2.1 The central schema and segment profiling

Although Brugman (Reference Brugman1981) and Lakoff (Reference Lakoff1987) presume that the central schema for over is a combination of the stative location ABOVE and the boundary-traversing path of ACROSS, Dewell (Reference Dewell1994) posits as the central schema of over the semicircular path shown in Figure 1. In Figure 1, the path of the trajector (TR) semi-encloses the landmark (LM).

Figure 1:

The central schema of over (Dewell Reference Dewell1994: 353)

This ‘semicircular path’ sense is reflected in over, as in (3).

1. (3) The dog jumped over the fence.(Dewell Reference Dewell1994: 353)

Dewell (Reference Dewell1994) states that if we take the arced path to be central, we can take the image-schema seriously enough to account for all of the variants of over, using natural image-schema transformations or metaphorical applications of spatial senses to other domains.Footnote ⁴ Dewell (Reference Dewell1994), for example, suggests segment profiling as the most obvious image-schema transformation. Briefly, segment profiling picks out a segment of the path. First, consider examples (4a) and (4b).

1. (4)

   1. a. The plane flew over the hill. (Dewell Reference Dewell1994: 352)

   2. b. The bird flew over the yard. (Dewell Reference Dewell1994: 352)

Over, in these sentences, profiles the central region of the arc near the peak, as shown in Figure 2. The rest of the path, upward from the starting point and downward from the peak, is implicit pragmatically.

Figure 2:

Profiled central region (Dewell Reference Dewell1994: 355)

Also, according to Dewell (Reference Dewell1994), over, in (5), profiles the upward trajectory in Figure 1 from the starting point to the peak. This over is illustrated in Figure 3.

1. (5) The sun came up over the mountains.(Dewell Reference Dewell1994: 356)

In example (6), over profiles the downward trajectory of the semicircular path illustrated in Figure 1. This variant of over is illustrated in Figure 4.

1. (6) Sam fell over the cliff.(Dewell Reference Dewell1994: 356)

Figure 3:

Profiled upward trajectory (Dewell Reference Dewell1994: 356)

Figure 4:

Profiled downward trajectory (Dewell Reference Dewell1994: 356)

Next, according to Dewell (Reference Dewell1994), over in an example like (7) profiles the region of the peak of the semicircular path, as shown in Figure 5, giving what he calls a “freeze-frame at the peak.” In his article, Dewell (Reference Dewell1994) states that this use of over “retains the backgrounded sense of continued motion on a journey that will eventually lead to a landing.”

1. (7) The plane should be over Baltimore by now.(Dewell Reference Dewell1994: 357)

These four instances of over involve image-schema transformations of segment profiling, in which part of the semicircular path is profiled.

Figure 5:

Freeze-frame at the peak (Dewell Reference Dewell1994: 357)

Figure 6:

Resulting-state: endpoint location (Dewell Reference Dewell1994: 358)

Figure 7:

Subjective path to endpoint (Dewell Reference Dewell1994: 358)

Now consider example (8). Here, a TR (Sam) is at an endpoint location which is reached after a physical movement. Dewell (Reference Dewell1994) describes an image-schema transformation like this as an image-schema transformation to a resulting-state, as illustrated in Figure 6. In resulting-state variants, the entire trajectory is intact.

1. (8) Sam is over the bridge now.(Dewell Reference Dewell1994: 357)

Over in (9), on the other hand, does not suggest a physical movement. There is no suggestion that this is the path that Sam took to get to the endpoint. Therefore, Dewell (Reference Dewell1994) distinguishes the sense of over in (8) from that in (9). Lakoff (Reference Lakoff1987), in contrast, does not distinguish between these two uses of over. For him, both senses involve the image-schema transformation of “path focus ↔ endpoint focus.” In Dewell's (Reference Dewell1994) framework, the sense of over in (9) is explained by the image-schema transformation of a subjective path to an endpoint, illustrated in Figure 7. In this case, the speaker/interpreter mentally traverses the OVER-path.

1. (9) Sam lives over the bridge.(Dewell Reference Dewell1994: 358)

2.2 Extending paths: linear-extending trajectors

According to Dewell (Reference Dewell1994), in one reading of (10), the rope is not a holistic TR maintaining a constant shape as it moves entirely over the LM. Rather, it is an extending TR, part of which remains at the starting location.

1. (10) Sam threw the rope over the limb. (Dewell Reference Dewell1994: 359)

In this case, the focus is on the leading point of the TR. The resulting shape of the whole extended TR corresponds, more or less, to the summarily scanned path taken by the leading point, as shown in Figure 8.

