscure the aspect of blending that makes itfundamentally important to the cognitivesciences: blending is a general phenomenon,running across all varieties of cognition. Like

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categorization, inference, the making ofhypotheses, and metaphor, it is routinelyemployed and generally indispensable. It is notan advanced performance added optionally tomore basic phenomena for special effect, likepaint to a house. On the contrary,categorization, inference, the making ofhypotheses, and metaphor depend in crucialways upon the existence of the generalcognitive capacity for blending.

Both the angry cartoon character andBertran de Born are visual, but the categoryextension of sounds controlled by the radiovolume button is not. The cartoon, the radiomistake, and the riddle of the Buddhist monkare striking blends that cannot fail to benoticed, but "I am getting ahead of myself"depends upon a covert blend detectable only onanalysis. The radio mistake involves themaking of a hypothesis, but "I am gettingahead of myself" does not. "I am getting aheadof myself" and the riddle of the Buddhist monkconstruct central inferences in their blendedspaces. The cartoon is a case of making aconventional metaphor literal, but the exampleof Bertran de Born is not, since a literalpresentation of social "division" as spatialdivision would produce a spatially dividedfather and son, not a spatially divided Bertrande Born.

The cartoon and Bertran de Born dependupon a metaphoric relation between source andtarget, but the boat race and the riddle of theBuddhist monk are not based on metaphoricrelation between source and target.

The radio mistake is a mistake but thecoiling of the cord is a success. Both involvethe construction of a hypothesis and theexecution of corresponding action, but neitheris an analogy—a transfer of abstract schemasfrom one domain to another. Neither is ametaphor, since metaphor establishes a systemof figural correspondences, not of identities:here, the radio volume knob and the pattern ofcoiling do not correspond figurally tosomething in the target; rather, they applyidentically to blended categories built up on thebasis of the source and target spaces.

In some cases of blending, there islinguistic evidence for the independentexistence of the blended space: in the blendedspace of the boat race, there are two boatssimultaneously racing, and we can refer tothem accordingly, but there are vestiges of

Northern Light's having come from a spacethat provides the reference frame, so that in theblend, Northern Light provides the landmarkand Great America II is conceived as thetrajector: We would say "Great America II isahead of Northern Light" but not *"NorthernLight is behind Great America II." Yet in othercases, as in the radio mistake, there may be nolinguistic evidence at all.

In the rest of the paper, we will mention ahost of other contrasts between specific uses ofblending. We will see cases of blending inanalogical counterfactuals where projection isnot principally direct, positive, or one-way.We will see additional cases where blendingprovides category extension. We will seeblends that are funny and blends that evokemirthless ideological debate. We will seeblends that concern scientific reality, others thatconcern social reality, and others that concernpersonal reality.

This illustrative summary of differences isoffered as a talisman to ward away from thereader any reduction of blending to one of itsmerely noticeable uses. Instances of blendingare amazingly diverse, naturally so, given thatblending is a general cognitive instrument.What all these instances share is an intricateform of cognition which can be analyzedthrough the many-space model of conceptualprojection.

IV. Further evidence for conceptualprojection into a blended space

We have suggested that important cognitivework was performed in middle spaces, genericand blended; that a blended space had its ownstructure and organization, not reducible to anamalgamation of structure from the source andtarget; that blending could manifest itself inmany ways, verbal or non-verbal, vividlyimaged or masked from consciousness, inpoetic invention, everyday language, orscientific inquiry.

This view raises multiple theoretical andempirical issues, most of which remain beyondthe scope of the present report. In this section,we attempt to increase awareness of suchissues through the examination of a rich arrayof examples that highlight theoretically relevantproperties of conceptual merging.

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1. President Bush on third baseWe start with a case of metaphorical

projection that is not exotic, literary, oridiomatic, but is meant to be a joke:

George Bush was born on third base and thinks he hit

a triple.27

The source is baseball and the target issociety and one's image of one's relation tosociety. As is often observed, a projectionsuch as this, which carries baseball onto life,does so by virtue of a shared schema thatstructures a generic space. In this genericspace, there are agents in competition, goals tobe reached, and so on. This generic space canbe projected onto an indefinite range of specifictargets, as in "He hit a home run at themeeting," "She scored the other night," makingbaseball an archetype of such competitivebehavior. The example, "George Bush wasborn on third base and thinks he hit a triple," isan inventive use of the standard projection ofthis generic space.

However, not all of the meaning can beconstructed in this fashion. Central inferencesoriginate in a distinct blended middle space.One such central inference of this expression isthat George Bush is not just stupid in theexpected ways we are all stupid, but to a muchhigher, "inconceivable" degree. Where doesthis inference come from? It is not availablefrom the source, because although there ismore than one way to get on base (the battercan be walked, a pinch runner can be put on,and so on), in none of them is it possible to beconfused about how you got on base. There isstupidity in baseball, of remarkable kinds suchas those sampled in bloopers films,28 andstandard kinds, such as mental errors in theexecution of an intended double play, orforgetting a complicated rule, and so on. Butthis kind of stupidity in baseball does notinclude not knowing how you got on base.None of the stupidity in the source domain isused to project the stupidity in the target in thiscase.

It is not impossible to project stupidity frombaseball to the target. One could say of Bush'shaving lost the election, although he waspresident during the dissolution of the Sovietempire, that he "got on third base without ever

having hit even a single ball, and had thechance to steal home, but he blew it." But in"George Bush was born on third base andthinks he hit a triple," none of the stupidity inthe target accords with a stupidity in the source.

Neither is the inference that Bush is aparagon of stupidity available from the target.It is nearly the human condition that we are alldeluded about our position in life. If PresidentBush is deluded, he is not exceptional in thisregard.

But, in the blended space of life asbaseball, we have from the source theinformation that someone is on base, and fromthe target the information that he is deludedabout his position or how he attained it. Theblended result is being deluded about how onegot on base. The counterpart in the source isimpossible. The counterpart in life is thestandard condition. But the blend is stupid inthe space of life as baseball. The stupidity is inthe blended space.

It might be argued that, on the contrary, itis indeed possible to be ignorant in baseball ofhow one got on base, perhaps because therunner has had a stroke while running bases oris on drugs or because he has beenbrainwashed into insanity by a cult figure whohas told him that the wheel of fortune assignsto every runner a base, or because of someother scenario alien to our concept of baseballbut not absolutely impossible, and that such adelusion would be regarded as stupidity inbaseball, and so the relevant inferences canindeed be projected to the target from thesource. But now consider a second projection:

Dan Quayle was born on third base and thinks he

kicked a field goal.29

The inference that the Vice-President of theUnited States Dan Quayle is an "even moreinconceivable idiot" than President Bush is notavailable from the source space of baseball,because the scenario of thinking you got onthird base by kicking a field goal is not merelyrare or unlikely, but fantastic. There is nothingin the game of baseball that allows for notknowing the difference between baseball andfootball. Dan Quayle has not had a mere lapseof memory; he is abidingly obtuse about eventhe distinction between the two differentgames. Again, the inference of exceptional

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stupidity is not available from the target, wherepresumably everyone is in some measuredeluded. It is available only from the blendedspace in which one can be simultaneouslyplaying baseball and living life and bestaggeringly confused about how one attainedone's place on base.

There is another inference that can arisefrom the blended space but not from the sourceor the target. In the blended space, GeorgeBush has been on third base all the time, i. e.,68 years, and has never advanced. In thesource of baseball, it is not principally therunner's responsibility to make opportunities toadvance bases; typically, it is the responsibilityof the people who follow him in the battingorder to bat him in. In the source, there isnothing wrong with Bush's staying on third,and no possibility of his staying there for 68years. In any event, in the source, thissituation does not count against Bush. In thetarget, certainly there is nothing wrong withhaving lived one's life at a high social station,been president once, and so on. But in theblended space, a runner is responsible foradvancing, and it is is possible to stay in thesame place forever. In the blended space, wehave the inference that the longer the runnerstays in one place, the less competent he is.Since Bush has never moved, the inferencearises that Bush is exceptionally incompetentand lethargic. As in the case of the boat race,or the Inferno, the middle blend displaysadditional cognitively relevant structure (theagent's responsibility for not advancing), thatwas absent in the source and the target.30

George Bush and Dan Quayle weredescribed in this fashion in order to indicatethat, while it must be admitted that Bush andQuayle have a certain social, financial, andpolitical status (third base), this does not meanthey are to be given any credit, or regarded ascompetent for having attained this status, andthat therefore, no one should vote for thembecause of their status. In fact, their delusionabout the nature of status in general is positivereason to vote against them.

Although the blended space has many ofthe trappings of baseball—bases, runners,etc.—it also has many features of the targetsocial world—birth is a means of arrival, thegame can last for decades, players can bepathetically deluded. As in previous examples,

the pragmatic anomaly of the blend does notprevent it from being logically coherent, fittingthe schematic structure of the generic space,and thereby exporting the appropriateinferences and emotions to the target.

