figure 8.5. Generic statement.

several actual occurrences. How it is conceived as deriving from actuality is part of the semantic value of such sentences.

Virtual structures derive from actuality in a variety of ways, so there are numerous kinds of virtual planes. The type plane in 8.3 and the generalization plane in Figure 8.4 both represent generalizations, but generalizations of different sorts. Yet another kind of generalization leads to generic expressions. There are of course numerous kinds of generic statements (Langacker, 1997b), including some employing universal quantifiers (considered later). All involve fictivity, but I will only mention the kind that uses singular nouns, e.g., (13):

(13) A cat plays with a mouse it has caught.

A singular generic is quite analogous to the fictive statement in (i2)(b), except that the generalization expressed by the directly coded virtual event is a global generalization, pertaining to what is conceived as the world's stable structure (cf. Goldsmith & Woisetschlaeger, 1982), whereas (i2)(b) is a local generalization capturing what is common to just a few occurrences, not construed as being characteristic of the world's inherent nature. I thus describe the virtual event - involving a virtual cat and a virtual mouse - as inhabiting the structural plane, as seen in Figure 8.5. The gener-icity is not specifically coded, but inheres in the nature of the conceived relationship between actuality and the plane in which the profiled event is found. Owing to the different nature of the abstraction, vis-a-vis the one in Figure 8.4, here the number of actual instances corresponding to the virtual event is indeterminate.5 The virtual event projects to actuality in an open-ended way, with the possibility of instantiation at any time and any place, pending the availability of a cat and a mouse. Actuality is being

5 Five instances are shown, but merely for diagrammatic purposes.

figure 8.6. Fictive change.

described - the statement pertains to the world's actual nature - but no actual event is directly mentioned.

Various sorts of virtuality fall under the rubric of fictive change (Matsumoto, 1996a; Sweetser, 1997). One kind of fictive change is exemplified by (14):

(14) The general's limousine keeps getting longer.

On the relevant interpretation, no actual limousine changes in length. There is only the fiction of change, hinging on the distinction made by Fauconnier between roles and values of those roles. The general's limousine is a role description: it describes a role filled by different particular vehicles at different times, each then being a value of that role. Like a type, a role per se is a fictive entity.6 You may be able to drive a Rolls, but you cannot drive a role, which is not an actual, individual object. Reference to a role is only one of three levels of virtuality that figure in this example. A second level is the general type (e.g., limousine) that the role instantiates. Beyond this, we view a number of distinct values instantiating the role - a number of different actual limousines - as if they were all the same entity. This yields the conception of a single, albeit virtual object whose length at different times can be compared. Such comparison with respect to a single entity is required for a coherent conception of change. The resulting change, profiled in Figure 8.6, constitutes a third level of virtuality.

6 They are different in that a role is itself a virtual instance of some type, in this case the limousine type. Note that the role description is a full noun phrase and incorporates grounding.

A special case of fictive change is fictive motion (Langacker, 1986; Matsumoto, 1996a; Talmy, 1996). Of the various kinds of fictive motion, I will only consider examples like (i^)(b)-(c). Paths are usually immobile -they do not actually move, as suggested by a verb like rise or an adverb like quickly. Yet we describe them with dynamic language that normally pertains to actual motion. We need to distinguish and characterize three distinct uses. In (i^)(a) the motion is actual. Virtual motion can either be perfective, as in (i^)(b), or imperfective, as in (i5)(c).

(15)(a) The balloon rose quickly. [actual motion]

(b) The path is rising quickly as we climb. [perfective virtual motion]

(c) The path rises quickly near the top. [imperfective virtual motion]

Being perfective, the verb rise in (i^)(b) indicates a change through time. It is shown to be perfective by occurrence in the progressive, which in English only occurs on verbs construed perfectively (Langacker, 1987b). But if the subjects of these verbs are static entities and do not move, where is the change?

Such uses do involve motion on the part of the subject, but the motion is virtual rather than actual. Though imagined, the motion has an experiential basis, reflecting what a person experiences while moving along the expanse of the path. In (i^)(b), the movers and the motion are mentioned explicitly in the adverbial clause. This type of sentence is infelicitous when, as in (16), the object in question is too small to imagine someone traveling along it. Of course, as noted by Elena Dapremont, it becomes acceptable in a special context where we can indeed imagine this, e.g., for a party of hikers climbing Mt. Rushmore.7

(16) *His forehead is rising less steeply near the hairline.