Figure 8:

Linear-extending trajector (Dewell Reference Dewell1994: 359)

Dewell (Reference Dewell1994), calling such a path an “extending-path”, describes this type of image-schema transformation as an “extending-path transformation.”

Dewell (Reference Dewell1994) argues that segment profiling also applies to the schema of Figure 8. Consider the sentences in (11):

1. (11)

   1. a. He leaned over the rail.(Dewell Reference Dewell1994: 359)

   2. b. We stretched the rope over the yard. (Dewell Reference Dewell1994: 359)

   3. c. We dropped the rope down over the edge. (Dewell Reference Dewell1994: 357)

For Dewell (Reference Dewell1994), the uses of over in (11a), (11b), and (11c) correspond respectively to the left, middle, and right segments shown in Figure 9.

Figure 9:

Profiled linear-extending trajector (Dewell Reference Dewell1994: 359)

2.3 A three-dimensional conception

Consider example (12). In Dewell's (Reference Dewell1994: 362) words, “[a] vantage point above the TR reveals its linear shape as an edge extending horizontally and perpendicular to the OVER-path. In effect, each point in the TR may be seen as tracing its own OVER-arc ….”

1. (12) A line of soldiers marched over the ridge.(Dewell Reference Dewell1994: 362)

According to Dewell (Reference Dewell1994), the image-schema for over in (12) is three-dimensional, as shown in Figure 10.

Figure 10:

Edge-trajector (Dewell Reference Dewell1994: 362)

Now consider example (13):

1. (13) He draped the sheet over the clothesline. (Dewell Reference Dewell1994: 363)

According to Dewell (Reference Dewell1994), the edge-TR image of Figure 10 can be transformed naturally into an image like that in Figure 11. Example (13) can thus be read as a planar TR extending; in this case, the leading edge moves uniformly over the LM.

Figure 11:

Planar-extending trajector (Dewell Reference Dewell1994: 363)

Next, look at the sentences in (14):

1. (14)

   1. a. She poured the syrup out over the pancakes. (Dewell Reference Dewell1994: 363)

   2. b. He spread the cloth out over the table. (Dewell Reference Dewell1994: 363)

Dewell states that example (14a) describes a situation in which a fluid moves outward in several directions at once, as in Figure 12, and (14b) gives essentially the same image. Figure 12 represents a planar TR with an edge extending outward in multiple directions at once, ultimately semi-enclosing the LM in at least one of those directions. This schema is essentially a curved-edge variant of the schema for planar-extending TRs (Figure 11), profiling the downward arc.

Figure 12:

Multi-directional planar TR (Dewell Reference Dewell1994: 364)

3.1 Problem 1: two-dimensional/three-dimensional image-schemas of over

Dewell (Reference Dewell1994) distinguishes between two-dimensional and three-dimensional image-schemas for over. However, is a distinction between dimensions like this necessary (Ando Reference Ando2007)? The issue is rooted in the spatial-cognitive ability of human beings. We should understand three-dimensionally the image indicating a sense of over, and so the image-schema of over should be captured three-dimensionally (Van der Gucht et al. Reference Van der Gucht, Willems and De Cuypere2007). This is motivated by the fact that a container image-schema is captured three-dimensionally. According to Lakoff and Johnson (Reference Lakoff and Johnson1999: 31–32), a container schema can be instantiated as a “bounded region in space, like a basketball court,”Footnote ⁵ which suggests that a container schema is captured three-dimensionally (Freeman Reference Freeman1995, Regier Reference Regier1995, Sandra and Rice Reference Sandra and Rice1995, Gibbs Reference Gibbs1996, Sinha and Jensen de López Reference Sinha and de López2001, Evans and Green Reference Evans and Green2006, Radden and Dirven Reference Radden and Dirven2007, Lakoff Reference Lakoff2012).

In cognitive-psychological terms too, images are captured three-dimensionally (Downs and Stea Reference Downs and Stea1973, Roth and Frisby Reference Roth and Frisby1986, Thagard Reference Thagard1996, Richardson Reference Richardson1999, Smith et al. Reference Smith, Nolen-Hoeksema, Fredrickson and Loftus2003, Anderson Reference Anderson2010). In fact, mental rotation in cognitive psychology, first discussed by Shepard and Metzler (Reference Shepard and Metzler1971), is captured stereoscopically, that is, three-dimensionally. We should therefore assume that the image-schema of over is structured three-dimensionally (Vandeloise Reference Vandeloise1991).

3.2 Problem 2: over in (15)

As we saw in section 2, Dewell (Reference Dewell1994) represents over in (15) as in Figure 2, and argues that the rest of the path upward from the starting point and downward from the peak in Figure 2 is implicit pragmatically.