Notice, furthermore, that the conceptualdomain corresponding to the blend is felt to bean extension (fantastic to be sure) of the gameof baseball, not an extension of our social lifeas voters and candidates. In that sense, itfunctions like a source, in the traditional two-space sense, for projection to the target. Thisreflects, we think, an important asymmetry inthe construction of blends, where the sourceprovides landmarks and locations and the targetprovides trajectors and intentions. The boatrace example, as we noted, displays similarasymmetry.

2. Nixon in FranceWe are convinced that jokes, poetry, or

idioms often provide very useful data, becausethey make certain cognitive processes highlyvisible. Our next example, however, is notexotic, literary, idiomatic, or humorous, anddoes not seem to involve metaphor or categoryextension. It is an analogical counterfactual ofthe type studied by Fauconnier (1990, toappear):

"In France, Watergate would not have harmed Nixon."

Uncontroversially, understanding thiscounterfactual includes building a genericmiddle space that fits both American politicsand French politics. It includes a leader who iselected, who is a member of a political party,and who is constrained by laws. This skeletalmiddle space fits the space of American politicsand French politics so well and intricately that itis natural for someone to project a great dealmore skeletal information from Americanpolitics into the generic middle space on theassumption that it will of course apply toFrench politics.

The rhetorical motive for saying, "InFrance, Watergate wouldn't have done Nixonany harm" is exactly to stop someone fromprojecting certain kinds of information to thegeneric middle space on the assumption that itapplies to French politics. It is the power ofthe non-counterfactual generic middle spacethat causes the speaker to lay down a barrier.

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The speaker does this by constructing aspecific, counterfactual, and pragmaticallyanomalous blended space.

Into this middle space, the speaker hasprojected information associated with PresidentNixon and the Watergate break-in. Nixon andWatergate and so on are brought into themiddle space with only skeletal properties,such as being a president who breaks laws inorder to place members of a political party at adisadvantage. It may be that such informationin fact in no way belongs to French politics,that something like Watergate has in fact neverhappened in French politics. No matter, it canbe imported to the middle space from thesource. Additionally, into this space isprojected, from the target, French culturalperspectives on such an event. Such a space isa blend; its counterfactuality is a consequenceof this blending.

This counterfactual space operatesaccording to its own logic. In thiscounterfactual space, an illegal act directed withthe knowledge of the elected leader against theopposing political party leader will not causethe public outrage associated with Watergate.For this central inference to take place, we musthave both the nature of the event from thesource and the general cultural attitudes fromthe target. The blended space is again not aside-show or curiosity or merely anentertaining excrescence of the projection. It isthe engine of the central inferences.

Clearly, in the case of such an analogicalcounterfactual, the construction of meaningcannot be mistaken as an attempt to imposestructure from the source onto the target. Infact, this particular analogical counterfactual istrying to do exactly the opposite. It is trying tomake clear in just what areas informationprojected from the source cannot be imposedon the target. Moreover, its purpose is toilluminate not only the nature of the target, butalso the nature of the source. The inferencesare thus not one-way. They can go from thecounterfactual space to both the source and thetarget.

Nor are the analogical connectionsexclusively positive. It is disanalogy ratherthan analogy that is the central assertion of thestatement. We recognize that a scenario can beshared by American politics and French politicsbut that in certain key respects these spaceshave negative counterparts rather than positive

counterparts. The utterance sets up a blendedmiddle space exactly for the purpose ofilluminating these counterparts and theirnegative relation to each other. The projectionin the case of "In France, Watergate would nothave harmed Nixon," is thus not direct, notone-way, and not exclusively positive.

This, then, is a case demonstrating awholesale theoretical inadequacy of the two-space model, since under the two-space modelthere are no processes by which the intricatemeaning of "In France, Watergate would nothave harmed Nixon" can be constructed.

Of course, one may object to the assertionabout France. One can respond, "You arewrong, look at all the harm the Greenpeaceincident did to Mitterand." This can beinterpreted as asking us to change the blendedmiddle space so that the illegal act is nowgeneral enough to include not only acts directedat an opposing political party but even actsdirected against any opposing group(Greenpeace). It asserts that the space doesindeed include cultural perspectives that,contrary to the previous assertion, do apply toboth American politics and French politics.This, in turn, has the effect of expanding thegeneric middle space. This is a fundamentaland general point that will arise repeatedly inour analyses: the four spaces are built updynamically and inventively in order to achievea conceptual projection. The four-space modeldictates no fixed sequence in this constructionof meaning. It additionally accords notableplace to energetic and imaginative effort andrevision.

We might ask, in what space does it holdthat Watergate does not harm Nixon? Not inthe source, or the target, or in the genericspace. But if we shift to the blended space,then the claim holds. It appears that a centralpart of conceptual projection is knowing howto construct a blended space and how to shift tothat blended space in order to do realconceptual work, with the consequence that thevestiges of that real conceptual work are oftenprojected to the target and often even thesource. But the structures of the blended spacethat would be impossible in the other spaces areleft behind in such projection. That they areleft behind does not mean that they are notindispensable to the central conceptual work.

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3. PersonificationNow let us consider personification. As

Lakoff and Turner have analyzed, the generic-level metaphor EVENTS ARE ACTIONS is aninstrument for understanding events withoutagents metaphorically in terms of actions byagents by projecting generic-level informationfrom the source action to the target event. Thegeneric-level information in a given action canbe projected to a generic space and projectedthence to a range of specific events. In thisprojection, something in the target space of theevent causally related to the occurrence of theevent can correspond, under projection, to theagent of the source action. The result is thatsomething in the target that is not a person isunderstood by projection from something in thesource that is a person. This is the generalmechanism of personification, and underliessuch specific personifications as themetaphoric understanding of Death as someonewho takes you away, or the metaphoricunderstanding of Time as a thief who stealsyour youth.

By now, it may be apparent that theprojection of the agent from the source actiononto the target event cannot be direct. To besure, information is ultimately carried from thesource to the target, and indeed we do have aconception of Death as a person, of Time as athief, of situations we are trying to master asintentional opponents, and so on. But suchpersonifications belong to an impossibleblended space that can be extraordinarily robustand dramatic—with Death the Grim Reaperwhose body is a skeleton, who wears a darkcowl, and who carries a sickle, for example.No one ever confuses this blended space withthe actual target space of the biological event ofdeath. Information and inferences are projectedto the target from the blended space, but theclashes that are possible only inside the blendedspace are not projected to the target space. Wedo not identify the target space and the blendedspace. The construction of meaning involvesmany spaces, simultaneously active, andconnections between them. There isn't an endstate in which the meaning has been depositedin the target and the other spaces havedisappeared. Personification involves—in adynamic and interconnected fashion—a sourcespace, a generic space, a blended space, and atarget space. The blended space and the targetspace are both active and both necessary to the

construction of the meaning of the target. Itwould be a mistake to assume that becauseinferences are ultimately carried to the targetthat they are carried directly from the source,and equally a mistake to assume that becausepeople do not identify the target and theblended space, and in fact regard the blendedspace as false, that the blended space is merelywhimsical or parasitic and not essential for theconstruction of meaning in the target.

It would also be a mistake to assume thatblended spaces are arbitrary and free playspaces. We have seen various cases in whichthe blended space operates according to anintricate logic of its own, as in counterfactuals,such as "If I were you, I would have done it,"said by a man to a woman who declined earlierto become pregnant: the woman did not do it,the man cannot do it, but in the blended space,the blend of selves is such as to combine theman's judgment with the woman's conditions,enabling the man-woman to become pregnantin the counterfactual past of the blend.

Such intricate logics, and their intricateorigins, are beyond the scope of this paper, butwe can increase awareness of their existence byconsidering some of the phenomena of trajectorand landmark in examples. In the conceptionof death as departure, the source has a cleartrajector — the traveller — and a clearlandmark — the place departed. There may bemany different ways to conceive of the event ofdeath, with various trajectors and landmarks,as when we buy the farm or God cancels ourrumba tickets, but the established trajector andlandmark of the source in this projectioninduces a trajector and landmark in the blend:blending the person leading the life with thetraveller, and "here" with being alive, makesthe person a trajector with respect to thelandmark of being alive.

In other cases, the target induces thetrajector and landmark, as in "I'm getting aheadof myself." In the source, with two runners,each runner is a trajector with respect to thelandmark path, and each runner is a trajectorwith respect to the other as landmark: eachrunner inhabits various roles as trajector andlandmark. But in the target, the actual event isthe trajector with respect to the landmarkschedule. Therefore, in the blend, the runnercorresponding to the actual event must be thetrajector with respect to the runnercorresponding to the scheduled event. "I am

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getting ahead of myself" does not mean that thescheduled event is ahead of the actual event.Here, the induction of specific trajector andlandmark comes from the target.

In "George Bush was born on third baseand thinks he hit a triple," there are trajectorsand landmarks in both source and target(runner and bases in baseball, person andsocial hierarchy in life), and they are aligned,but the source trajector and landmark are morelimited than the target trajector and landmark.It is possible for someone to go down thesocial hierarchy in life, but not possible forsomeone to be demoted to a prior base inbaseball. So in the blend, it would be"illogical" to say that someone was born onthird base but soon found himself sent down tosecond base and then, before long, coming upto bat for the first time.