As shown in Figure 8.7(a), I analyze these perfective cases of fictive motion in terms of a viewer (V) who moves along the path-like entity coded by the subject. Through time (t), the moving viewer occupies different positions along this spatial path. The area around the viewer at a given moment - perhaps to be identified with the immediate field of view -is given as a rectangle. What counts as the path (or the forehead, etc.) for purposes of these expressions is that portion of the overall entity which falls within that area, hence in actuality it differs referentially from moment to moment. As in Figure 8.6, these distinct entities are fictively construed as if they were a single entity. Construed in this fashion, the path (identified as the portion of the path we see right now) is experienced as itself moving through space, hence rising. Such instances of fictive motion on the part

7 Mt. Rushmore is a mountain in South Dakota on which are carved giant heads of four American presidents.

figure 8.7. Fictive motion.

of a fictive mover are generated by the viewing experience of someone actually moving along the extended object.8

The key to this kind of fictive motion is a local view generated by moving along an extended object, such that only a portion of that object is subtended by the field of view at any one instant. Closely related are fictive motion expressions like (i5)(c), which take a global view of the object in question. These expressions are imperfective, i.e., the situation they profile is construed as stable and temporally unbounded. In English, occurrence in the simple present tense is diagnostic of imperfectivity. These imperfectives are generalized statements, describing the global configuration observable at any time by any viewer. They do not in any salient way evoke a viewer moving along the path or depend on such a viewer to generate the change suggested by the motion verb. Instead, this sense of change resides in the conceptualizer's mental scanning through the global scene in building up to its full conceptualization, as sketched in Figure 8.7(b). The time involved

8 We can further describe such cases in terms of whole-for-part metonymy, in regard to the subject, and conceptual blending whose constitutive elements are the conception of actual motion and of a static scene. These characterizations are all consistent with one another.

is thus processing time (T), i.e., time as the medium of conception, rather than conceived time (t), where time functions as an object of conception. By mentally scanning along its expanse, in building up to its full conception, the conceptualizer experiences the path as "growing" in a particular direction. The full configuration thus arrived at is portrayed as being stable through time, and since this is the profiled relationship, the resulting sentences are imperfective.

This is the kind of scanning previously illustrated in (8)-(9) and Figure 8.2. Nothing actually moves, neither the subject nor any viewer. What motivates the use of a motion verb is a subjective counterpart of actual motion, namely mental scanning along a spatial path in the course of building up the full conception of a global configuration (Langacker, 1990, 1999e). A sense of motion remains, as reflected in the motion verb as well as directional phrases (e.g., from his ankle to his knee), however it becomes less salient as one goes from actual motion, to perfective virtual motion, to imperfective virtual motion. The use of motion verbs despite such attenuation is a linguistic manifestation of embodiment. The bodily experience is that of moving around in space, and observing other objects doing so. Linguistic elements whose prototypical values are grounded in such experience are extended to other situations where we are able to discern a virtual and/or subjective analog of the actual entities they designate.

fictive scanning

Once we have made the transition from actual motion to mental scanning through processing time, we are no longer limited to the spatial domain. Indeed, I have already smuggled in an example. Consider a portion of the previous paragraph, viewing it as a linguistic expression: as one goes from actual motion, to perfective virtual motion, to imperfective virtual motion. This expression itself is a case of imperfective virtual motion. Probably it caused you no problem, since we resort to such scanning all the time - it is a perfectly normal feature of everyday language use. Here are a few more examples:

(i7)(a) From one restaurant to the next, prices vary greatly.

(b) Through the centuries, we have had many great leaders.

(c) As body size increases, the average gestation period gets longer.

(d) Reliability improves with the more expensive models.

(e) When you think of our options, each one seems worse than the last.

(f) From the brightest student in the class to the dumbest, they all work very hard.

These sentences describe static overall situations in dynamic terms. While they do not use motion verbs, they certainly do induce us to mentally scan in a certain order through a range of alternatives. This scanning is prompted in various ways: by prepositional phrases specifying source (from X), path (through Y), and goal (to Z); by expressions of fictive change (improves, increases); by comparatives (gets longer, worse than the last); and so on. While I am not prepared to offer a detailed description of such expressions, I believe a correct characterization of their conceptual import has to incorporate abstract mental scanning as a basic organizing feature.

Observe, moreover, that even this mental scanning exhibits a kind of Activity. For instance, apprehending (i7)(f) invokes the idea of mentally accessing the students in the class in the order of their ranking for intelligence, but obviously we do not actually do so - we can understand the sentence without knowing the individual students or even how many there might be. Similarly, while (i7)(c) invokes the notion of sequentially examining species in accordance with their body size, in actuality we need not direct our attention to any particular species. Instead, we simply imagine the requisite kind of scanning experience. We conjure up a small-scale model of the sequenced alternatives, limited in number and represented only schematically, and simulate the scanning experience by mentally running through these fictive entities. That is, I believe we employ mental models, in the sense of Johnson-Laird (1983), as well as mental simulation, in the sense of Barsalou (1999).