In the boat race, the spaces of 1853 and of1993 each have a boat as trajector and itscourse as a landmark. In neither space can oneboat be the trajector relative to the other aslandmark, since there is only one boat. In theblended space, there are two boats in a race. Inan actual race, either boat can be the trajectorwith respect to the other: we can say either"Great America II is ahead of Northern Light"or "Northern Light is ahead of Great AmericaII." But the status of the space of 1853 asproviding the actual reference course and timeis inherited in the blend, so that Northern Lightmust be the landmark, and we can say only"Great America II is ahead of Northern Light,"not *"Northern Light is behind Great AmericaII." By contrast, in the riddle of the Buddhistmonk, neither the space of his ascent nor thespace of his descent supplies the necessaryreference, and so either can supply the trajectorwith respect to the other: either "The place iswhere he (ascending) meets himself(descending)" or "The place is where he(descending) meets himself (ascending)" isperfectly fine.

V. Category extension

We now discuss blends that producetemporary or permanent category extensions,of the sort we saw in the discussion of complexnumbers.

Consider first examples like the following,which readers may or may not consider

intuitively metaphoric:

He's a real fish.

The source space has fish and water. Themore abstract generic space projected from thissource space includes the information that thereis an agent who moves through the waterexcellently. This generic space can beprojected over a great range of specific targetspaces, so that, for example, one could say"My native Newfoundland water dog is really afish" or "This roving pool cleaner is a regularfish." In the case we are considering—"He's areal fish"—the agent of the generic space isprojected onto a human being in the targetspace. The blended space has the framestructure of the generic space as well as moreinformation from the source and the target. Inthe blended space, all things that moveefficiently through water are fish, including realfish. In fact, in the blended space, all thingsthat move efficiently through water are realfish. This may seem confusing, but it must beremembered that to be a real fish in the blend isnot the same thing as to be a real fish in thesource or the target. This again raises a generalpoint: what is true, what is possible, what isreal, what is what all depend upon the spacewith respect these questions are asked; theanswers in general vary as we shift from spaceto space.

In the blended space, a new provisionalcategory has been constructed, for localpurposes. It gets its name in the usual fashionfrom the source, and so is called "fish." It hasbeen considered a mystery why the word "real"would be used as a hedge to designate thingsthat don't really belong to the category. Theanswer is that "real" signals a mental spaceshift to provisional reality. In our example,the provisional reality is constructed in theblended space. In "If he were a real spy, hisname wouldn't be James Bond," theprovisional reality is the counterfactual space.In "He thinks this is a real gun," theprovisional reality is the space of his beliefs,which might be wrong. Finally, if someoneasserts that a gun is a toy, we can reject thatproposal of a provisional reality by retorting"No, it's a real gun," in which case "real"indicates shift back to real reality (which ofcourse is only the speaker's reality).

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In the blended space constructed under"He's a real fish," or "My dog is really a fish,"something can be both a human being and afish, or a dog and a fish. Consider the use ofthe words "real" and "actually" in theseexpressions. It is completely false of bothsource and target that the human being is a fishor that the dog is a fish. "He's a real fish" and"My native Newfoundland water dog isactually a fish" are both false with respect to thesource and the target. But they are both true ofthe blended space, which instantiates theextended category. With respect to the blendedspace, the human being is indeed a real fish andthe dog is actually a fish. The effect of "real"and "actual" in these cases is scopal: it indicatesthat the locus of truth is the blended space. Ifno blended space were involved in theconstruction of this conceptual extendedcategory, there would be no reason for "real"and "actually" to occur in these expressions.Of course, it is important to remember that noone is confused about the status of thesevarious spaces: that the swimmer in the blendedspace counts as a "real fish" never leads anyoneto imagine that he counts as a "real fish"outside the blend. The category extension isstrictly limited to the blend. It does not spreadto other spaces. In that sense, then, it is localand temporary. It serves a certain purpose at acertain point of the conversation, but does notset up a novel conceptual scheme. In the longterm, fish are still fish and dogs are dogs.

But the four space projection mechanismcan also lead to more permanent categoryshifts. Consider now the relationship betweenanalogical connections and categoryconnections. Analogies place pressure uponconventional category structures. A successfulanalogy can, through entrenchment, earn aplace in our category structures. The assault ofan analogy on conventional categories is oftenexpressed in its early stages in a noun phrasethat draws its adjective from the target and itshead from the source. "Same-sex marriage,"for example, asks us to project the scenario ofmarriage onto an alternative domestic scenario.People of violently opposed ideological beliefwill freely agree that the generic middle spaceof this projection carries information thatapplies to both the conventional marriagescenario and the alternative domestic scenario;this information includes people living in ahousehold, division of labor, mutual

protection, financial planning done as a unit, orwhatever. What is at issue is the status of thisinformation. For someone whoseconceptualization of conventional marriage hasas a criterial component "heterosexual union forthe sake of children," the result of constructingan understanding to account for "same-sexmarriage" will be an analogical projectionwhose middle space does not carry this criterialcomponent from the source. From the view ofsuch a person, "same-sex marriage" willremain an analogical projection whose blendedmiddle space is as conflicted as any we haveseen in Dante or Shakespeare —this blendedspace includes married couples that are not manand wife, a strong clash with the criterialcomponent of the Source. But in spite of thisclash, and in fact in part because of this clash,the blended space captures legitimateconnections between one kind of scenario andan entirely different kind of scenario.

However, someone of differing ideologicalviewpoint may regard the skeletal informationin the generic space as the central informationin the scenario of marriage. He may regard"heterosexual union for the sake of children" asnon-central, even marginal, information in thissource scenario. For someone holding such aview, a "same-sex marriage" is not anaggressive analogical construction; it simplyrefers to a subcategory of marriage in the waythat "light wave" refers to a kind of wave.

The distinction is not one of professedbelief. Agreeing to treat two scenarios asbelonging to the same category for purposes ofprotection under the law or taxation or healthcoverage or whatever is not the same asactually having a conceptual structure in whichthese two scenarios belong to the sameconceptual category. Liberal goodwill towarddiverse scenarios, on a philosophy of live andlet live, is very far from the phenomenon ofrecognizing light to be a wave or recognizing aworking mother to be a mother or recognizing aheron to be a bird.

Were the generic information in the genericspace of "same-sex marriage" to come toachieve a different status as the defaultinformation in the source, the concept andcategory of marriage would change, not byincluding new information but rather byshifting the information that structures thesource. In that case, the generic space thatlinks "same-sex marriage" and traditional

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marriage in the analogy would come to definethe category structure of "marriage" in general.To do so, of course, it would have to displacethe conventional category structure of"marriage" in general. In that event, theblended space would be, instead of a locus forimpossible or fantastic clash, the defining spacefor the new and wider category. The blendwould, for many people, begin as animpossible clash, like a messenger's beingnature or one person being in two places at thesame time. But as the generic space is returnedto structure the source and the target as thesubsuming category, the blended spacebecomes simply a possible union, and theresult is a newer category. The final resultwould be that the blended space would come tohave the names associated with the originalsource, and therefore so would the originaltarget, because it is contained in the blend.

The cultural tussle over the pressure placedby the analogy of "same-sex marriage" uponconventional category structures provides dailyjournalistic copy and stirs some passions. Ithas an equally profound but more temperateparallel in the contemporary discussions of"artificial life."31 If our mental space of lifeincludes as central information "developmentthrough biological evolution, carbon-based,"and so on, "artificial life," which comes fromthe lab and is not based on carbon, will alwaysbe an analogical concept, and "artificial life"will not belong to the category "life." Butcomputer viruses, for example, share manythings with biological organisms. As thegeneric space that can be projected from lifeand imposed on artificial life grows moreuseful, it may become attractive to change ourconception of the status of this information ascarried in the source category of life. Thisgeneric space may come to constitute the centralcategory information in the source category"life." In that case, "artificial life" will becomea subcategory of life, rather than a projectionfrom life to technological phenomena that havemanifest connections to "life" that arenonetheless resisted by the categoryconnections between "life" and its conventionalsubcategories.

As we have seen in all our examples,generic spaces provide abstract scenarios forsource and target, while blends provide in asense richer, more developed scenarios into

which source, target, and generic, can allproject.

The evidence we have considered so farshows that conceptual projection does not carryinformation directly from a source to a target ina manner that is one-way and positive.Although the two-space model accountspassably for certain special events ofconceptual projection under reducedcircumstances, it is radically inadequate inprinciple. A better analysis reveals the role ofmiddle spaces, both blended and generic, andleads to the many space model.

VI. Generic Spaces

We imagine that the claim of the existenceof generic spaces is one of our leastcontroversial. Most researchers willacknowledge that source and target in aprojection share skeletal information. Nearlyall forms of traditional representation dependupon some shared skeletal information betweenwhat is represented and the representation.Charts and maps, for example, are understoodas sharing geometric structure with what theyrepresent, according to some customary modeof representation. A Mercator projection, forexample, does not preserve area but doespreserve angular relations, order relations, andso on.