These mental gymnastics are really quite pedestrian. They are not unlike what we do, for example, in handling large numbers that we cannot really grasp directly. Suppose I tell you that three million people visited the San Diego Zoo last year. You are likely to apprehend this statement by conjuring up the image of people going through the turnstiles, but the number of individuals you mentally observe in this fashion will be far less than three million - you will imagine just a few people, characterized only schematically, and take them as representative of a larger whole.

The scanning invoked in (i7)(f) is sketched in Figure 8.8. The dashed arrow indicates sequence of mental access. Arranging the students in order of descending intelligence, and scanning through them in this sequence,

figure 8.8. Fictive scanning.

is something that happens only Actively, hence it is shown as taking place in the virtual plane. The students evoked correspond to actual students, but precisely how they map onto actual students is unspecified - even if we know who the actual students are, we do not necessarily know which ones are the brightest, the dumbest, etc. Hence the dotted correspondence lines merely indicate that the students scanned correspond to students in the actual plane, without indicating which particular individuals they correspond to. The situation evoked pertains to actuality, and is abstracted from actuality, but the explicit conceptual content is mostly virtual.

The claim, then, is that many fairly mundane expressions, like those in (17), incorporate fictive mental scanning as a central facet of their conceptual semantic value. This imagined scanning through a virtual range of alternatives combines fictivity with dynamicity, often as a means of apprehending an actual situation that would not be easy to grasp or describe directly. Evidence that we do in fact resort to fictive scanning - that it is not just a figment of my own imagination - comes from otherwise peculiar uses of certain temporal adverbs, notably still and already (cf. Michaelis, 1991,1993,1996):

(18)(a) You won't get very far with a contribution of $10,000, or even $25,000. And $50,000 is still not enough for a private interview with the president.

(b) Forget about calculus - elementary algebra is already too difficult for him.

Prototypically, still indicates that some activity continues past a potential stopping point, and already, that something happens earlier than expected:

(19) Jack is still writing his dissertation, but Jill has already finished hers.

In (18), however, nothing is happening. There is no actual activity or event to characterize in terms of its temporal distribution. I suggest that still and already are nonetheless employed in (18) with something approximating their usual values. What is special about them is simply that the activity in question is not the situation explicitly described by the clause ($50,000 not being enough for an interview; elementary algebra being too difficult), but rather an otherwise covert process of fictive mental scanning. In (i8)(a), there is scanning along a scale representing the possible size of political contributions. Still indicates that, when scanning reaches the $50,000 mark, one has not yet arrived at the amount necessary for a presidential interview. In (i8)(b), mental scanning proceeds through a range of mathematical subjects, ordered in terms of increasing difficulty. Here the scanning is more obviously fictive, since we are unlikely to actually think of particular subjects other than the two explicitly mentioned. In i8o (a)

figure 8.9. Fictivity with temporal expressions.

any case, already specifies that, in scanning along this scale, one encounters a subject that is too difficult sooner than might be anticipated.

Such uses of still and already are overt symptoms of the type of scanning proposed, or perhaps they themselves prompt us to engage in this mental construction. They have their usual values, except that they now pertain to the distribution of a conceptual activity through processing time, as opposed to an actual activity through conceived time.9 They pertain to the very activity of dynamically accessing the ordered elements of a fictive mental construct.

The actual and virtual uses of still are depicted in Figure 8.9. In diagram (a), representing still in expressions like (19), a bar represents the continuation through conceived time of the situation in question, labeled P. A rectangle indicates the span of time being singled out for examination, i.e., its immediate temporal scope. The segment of the ongoing situation that falls within this scope is the portion in focus, i.e., it is profiled by the clause. What still contributes is a scanning through time (dashed arrow), tracing through P's temporal extension, with the specification that P continues beyond a potential cut-off point (vertical dashed line) and obtains during the focused temporal interval.

Contrast this with Figure 8.9(b), representing still in a sentence like (i8)(a). Here the mental scanning is fictive in nature, so it inheres in the virtual plane and occurs only through processing time, not conceived time. Moreover, the entities sequentially accessed are alternatives of some kind (in this case sums of money), shown diagrammatically as circles. These

9 The activity, in other words, is subjectively rather than objectively construed, as defined in Langacker 1990 and I999e.

entities are arranged along a scale (such as a quantity scale), along which mental scanning occurs. As each entity is accessed in its turn, it proves to have the property labeled P (in this case, being insufficient to merit an interview with the president). Still indicates that finding property P associated with the accessed entity continues past a potential cut-off point and is characteristic of the entity currently in focus. In both 8.9(a) and 8.9(b), still has the experiential import of continuing to encounter property P longer (in processing time) than might be expected during the process of mental scanning. The difference is that, in the actual examples, this subjective process of mental scanning proceeds along the axis of conceived time (t), whereas in the fictive examples it proceeds along some scale.