The question is: must the generic spacehave an existence independent of its embeddingin the source and the target. One sort ofargument that it must comes from Lakoff andTurner's analysis of GENERIC IS SPECIFIC.Many proverbs are understood as having ageneric reading, in the absence of anyindication of a specific target. For example, wecan all understand "Don't get between a dogand his bone" without having to apply it to anyparticular specific target, and this reading just isa generic space. So the generic space existsindependent of its embedding in the source andthe target. This generic space can be applied atwill to an infinite range of specific targets. Ifall that were available were direct projectionfrom the source to a specific target, it wouldtake an infinite number of such individualprojections to account for the range of spaces towhich the proverb can be read as applying.

Generic spaces do not have a richvocabulary associated with them in the way

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source and target and therefore blended spacesdo. The vocabulary of the generic space islargely shifted to it from the source, and thenthis vocabulary applies whenever we imposethe generic space on a new target. To give justone example of this common activity: we donot have a generic word that means "whateverinstrument somebody uses all the time in hischosen work, an instrument that comes to beidentified with him, an instrument to which heapplies effort, and with which he has anunusually close association." One suchinstrument for one such worker is an axe. Therelation of the worker working with the axe,manipulating it, trying to get it to do what hewants done, has a skeletal structure, and thisstructure can be projected to a generic space.In music, especially jazz music, someone'sinstrument is called his axe. Of course asaxophone can be an axe, but so can a flute, aguitar, a drum set. A new projection of thegeneric space onto a new kind of instrument(perhaps some electronic synthesizer) does notlook unusual. The application of thevocabulary to the new target is expected,because it is used whenever the generic space isapplied. The existence of the generic space andits projection to a range of targets gives rise to aprovisional category, which is the blendedspace of all axes, including axes. This is thesame mechanism as we found behind "He's areal fish."

One of the clearest kinds of evidence for theexistence of generic spaces as independent oftheir embedding in the source and the targetcomes from analogies where the source and thetarget are identical. In these cases, structure isprojected from the source to the generic space,and then back to the target, which is the sameas the source. But the projections from thegeneric space to the target are not exact inversesof the projections of the source to the genericspace.

For example, consider the cartoon"Momma," in which Momma's son, Francis,prompts his friend Jack to report to "Momma"that Jack's mother, Victoria, pays all of Jack'scredit card charges, so he never has to botherher for money.32 Francis asks her, "Can't I dothat, too?" Momma replies, "It's fine with me.Check with Jack's mother." Francis isattempting to project from the conceptual spaceof family finances onto the same domain, not

onto a different type of conceptual domain. Heuses one generic space, in which the parentpays for the child's credit card bills.Obviously, he means for that generic space tobe projected back onto his own situation insuch a way that parent projects to Momma andchild projects to Francis. Momma builds adifferent generic space, in which Victoria paysfor a generic profligate's bills. This, in turn, isalso projected back to the target, with theprofligate projecting onto Francis and Victoriaonto Victoria. Francis is attempting tocategorize Momma and himself as belonging tothe ad hoc category of families where the parentpays for the child's credit card charges.Momma is resisting that ad hoc categorization,preferring to place her son into the ad hoccategory of people whose credit card chargesare paid for by Jack's mother.

Momma and Francis both recognize thatJack's situation can be mapped onto Francis's.Moreover, they do not disagree about theabstract structure underlying the situations—family ties, modes of payment, etc. But as itturns out, they are fighting over theconstruction of generic spaces—one in whichmothers pay for their sons versus one in whichVictoria pays for everybody. Such spaces aremore than schemas extracted from the source.They have their own (partial) mental spacestructure with roles, values, and frames, andonce established, they have a life of their own,like the commutative rings of our mathematicalexample, or the self-help injunction extractedfrom "Look before you leap."

Genericness is a relative notion. Genericspaces built up at one level may be mapped on,and blended into, each other on the basis of yethigher level generic spaces. In that sense,image schemas in the sense of Lakoff,Johnson, and Turner define generic spaces at avery high level, with extremely partial andskeletal structure with multiple projectionpossibilities. The same can be said of framesassociated with grammatical constructions. Wereturn to this issue in Section VI.

VII. Parameters and subschemes

The conceptual projection scheme we haveoutlined involves a dynamic construction ofmultiple spaces: source, target, and middle—both generic and blended. The spaces and the

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links between them are dynamically activatedand transformed or elaborated, yieldinginferences and meaning that are notconcentrated in one single locus. In the full-blown scheme of the four-space model,everything is maximally differentiated andactivated. From this general scheme, we canderive typical subschemes by consideringspecial or limiting cases. The parameters weconsider are:—number and type of spaces involved—degree to which the space is active as a

working space—degree of blending and of abstraction—vocabulary transfer (on line or permanent)—category relationship between source and

target, and consequently likelihood thatblending will give useful category extension

—number of conceptual domains involved—whether or not the conceptual domain

involved is consciously focused upon—the extent to which the blended space gives

birth to a new conceptual domain.Note that conceptual domains and the

spaces locally built upon them are different innature. In particular, a space can be activatedwithout the corresponding conceptual domainbeing consciously focused upon.

And, as an independent important point, theexistence of a blended space does not entail thatit serves as the basis for an imaginaryconceptual domain. When it does, we havecases like Dante's hell or Alice's wonderlandwith the talking Cheshire cat: an imaginaryworld that gives substance to the blend so thatit can become a common conceptual domain ineveryday life. Other blends, while servingimportant local cognitive functions, will haveno corresponding conceptual domains. This isthe case for examples discussed above such as"Pour down thy weather," "Get ahead ofmyself," and so on, as we will see below.

Let us consider a range of cases that differalong these particular parameters. In thenotation that follows, smaller type meansdiminished role as a working space (S vs. S),or absence of conscious focus for a domain (Dvs. D).

Case 1: [ D1, S, G ] There is only oneovert space S, and one overt domain underconsideration: the source is also the target, andthe projection is identity. For example,

imagine we are talking about hiking andclimbing, and saying things like: Long climbsare tiring. It's great to reach the top aftergetting over all the boulders. This is what oneusually, and no doubt correctly, thinks of asliteral talk. But in spite of the apparent absenceof projection, notice that the conventionalprojections of the space are primed: eventhough the first climber may have spokenliterally, it is straightforward for the second toreply: Yes, it reminds me of {my career,learning flamenco, reading Heidegger, ...}. Astandard generic space G is readily available,potentially active, independently of thespeaker's intent.

Case 2: [ D1, S, G ] The only overtvocabulary is in one domain, but the speaker'sintent is explicitly to build the generic spacealong with the source, by exploitingconventional projections of the source. Lookbefore you leap, on a fortune cookie, is the sortof thing we have in mind here. The source is agood archetype for the generic, and the genericis provided for the purpose of furtherprojection onto unspecified targets. Weunderstand the statement on the fortune cookieas a general purpose instruction, not a literalremark about jumping. The resultingconfiguration has two working spaces, asource and a generic, but no target andtherefore no blend. This is the SPECIFIC toGENERIC projection studied in Lakoff &Turner, and its conceptual dynamics consists inmaking the new space available for furtherprojection.

Case 3: [ D1, D2, S, G, T ] There are twoconceptual domains, and an active target space,plus weakly active source and generic spaces.This is the case where, through entrenchedconventional metaphor, the source vocabularyhas become directly associated with the target.For example, we may talk about Christmasbeing near, without strongly activating thesource of physical space for which near is aprimitive vocabulary item. This is not becausenear has changed meaning, or because the linkbetween time and space has been lost. Rather,it is because the relevant abstract orderingstructure, also found in the mediating genericspace, is conventionally available for time, byvirtue of the already established time-spacemapping. The important point here is thatphysical space is the archetype of the relevantgeneric (mental) space (probably by virtue of

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being its experiential basis), and thereby retainsits leading role, i.e. potential activation,whenever this generic space is projected onto atarget. As soon as less conventionalvocabulary is used, this reactivation becomesapparent (we're a stone's throw fromChristmas ). There is a paradox in this form ofconceptualization: it is precisely because thesource structure is widely shared in thinkingand talking] about the target, that the sourceneed not be a principal working space, and thatwe do not consciously perceive our way oftalking about time to be metaphorical; but if wewere, so to speak, to cut off the target from itssource, treating words like near as merelypolysemous, there would be no account for thereadily available extensions of the source totarget mapping. Having the source and genericmental spaces "in the wings" (potentiallyactive) is the key to this apparent paradox.