We can take this one step further (fictively speaking). When the temporal adverbs in question specify frequency, comparable mental scanning provides a means of quantifying over the entities thus encountered. Consider the examples in (20):

(2o)(a) A professional basketball player is usually tall.

(b) A professor is always arrogant.

(c) Theoretical linguists are {often/frequently/commonly} obtuse.

(d) Politicians are {seldom/rarely/never} honest.

On the relevant (and more likely) interpretation, these sentences are taken as quantifying over sets of individuals, specifying which proportion of them exhibit a certain property. Thus (2o)(a) effectively indicates that most professional basketball players are tall, (2o)(b) that all professors are arrogant, (2o)(c) that many linguistic theorists are obtuse, and (2o)(d) that few if any politicians are honest.

Once we appreciate the prevalence and naturalness of fictive mental scanning, these uses are straightforward. Once more, the temporal adverbs are employed with something approximating their normal values. What is special is simply the conceptual configuration to which they apply. We invoke the fictive conception of moving through the world and encountering multiple instances of a certain type (professional basketball player, professor, theoretical linguist, politician). The adverbs pertain to this tacit, fictive process of exploration and specify the frequency of events in which an encountered individual of the type in question exhibits the property in question. Granted the assumption that the individuals fictively encountered are representative, the frequency of events in which they exhibit the property translates into the proportion of type instances exhibiting the property.

This is sketched in Figure 8.10. The sequential examination of instances occurs in the virtual plane, as a mental simulation representing what is purported to be the nature of actual experience. A certain proportion of the instances fictively examined turn out to exhibit the property in question, P. The temporal adverb specifies the frequency of such events. The individual meanings of these adverbs pose interesting problems, but here

figure 8.10. Fictivity with frequency expressions.

I have merely indicated, in generalized fashion, that the set of events where P is encountered falls somewhere along a scale whose expanse is given by the totality of events. However, since each examining event resides in the examination of an instance of the type, the frequency of events where P is encountered correlates exactly with the proportion of instances exhibiting P. It is the frequency of events that the adverb explicitly encodes, yet from the fictive scenario evoked we can "read off" the proportion of instances. It is not the case that the temporal adverbs have the import of nominal quantification as their meaning per se - rather, we conventionally employ them, with fictive temporal value, as part of a mental construction from which such quantification can be inferred.

We use sentences like those in (20) to say something about what the world is actually like, but the entities directly mentioned or alluded to are virtual: e.g., no particular politicians are encountered, and the process of wandering the globe to encounter and examine them is imaginary. Hence the semantic problem of describing the quantificational use of temporal adverbs is not one of nominal quantification per se. Basically it reduces to the problem of characterizing the mental construction invoked and how we dynamically access it.

"logical" elements

Fictively, we have already wandered into the traditional territory of logic and formal semantics. Of prime concern in these disciplines have been such matters as quantification, negation, and implication. In cognitive semantics, even so-called "logical" elements like these are naturally considered manifestations of our imaginative capacities.

We can start with the claim by Johnson (1987) and Lakoff (1987,1990) that abstract image schemas are fundamental components of conceptual structure. Examples include such notions as container-content, center-periphery, part-whole, source-path-goal, linkage, force, balance, etc. Abstracted from everyday bodily experience involving perception, motion, and muscular exertion, these schematic notions are projected metaphorically to other domains of experience. The manipulation of image schematic structure is even claimed - quite correctly, I believe - to underlie mental constructions usually thought of as formal and disembodied, such as logical deduction and mathematics (Lakoff & Nunez, 1998, 2000).

To take a simple example, Lakoff (1987,272) explicates the deduction pattern known as modus ponens in terms of the inherent logic of the containercontent image schema, based on the metaphor that sets or classes are containers for their members. Lakoff's claim is that we carry out this reasoning pattern via image schema transformation, as illustrated in Figure 8.11. Each premise has an image schematic representation, employing the container metaphor for sets. We combine these via the image schema transformation of superimposition. From the resulting composite image, we derive the conclusion by means of the image schema transformation of fading out. In short, once we properly characterize the conceptual structures being invoked and manipulated, the logical deduction is simply a matter of "reading off" the results, apparent by simple (mental) inspection. Of course, all these structures are fictive in nature, even though the reasoning pertains to actuality (George Lakoff is an actual linguist, and an actual mammal).

(21) Modus ponens Premise^ All linguists are mammals.

Premise2: George Lakoff is a linguist.

Conclusion: Therefore Lakoff is a mammal.

Let me very briefly consider two other "logical" elements: the conditional if (used in implicational statements) and negation. I will then discuss quantifiers at greater length.

In mental space theory, if is treated as a space builder, setting up a hypothetical mental space in which a certain situation (P) holds (Fauconnier, figure 8.11. An imagistic account of modus ponens.

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