Case 4: [ D2, G, T ] In a sense, this thetwin of Case 1: only one space is set up, andonly one domain is talked about, but theattention of the participants is directed implicitlyto relevant generic structure. To say My sonbetrayed me is also to draw attention to themore abstract generic space in which betrayalby loved ones has culturally definedconsequences, and those inferences in thegeneric space are likely to be projected backinto the target space. This configuration opensthe way for introduction of an overt source intothe discourse, as in This is like a dog biting thehand that feeds him. The activation of an overtsource will then explicitly activate the genericspace G, transforming the initial configuration:

[ D2, G, T ] → [ D1, D2, S, G, T ]Case 5: [ G ] Specific domains are not

mentioned explicitly, and only a generic spaceis set up. This can happen only if abstractvocabulary is available to access the genericspace directly, as for instance in making therecommendation Before acting, measure theconsequences of your acts. The activatedgeneric space is the same as with Look beforeyou leap, but it is accessed directly, and there isno source, and no target. This configuration,of course, opens the way for a transformationto a more elaborate one, with explicit source ortarget or both. If we are discussing theadvisability of giving away all your money toyour lover, that context (technically, thecorresponding mental space) becomes a likely

target for projection from G. Or, in the vein ofConfucius and Mao Zedong, we can call up asource for G, as when we add to the genericadmonition, the specific one: ...in other words,look before you leap.

A key point is that vocabulary to access Gdirectly is seldom straightforwardly available.It would seem that we manipulate many moregeneric frames than we have names for. Infact, we make up new ones up as we go along.The extraordinary power of metaphorical andanalogical projection and blending lies in theaccess this complex process gives us to suchframes, both for building generic spaces, andfor projecting them back onto more specificones.

Case 6: [ D, S, G, T ] There is only oneconceptual domain, but distinct source, target,and generic spaces. The credit card exampleabove is a good instance of this configuration.We set up the specific source situation of Jackcharging his expenses to his own mother'sparticular credit card, project to a generic spacein which sons charge expenses to theirmother's card, and project back down to thetarget space in which Francis uses Momma'scard. Notice that we can't get a blend in thistype of case, because the counterpart categoriesin the two spaces are exactly the same. If thedistance between spaces is extended, assuggested in our discussion, blends becomeavailable, e.g. Francis hiking away on ashopping spree through expensive malls. It isonly, therefore, when we distinguish theconceptual domains, that blends are perceivedand operated on. But as noted for the "same-sex marriage" and "artificial life" examples,those very same blends may put pressure oncategory structure that leads to merging of theinitially distinct conceptual domains. Whenthat process succeeds, we are back to the Case6 configuration: a married couple is thecounterpart of another married couple,regardless of sex and gender, notmetaphorically, or by analogy, but as a simpleconsequence of the new category structure, likethe mother-and-son counterpart pairs in thecredit card example. The blend will then havedisappeared into the source and target.

Notice some of the differences between thecases considered so far. In 1, there is notarget, and no implied target, but a weaklyactive conventional generic space opens up theway for one. In 2, there is no target, but the

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need for a subsequent target is stronglyimplied. This target could be relative to adifferent conceptual domain, or the same one(as when Francis pointedly describes toMomma Jack's arrangement with his mother,without adding anything else). In case 3,source and generic are weakly activated, andthere is no blend, but the conceptual domainsare kept sharply distinct—no supercategory ofspace and time is formed. In 6, on the otherhand, the conceptual domains are notdistinguished, but the source and target spacesare both active and distinct.

Let us move on to further combinations.Case 7: [ D1, D2, S, G, T ] The source is

weakly activated, but the generic middle spaceis activated along with the target. For example,in the expression, "He is seeking a higher cupof coffee," there is a generic space of increaseof a quality along a gradient and even ofcategorized regions of that gradient. Thevocabulary comes from the archetype source ofincrease or decrease of height], which is to say,up and down. But that vocabulary has beenexported from the archetype source to the moreabstract realm of the generic. This "bleaching"of vocabulary will happen slowly over time andwill vary from individual to individual, so caseseven, like case three, is a matter of degree. AsEve Sweetser has shown, diachronically thesource may get lost altogether in suchconfigurations, because the correspondingdomain acquires new specialized vocabulary.Its former vocabulary shifts to the bleachedsenses or to specialized uses in specific targets.This historical evolution, however, takesconsiderable time when it happens. At anysynchronic stage, many abstract vocabularysets will remain linked to an active source. Asfor case three, the importance of the potentialactivation of the source should not beunderestimated. The source continues toprovide the strongest archetype for the moreabstract structure, and as a result it alsoprovides the primary basis for novel projection:the search for new conceptual structure, ingeneric or target spaces, will attempt to exploitthe source space. We will say, for example,"This coffee is stratospheric" or "This coffee isabove terrestrial orbit."

It should be clear by now that there is not aset list of cases. How many different patternsof activity over the four spaces can wedistinguish? As many as we have energy to

look for. Cases can be extended as spaces anddomains are added or activated.

Consider the celebrated case of the analogybetween taking a fortress and treating a tumorinside the body.33 Only a laser beam of lowintensity can be sent through healthy tissuewithout harming it, but such a beam will notkill the tumor cells. This is likened to a minedpath leading to the fortress that can be traversedsafely by a small number of soldiers but not alarge number; the small number would beunable to take the fortress. But, just as severalsmall groups of soldiers sent along severalmined paths to arrive simultaneously at thefortress can combine to overwhelm it, soseveral beams of low intensity sent alongseveral paths to arrive simultaneously at thetumor will add to kill the tumor cells. In thisanalogy, there is an active source, generic, andtarget, but an avoidance of the blend. There aretwo conceptual domains in conscious focus: themedical and the military. [ D1, D2, S, G, T ]

In the case of "Pour down thy weather,"there are two domains in conscious focus(nature and communication), a source, a target,and a blend, but the generic space, although ofcourse live, has very little role as a space ofnew conceptual work. Furthermore, eventhough the blend is highly active as a workingspace, it does not generate a correspondingconceptual domain. [ D1, D2, S, G, B, T ].

In the case of Dante's Bertran de Born, thesource, target, and blend are all fully active asworking spaces, the generic is weakly active asa working space, and three conceptual domainsare in conscious focus: the conceptual domainof physical objects and physical separation,which underlies the source, the conceptualdomain of social discord, which underlies thetarget, and, most interestingly, the conceptualdomain of hell: there is a conceptual domaincorresponding to the blend in a way that thereis not in the immediately previous case.Dante's hell becomes a conceptual domain thatcan be relied on not only for the rest of theInferno but may also spill into everyday talk,the way Sherlock Holmes has. [ D1, D2, DB,S, G, B, T]

In the case of "In France, Watergate wouldnot have harmed Nixon," the generic, too, isactive ("Western political system"), so that allfour spaces are fully active, and two conceptualdomains—the United States and France—are in

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conscious focus. [ D1, D2, S, G, B, T ]In the case of "I am getting ahead of

myself," by contrast, the generic is onlyweakly active, while the source, target, andblend are fully active. The conceptual domainof the organization of events is in consciousfocus, and the conceptual domain of movementalong an intended track is not in consciousfocus. [ D1, D2, S, G, B, T ] Activation as aworking space is not two-valued, strong versusweak. There is a gradient of activation betweenstrong and weak. In the case of the moreidiomatic "I'm getting ahead of myself," thesource space may be, compared to "I can'tcatch up with myself," less active, but it stillmust be active to supply conflicting positions tothe blend.

In cases of provisional extendedcategorization, like "He's a real fish" and"same-sex marriage," all four spaces are active;two conceptual domains are in consciousfocus. [ D1, D2, S, G, B, T ]

Now imagine the case in which thecategory of marriage has undergone a shiftunder the pressure of the analogical projectionof "same-sex marriage." Then the originaldistinct conceptual domains (traditionalmarriage and same-sex domestic arrangement)have united into one domain. The blend isfully active as the new category, and thegeneric can therefore subside into weakeractivation. [ D = D1∪D2, G, B ]

In the case of a projection of intentionality,such as "The nail doesn't want to go in," thesource, blend, and target are active, the genericis weakly active, the domain of carpentry is inconscious focus, and the domain of contestwith an intentional adversary is not inconscious focus. [D1,D2,S,G,B,T].

In a case of full personification, theconceptual domain with respect to which thesource is constructed will be in consciousfocus: in Euripides's Alcestis, Thanatos (thegreek word for death) is a wrestler who comesto take the body of Alcestis away to Hades.Here, the conceptual domain of contest with anintentional adversary is so fully focused uponas to be dramatically prominent. In addition,the blend itself has served as the basis for acorresponding conceptual domain. [D1, D2,DB, S, G, B, T]

Many different spaces can become active asthe operations of projection and blending areperformed over them. We began from the view

that two spaces—a source and target—are notenough, and introduced two more—blend andgeneric—for a total of four. But blend andgeneric are poles of a gradient, so in factinstead of four spaces, we may haveindefinitely many. Now we see that even thisarray of spaces—source, target, and a gradientof middle spaces—is not maximal.

It is therefore not possible to give ataxonomy of cases of projection in terms ofarrays of spaces and activations. What isimportant instead is the nature of the operationsof projection and blending, which can operateover however many spaces are active, and doso recursively and multiply.

To give just one example, consider "Thestork dropped George Bush on third base witha silver spoon in his mouth." One projectionhas in its source space arrival and in its targetspace birth. The stork bringing the babybelongs to the blended space of this projection.Another projection has in its source baseballand in its target life. Being born on third basebelongs to the blended space of this projection.Notice that the two blended spaces must beblended to get the inference that the stork'sdropping George Bush on third base meansthat George Bush was born on third base. Yeta third projection has in its source dining and inits target life and especially status in life. Thehierarchy of stations in life is understood interms of the hierarchy of dining scenarios.Having a silver spoon in one's mouth belongsto the blended space of this projection. Allthree of these blended spaces are then blendedinto a hyper-blended space, in which beingborn, the stork, third base, and the silver spoonall reside. Inferences, motivations, andemotions constructed in this hyper-blendedspace can then all then be applied to ourunderstanding and feelings about GeorgeBush, his social status, and his candidacy.

Here is a recapitulation of our examples,which differ along the parameters considered:

[Note on notation. Capital D: the domain isin conscious focus. Capital S, G, B, T: thespace is a working space.]

Case 1: [ D1, S, G ] Long climbs aretiring.

Case 2: [ D1, S, G ] Look before youleap

Case 3: [ D1, D2, S, G, T ] Christmas is

30

nearCase 4: [ D2, G, T ] My son betrayed me.Case 5: [ G ] Before acting, think of the

consequences.Case 6: [ D, S, G, T ] Momma and the

credit card [same-domain analogy]Case 7: [ D1, D2, S, G, T ] I am seeking a

higher cup of coffee.Case 8: [ D1, D2, S, G, B, T ] I'm getting

ahead of myself.Case 9: [ D1, D2, S, G, T ] Explicit

analogy: fortress/tumorCase 10: [ D1, D2, S, G, B, T ] Pour

down thy weatherCase 11: [ D1, D2, DB , S, G , B, T ]

Dante (a conceptual domain corresponding tothe blend is created)

Case 12: [ D1, D2, S, G, B, T ] Nixon inFrance

Case 13: [ D1, D2, S, G, B, T ] Realfish. Same-sex marriage.

Case 14: [ D = D1∪D2, G, B ] Marriageafter category shift (G fades).

Case 15:34 [D1, D'1, S, S', BS, G, B, T]Dracula [Two source spaces are blended into BS(vampire-repertory actors, etc.). This blend in turnserves as a source that may blend again with the targetspace to yield B (a middle space withactor/vampire/health professionals).

Case 16: [ D1, D2, S, G, B, T ] The naildoesn't want to go in [compare to Dante,personification]

Case 17: [D1, D2, D3, D4, S1, S2, S3, G1,G2, G3, B1, B2, B3, HB (B1, B2, B3), T] Thestork dropped George Bush on third base witha silver spoon in his mouth.

Any number of spaces can be made active,and any number of projections and blendings(including higher-order projections andblendings) may operate over them. The fourspaces are important as kinds of spaces aprototypical conceptual projection requires.The operations that occur across these fourspaces can, however, occur across fewer ormore, and they can occur multiply. We willreturn to this complex issue at the close of thepaper, "The Concept of a Concept."

VIII. Blending and Grammar

In cognitive linguistics, as represented byLangacker's Cognitive Grammar, Talmy's

conceptually-based grammar, and Fillmore'sConstruction Grammar, syntactic constructionsare representations of generic spaces of veryhigh order. For example, the caused motionconstruction studied by Goldberg (1994)

NP V NP P NPas in They hit the ball out of the park, or Theylaughed the poor guy out of the room, is arepresentation of a minimal generic space withroles a, t, and g, and the schematic structure(icm):

a CAUSE t MOVE gwhere the capital letter notation is used forconvenience to refer to the appropriate schema,perhaps better described ultimately in a diagramnotation like Langacker's which allowsimportant figure/ground and profilinginformation to be represented.

As in any mental space, what we find hereis partial structure with elements (roles) andrelations between them. When syntacticconstructions are filled in lexically, morespecific spaces are built. Since lexical items arethemselves grammatical constructions, we havewhat Goldberg (1994) calls a fusion ofgrammatical constructions. This fusion is infact a blend of the higher-order generic spacesset up by the grammar.

One of Goldberg's many examples, Isneezed the napkin off the table, will showhow this works. As Goldberg explains, itresults from the fusion of the caused motionconstruction just mentioned and theconstruction characterized by an English lexicalitem, the verb sneeze. The first construction(caused motion) has three roles, roughlyAGENT, THEME, GOAL, the second has onlyone role (the sneezer). The corresponding fourspace configuration that blends them is thefollowing:

The blended space, as in the general case,inherits structure from both input spaces: a issneezing, and a is causing the napkin t to moveto g (off the table).

But crucially, there is more structure to theblended space than to the inputs. First, the twoprocesses are incorporated into a singlecoherent process, where it is the sneezing thatcauses the napkin's motion. Second, not justany such process will do: a prototype isimposed on this understanding—it is the airdisplaced by the sneezing that moves thenapkin.

So, for example, the sentence cannot be

31

used to describe a situation where by sneezing,I cause someone to pass me the napkin, thusmoving it off the table, or a case where

sneezing makes me fall on the table and on thenapkin, which in turn falls off the table.

a'

a

gt a

a t g

1

11

2

a' ACT

a CAUSE t MOVE g a SNEEZE1 1 1 2

Blended Space

Figure 5

The same is true of a grammatically similarexample like They laughed the guy out of theroom. The highly preferred interpretation ofthe elaborated blend, is that "the guy" leftbecause they were laughing at him, not becausethe laughing was too loud, or because he wasoverwhelmed with joy by the great response tohis best jokes.

Goldberg (1994) notes the existence ofgeneral constraints on conflation patterns andcites relevant work by Croft (1991) and

Matsumoto (1991).What is striking in the context of the

present report is the technical uniformity ofblending in all cases, whether they are highlygrammaticized as in the examples justreviewed, or locally constructed, as in most ofour other examples. The formal treatment ofthe boat race example proposed in section III isdirectly applicable to Goldberg's fusion ofgrammatical constructions. This is no accident:grammar as we view it has among its functions

32

to enable us to combine very general framesand image schemas to produce more and morespecific ones until we zero in on the mentalspace partial structure that fits the context athand. And blending is a creative component ofthis general process. It is remarkable that in allcases, blending allows the whole to be morethan the parts. The fusion of grammaticalconstructions is yet another example of thegeneral properties of blending outlined insection III (Prototypes of blending andmistaken reductions): projection of partialstructures and embedding into backgroundframes generates novel structure notcompositionally derivable from the inputs; thefull interpretation of any sentence in a particularcontext is a sequence of successive blendsmeeting more and more specific localconstraints. Grammar makes generic frames,lexical frames, and their blends available inorder to guide and constrain this process. Thepartial structures ultimately obtained, however,are at a greater level of specificity.

Without proposing to assimilate to ouranalysis theoretical work by Langacker and byFillmore and Kay, we see in their work explicitconceptions that fit in with our view ofgrammatical blending, as well as some supportin the form of compatible specific analyses ofspecific grammatical constructions.

There is no question that Langacker'sCognitive Grammar and Fillmore and Kay'sConstruction Grammar view the combining,unification, or blending of grammaticalconstructions as an essential, perhaps theessential, mechanism of grammar. Langackerwrites, "Grammar, I claim, is nothing morethan patterns for successively combiningsymbolic expressions to form expressions ofprogressively greater complexity. Thesepatterns take the form of constructionalschemas, some of which incorporate others ascomponents."35 Fillmore and Kay provide anelaborate technical model of the nature of suchunification of constructions.

Cognitive Grammar treats, under the name"accommodation," ways in which negotiationhappens over the structures of the input spacesto arrive at appropriate structure for the blend:"It must be emphasized that syntagmaticcombination involves more than the simpleaddition of components. A composite structureis an integrated system formed by coordinating

its components in a specific, often elaboratemanner. In fact it often has properties that gobeyond what one might expect from itscomponents alone. . . . For example, themeaning of run as applied to humans must beadjusted in certain respects when extended tofour-legged animals."36 37

The metaphor of "projection" in describingthe general cognitive phenomenon of blendinghas been used by Fillmore and Kay tocharacterize the unification of constructions.They speak of the semantics of the sentence asarising by a chain of projections from thelexical verb to the Verb Phrase to the sentence.More technically, in our terms, the particularlexical verb construction and the higher-orderVerb Phrase Construction, as input spaces,project to a blended space which is not identicalto either; this space and the Subject-PredicateConstruction, as inputs, project to yet another,hyper-blended space, the full construction,which is identical to none of its inputs; andthere is projection of semantics from the spaceof the lexical verb to the first blend, and fromthere to the hyper-blend.

We know, of course, that grammar alsogives precise indications as to the dynamicspace building and space linking that occurs asdiscourse unfolds: tenses, moods, copulas andsome verbs , adverbials and conjunctions, aresome of the devices that serve this purpose.38

This suggests a global view of language asguiding the space construction process throughspace building, space blending, and projectionof generic spaces. The XYZ metaphorsanalyzed in Turner (1991) give a powerfulillustration of this type of process. Thesyntactic construction is deceptively simple:

NP be NP of NPX Y Z

as in Vanity is the quicksand of reason . Thissimple construction has a complexsemantic/pragmatic interpretation: construct ametaphorical mapping such that X in the targetis the counterpart of Y in the source, and Z inthe target is the counterpart of a fourth elementW in the source, and use this construction toproject appropriate inferences into the target.In the example, W is the traveller, who shouldreach a goal; as quicksand destroys thetraveller, vanity destroys reason. The

33

grammatical information is minimal and highlyabstract: find a mapping and a missing element;the rest is left to the cognitive competence ofthe user. Notice that an implicit generic spacemust also be constructed. And interestingly,syntactic concatenation can activate a blendedspace, as in Turner's example Language isfossil poetry. With language as X, and poetryas Z, the modifier fossil identifies Y, a sourcecounterpart for language , and a missing W('living organism') completes the mapping.But this time a blended notion of somethingwhich is simultaneously language, poetry andfossil has been constructed: in the blendedspace, poetry IS a living organism that canevolve into a fossil (language). As in our otherexamples, this is achieved through a localcategory extension in the blended space, wheremore things count as organisms and fossilsthan in the source. Rather strikingly, then, theapparently innocuous syntactic construction'NP be N NP' exhibits all the features ofmeaning construction we have been talkingabout: it triggers a multi-space configuration,with source, target, generic, and blend, and itleads to the introduction of elements andstructures (the living organism and itsevolution) for which no explicit vocabularyappears.

IX. The concept of a concept

Conceptual projection involves the dynamicconstruction of source, target, generic, andblended spaces, multiply linked. In thisscheme, inferences and meaning are notbounded in a single conceptual locus. Meaningconstructed by conceptual projection is not amental object but rather a complex operation ofbinding, linking, blending, and integration overmultiple spaces. This meaning never "settlesdown" into one residence.

This view runs counter to everydaynotions. We customarily think of concepts aslittle packets of meaning whose boundariescircumscribe our knowledge of them. Theyseem to ask for labels: marriage, birth, death,force, electricity, time, tomorrow. When weview concepts in this way, meaning werecognize as distributed looks secondary,marginal, or parasitic. A blended space mustlook like an exotic mental event, put together inexceptional ways.

The variety and the diversity of ourexamples suggest, on the contrary, that thedynamism, distribution, projection, andintegration we see in blending are central andpervasive. But how central are they? We willsuggest that they are standard for even the mostbasic thinking.

As we have seen in the analogy between thetumor and the fortress, the provisionalcategorization in "real fish," the attempt toextend a category with "same-sex marriage"and "artificial life," and so on,conceptualizations are not static and notpermanent. Different projections, categoryassignments, and space configurations areactivated locally in given situations. Theability to project is a central component of theability to conceive.

Consider something that we think of as abasic everyday concept, like house. It seems tous static and permanent, stable and unitary,cohesive and self-contained. It is oursuggestion that there are no such concepts, thatthis folk notion of concept, which enjoysconsiderable influence, should be dispensedwith. We have no concept house, but we dohave a word, "house," and being able to usethat word—like the words "fish," "marriage,""life"—requires the ability to construct, link,and activate the appropriate spaceconfigurations, frames, and cognitive models.We may not perceive this activation for a wordlike "house," exactly because the array andlinks activated for "house" are so often thesame, again and again. But a great range ofspaces is activated over and over again forhouse: shelter from the elements, boundedinteriors, security from intruders, financialinvestment, artifacts, aesthetic design,instrumentality for inhabitants, socialresidence, partitioning of activities intodifferent physical spaces, rental property, andon and on indefinitely. Any single use of theword "house" for any particular purpose willinvolve construction of meaning as anoperation of selective integration over thesevarious distributed spaces.

But what does it mean to say that a greatrange of spaces can be activated? Let usconsider an example: "Italian is the daughter ofLatin." The source space contains very littleovertly; it has a parent and a daughter. Thetarget space also contains very little overtly; ithas Italian and Latin. Ultimately, the projection

34

will connect parent in the source to Latin in thetarget, and daughter in the source to Italian inthe target. The result is a doublepersonification. But this hardly accounts forthe meaning we construct on hearing thisphrase. One normal interpretation might beparaphrased: "Latin existed first, and Italiancame into existence second by deriving causallyfrom Latin." It may seem as if the materialneeded for constructing this meaning isintrinsically in the source space of parent-childand the target space of Latin-Italian. But itisn't. It must be imported to the source and thetarget. It can be imported by activating otherspaces and projecting those spaces to theskeletal source and target. Onto the skeletaltarget, we may project a space concerninglanguages, according to which some languagesderive from others, and in particular, Italianderives diachronically from Latin; and onto theskeletal source of parent and child, we mayproject a particular space concerningprogeneration, according to which a parentbears a causal and sequential relation to thechild: the parent produces the child; the parentprecedes the child in the sequence.

If the source and the target are elaborated inthis way, they come to share a causal andsequential structure. This causal andsequential structure will then be available toconstitute the generic middle space thatunderlies the interpretation "Latin precedes andresults in Italian."

But now consider the following fact:suppose the subject of our conversation is theprogram of studying foreign languages in aparticular high school, and we are making thepoint that nearly all the students of Latin takethe subject up because they first got interestedin it when they were taking the Italian courses.We might say, "Italian is the mother of Latin."

Does this contradict the earlier statement that"Italian is the daughter of Latin"? Clearly not.In this case, the target has been elaborated in adifferent way: what has been projected onto thetarget is the sequential order in whichlanguages are learned. In the space of learninglanguages, the sequential order of Latin andItalian is the reverse of their sequential order inthe space of the history of languages. Underprojection from the space of learninglanguages, Italian is the mother of Latin, whileunder the projection from the space of thehistory of languages, Italian is the daughter ofLatin. In general, there is no fixed structure ofthe target space that the source has to match,because the target space has different structureunder different projections.

What about the source? Suppose we arediscussing the relative aesthetic qualities ofItalian and Latin. Suppose we are remarkingthe precision of Latin in Vergil or Propertius orHorace and comparing it to what seem floridand ostentatious qualities of Italian inBoccaccio or Tasso. Our companion remarks,"Well, Italian is the daughter of Latin, and herostentatious beauty is really a rebellion againsther mother's austerity." Here, the projection tothe source of mother and daughter concerns notprogeneration but rather social relationsbetween mothers and daughters, for example,adolescent rebellion over appearance andbehavior. Under this projection to the source,Italian is still the daughter of Latin, but in anentirely different sense.

In all these examples, the conceptualdomains—kinship and languages—are thesame, but the spaces selected for projection tosource and target are different. The resultingconfigurations—source space, middle spaces,target space—are different in each case.

35

Notes

1Mark Turner gratefully acknowledgesthe support of the John Simon GuggenheimMemorial Foundation and the assistance ofthe department of linguistics, the departmentof cognitive science, and the Center forResearch in Language at UCSD. We aregrateful for comments from Adele Goldberg,Todd Oakley, Seana Coulson, and NiliMandelblit.

2 We return throughout the paper, andespecially in sections IV and V, to theimportant difference between generalconceptual domains and particular mentalspaces set up on the basis of such domains,and used for analogical, metaphorical, andother conceptual projection purposes.

3 Arthur Koestler, The Act of Creation(NY: Macmillan, 1964); see "Concretizationand Symbolization," pages 182-184.

4 Ziva Kunda, Dale T. Miller, and TheresaClare, "Combining social concepts: The role ofcausal reasoning," Cognitive Science 14: 551-577 (1990).

5 See the analyses in sections II.9, V, andVIII below.

6 Inferno, canto 28, lines 139-142.7 In studies of analogy, this process is

often called schema induction. (See Gick andHolyoak (1983)). See also Langacker (1991)on the induction of abstract schemas in suchmappings. In Sec. III, we show that suchschemas build up higher level "generic" middlespaces.

8 A complete analysis of the Bertran deBorn example is more complex than indicatedin the text, because it additionally involves ametonymy between sinner and sin. In theblend, the source counterparts of sin and sinner(the broken object and the object breaker) areprojected onto the same counterpart: the manwith the detached head). So, in fact we have ablend not just of the metaphorical source andtarget, but also of the metonymic trigger andtarget.

9 I.e. it can't have a true projection in aworld without ghost-ships.

10 It is therefore not the case that blendsare constructed in general for the sake ofproducing something exotic, contradictory, or

bizarre. This is easy to see for counterfactuals(which, as we shall see, are also blends): onemay construct a counterfactual, for the purposeof showing an impossibility, as in reductio adabsurdum proofs in mathematics, or one mayconstruct a counterfactual to export other kindsof inferences. For instance, in the boat racecontext, one could say: If the two ships hadbeen racing, Great America would now be 4.5days ahead of Northern Light. As before, thepragmatic impossibility of the boats' travelingtogether is now irrelevant. The exportedinference is directed at the speed of the boats,and the likelihood of breaking the record.

It should also be added that the fact that afeature of the blend is not used for inferencetransfer does not mean it couldn't be used.One can imagine using ironically the expressionYou're 4.5 days ahead of the ghost of NorthernLight to criticize sailors who try to breakrecords established by completely differentvessels—a high-tech racing catamaran versus ahuge wooden clipper ship fully laden. For thatunderstanding, the pragmatic clash in the blendwould be relevant.

11 A fantastic blended conceptual domaindoes not necessarily produce pragmatic clashesthat would be transferred inferentially to thetarget or the source. Cf. also the Buddhistmonk example below.

12 Because of some underspecification ofthe blending, the example has anotherinteresting feature. The preferred readingseems to be that 4.5 days is the differencebetween the time N it took Great America II toreach its current position (point A), and thetime N+4.5 it took Northern Light back in1853 to reach point A. Under thatinterpretation, the boats' positions in the initialspaces (1853, 1993), and in the blend, are theirpositions (point A for GA, and point B for NL)after N days, which is the time on the clock inthe 1993 space at the time of writing. But then,the 4.5 days are a time in the 1853 space—thetime it took NL to get from B to A. Anotherconceivable reading has this reversed, takingthe time on the clock in the 1853 space and the4.5 days in the current 1993 space. Under thatinterpretation, Northern Light got to point B'after N days, Great America II got to point Aafter N days, and it took Great America II 4.5days to get from B' to A.

36

Other readings may be available. SupposeGreat America II is following a different coursefrom its illustrious predecessor's, so thatpositions on the two journeys cannot bedirectly compared. But suppose also, thatexperts can estimate, given current positions,how long it "should" take Great America II toreach Boston. Then, the example sentencecould be interpreted as saying that given itscurrent position, Great America II should endup making the run to Boston in 76 days, 8hours minus 4.5 days, i.e. in 71 days, 20hours. This time, in the blended space of 1853and the experts' hypothetical 1993 space, GreatAmerica II reaches Boston 4.5 days ahead ofNorthern Light.

All these readings involve blended spaces.The blended space is different in each case, andits structure accounts for the correspondingdifference of truth values in the interpretations.This is a nice point: far from being fuzzy andfantastic, the blends allow a totally precisequantified evaluation of the truth conditionsthey impose on the actual world.

13 A version of this riddle appears in ArthurKoestler, The Act of Creation (NY:Macmillan, 1964) pages 183-189; Koestlerattributes the invention of the riddle to CarlDunker.

14 E.g. Answering machines that say "I'mnot here."

15 There are other idioms in whichunnatural division of a person signifies error.In English, we would indicate that we haveneglected to pay attention to the sequence ofevents by saying that we "lost track of time,"but in French, we would say that we have"forgotten ourselves," as in "Elles s'oublièrentà causer" ("They forgot themselves whilechatting.") This phrase does not mean that theystopped paying attention to themselves, butrather that in paying attention to the actualsequence of events, they forgot about thescheduled sequence of events. In the blendedspace, there is a split. One half of the split istheir imaginary "double," who dutifullyperforms the scheduled events in the scheduledorder. It is this imaginary "double" that theyhave forgotten while paying attention to theiractual selves.

It is not only imagined scheduling that isnormative. Imagined etiquette is alsonormative. Just as, in a blended space, a non-

actual imaginary double can perform properlyaccording to schedule, so a non-actualimaginary double can perform properlyaccording to etiquette. We can say in English,"I forgot myself utterly and said somethingpositively beastly to John." The idiom isidentical in French: "Il s'oublia jusqu'à lafrapper."

16 Moser and Hofstadter (ms.) bring upinteresting examples of contamination in action,and capture errors (Norman 1988), whichblend frames in an apparently incongruousway. Although incongruity is one feature thathighlights a blend and makes us consciouslyaware of it, as in the Inferno example, ourevidence suggests it's only an incidentalfeature, not a necessary or defining one.

17 Blends are thus to be distinguished from'blurs', where frames are simultaneouslyevoked and superimposed. Moser andHofstadter provide nice examples of both, butdo not make a sharp distinction. They cite thecase, for example, of a recently engagedmiddle-aged man talking about his new house:

"I used to think there was a perfect house, but afterlooking around for a long time, I've come to realizethat no house is perfect, and I'm willing to settle forthis one."

His friends understand that he is 'talking'(thinking?) about selection of mates as much ashe is about choosing houses. This analogicallyconnected double frame does not build up ablended space, however.

1 8 See Fauconnier and Turner (inpreparation).

19 Also called absolute values.20 See Kline (1980).21 Of course, this source domain has a

conceptual history of its own. We argueelsewhere that in fact it is itself the product of anon-trivial conceptual blend.

22 For example, if (ρ,θ) = a +bi and

(ρ',θ') = a' + b'i , then

(ρ,θ) × (ρ ', θ ') = (ρρ ', θ+θ ') =

(a+bi) × (a'+b'i) = aa'-bb' + (a'b+ab')i23 The generic space is not consciously

conceptualized as an abstract domain when thefull-blown concept of complex number getsformed. It becomes a conceptual domain in its

37

own right when mathematicians later study itand name it.

2 4 Douglas Hofstadter (personalcommunication) reports his discovery of howto "make" new geometries by blending.Taking projective geometry as a generic, andEuclidean as a source, he obtained a dualtarget for the latter, and a new "contrajective"geometry as a blend of the Euclidean and theEuclidual.

25 In giving the response "four" to thequestion "If the tail was called a leg, how manylegs would this cat have?"

26 Wonderful examples of cartoonblends (in particular in Gary Larson andW.B. Park) have been studied insightfully byD. Hofstadter and his collaborators. SeeHofstadter et al., 1989.

27 This was a description of George Bush,incumbent president and presidential candidatein 1992, provided in a speech by rivalcandidate Tom Harkin.

28 Smead Jolley making three errors on asingle play, or Jimmy St. Vrain running thebases in the wrong direction.

29 Thanks to Brian Ladner for pointing outthis new joke built on the first.

30 Remarkably, in this example, theadditional structure is also detectable in theprototype schema of the generic space: it isprototypically good to advance, and not toadvance reflects unfavorably on the agent. It'salmost an accident that this prototypical featuredoes not project directly to the source andtarget: an accident due to the rules of baseballfor the source (runners are not masters of theirdestiny); an accident due to Bush's eminentposition in the target: he has already reached thetop, and so can hardly be blamed directly fornot advancing.

31 See John Markoff, "Beyond ArtificialIntelligence, a Search for Artificial Life," NewYork Times, 25 February 1990, "Week inReview" section, page 5.

32 See Fauconnier (to appear).33 M. L. Gick and K. J. Holyoak (1983)

"Schema induction and analogical transfer,"Cognitive Psychology, 15, 1-38; DedreGentner, "Structure mapping: A theoreticalframework" Cognitive Science, volume 7(1983), pages 155-170 ; Dedre Gentner, "Themechanisms of analogical learning" in S.

Vosniadou and A. Ortony, editors, Similarityand analogical reasoning (New York:Cambridge University Press, 1989); FeliceOrlich and Jean Mandler, "Analogical Transfer:The Roles of Schema Abstraction andAwareness," UCSD manuscript.

3 4 See Fauconnier and Turner (inpreparation).

35 Ronald W. Langacker, "An Overview ofCognitive Grammar," Topics in CognitiveLinguistics , ed Brygida Rudzka-Ostyn(Amsterdam and Philadelphia: John BenjaminsPublishing Company, 1988), pages 1-48.Published as volume 50 of the series CurrentIssues in Linguistic Theory.

36 Ronald W. Langacker, Foundations ofCognitive Grammar volume 1: TheoreticalPrerequisites (Stanford: Stanford UniversityPress, 1987), pages 75-76.

3 7 For syntactic example of suchaccommodation, we point to any of theanalyses in Construction Grammar, even ofsomething as simple as "the mud." The basicidea of the syntactic attribute maximality isthat a maximal constituent can play a "majorrole" in a sentence, such as subject or directobject. The lexical construction for mud hassyntax in which the value of max i sunspecified; the right daughter of theDetermination Construction has syntax inwhich the value of max is negative; theDetermination Construction itself has(external) syntax in which the value of maxis positive. Just as in the example ofblending the lexical verb construction sneezewith the more abstract caused-motionconstruction, the blend of mud with theDetermination Construction draws itsstructure from different input constructions.In blending mud with the right daughter ofthe Determination Construction, thesemantics (boundedness, configuration,number) comes from mud , some of thesyntax comes equally from mud and the rightdaughter (improper noun), but the value ofthe syntactic attribute max comes from theright daughter. And this blend of mud withthe right daughter in turn blends with thelarger Determination Construction to producean external syntax for the final constructionwhose value for max is positive—that is, nottaken from mud, from the right daughter, orfrom the blend of mud and the right daughter.

38

In general, "unification" of grammaticalconstructions in Construction Grammarrequires negotiation between the inputconstructions as to the structure of the blend.

38 Fujii 1992, Sweetser (to appear),Mejias-Bikandi 1993, Cutrer (1994).

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