1. (15)

   1. a. The plane flew over the hill.(= (4a)), (Dewell Reference Dewell1994: 352)

   2. b. The bird flew over the yard. (= (4b)), (Dewell Reference Dewell1994: 352)

Meanwhile, he states that over in (16) “retains the backgrounded sense of continued motion on a journey that will eventually lead to a landing” (Dewell Reference Dewell1994: 357).

1. (16) The plane should be over Baltimore by now.(= (7)), (Dewell Reference Dewell1994: 357)

The question I would like to pose about over in (15) is why the rest of the path is “implicit pragmatically”, a question not answered by Dewell. Presumably, the semicircular path (upward from the starting point and downward from the peak) in Figure 2 is drawn by the common knowledge that the plane/bird takes off and lands. Furthermore, Dewell’s (Reference Dewell1994) analysis does not clearly capture the semantic difference between over in (15) versus (16).

3.3 Problem 3: over in (16)

As we saw in the last section, Dewell (Reference Dewell1994) analyzes over in an example like (16) as profiling the region of the peak of the semicircular path. As he puts it, “the TR seems to pause in ‘freeze-frame’ suspension at the peak of the arc” (Dewell Reference Dewell1994: 357). However, can this analysis be correct? I wonder whether speakers use this cognitive process in everyday language. It is technically true that when an object moves parabolically, its vertical velocity is briefly zero when it is at the peak of the path, but this is not something that ordinary speakers can be expected to know. Thus, it seems reasonable to assume that the process proposed by Dewell does not occur when native speakers of English use sentences with over. In fact, some senses of over suggest no actual physical movement, as in (17).

1. (17)

   1. a. The picture is over the mantel. (Tyler and Evans Reference Tyler and Evans2003: 110)

   2. b. Hang the painting over the fireplace. (Lakoff Reference Lakoff1987: 425)

As will be argued in section 4, over in (17) expresses a distinct ‘above’ sense.

3.4 Problem 4: on linear-extending trajectors

Dewell (Reference Dewell1994), calling a TR in an example like (18) “linear-extending trajector,” distinguishes between the TR in (18) and that in (19).

1. (18) Sam threw the rope over the limb. (= (10) (Dewell Reference Dewell1994: 359)

2. (19) The dog jumped over the fence. (= (3)) (Dewell Reference Dewell1994: 353)

This distinction, however, is unnecessary, for three reasons. First, linear-extending is a physical property of TR. Therefore, we should not attribute it to the meaning of over. Second, in (18) the leading point of the rope moves along the semicircular path, so it should be analyzed as the active zone in the sense of Langacker (Reference Langacker1990) (see also Taylor Reference Taylor2002: 110–111). Finally, although Figure 8 is proposed by Dewell (Reference Dewell1994) as the image-schema of over in (18), that figure is merely a picture that represents the state in which the rope hangs on the limb, and is by no means in line with an image-schema in the sense of Johnson (Reference Johnson1987). In fact, Figure 8 is not based in bodily experience: the notion of linear-extending does not emerge through our bodily experience (see Taylor Reference Taylor2002: 523).

I conclude from this that linear-extending is not part of the image-schema of over. Rather, over in (18) reflects the central schema of the semicircular path.

3.5 Problem 5: the image-schema of over in (20)

Above, we argued against using linear-extending trajectors to account for examples like (18) and rejected linear-extending trajectors. However, even if we had adopted linear-extending trajectors there, over in (20) should profile not the upward trajectory of the path, but the downward trajectory. That is, the image-schema of over in (20) should be the same as that of over in (21).

1. (20) He leaned over the rail. (= (11a)) (Dewell Reference Dewell1994: 359)

2. (21) We dropped the rope down over the edge. (= (11c)) (Dewell Reference Dewell1994: 357)

This contradicts Dewell's (Reference Dewell1994) account, where he describes over in (20) as profiling the upward trajectory of the path.

3.6 Problem 6: over in (22)

In my view, over in (22) indicates a ‘covering’ sense. This will be discussed in detail in section 4.

1. (22)

   1. a. She poured the syrup out over the pancakes. (= (14a)) (Dewell Reference Dewell1994: 363)

   2. b. He spread the cloth out over the table. (= (14b)) (Dewell Reference Dewell1994: 363)

Although Dewell (Reference Dewell1994) does not recognize a ‘covering’ sense of over, I will argue that it is one of the senses of this preposition.

3.7 Problem 7: whether or not the shape of TRs is involved in meanings of over

As we saw in the last section, Dewell (Reference Dewell1994) distinguishes over in (23) and (24) from over in (25)–(27) on the basis of whether the shape of the TR is linear or planar. However, I am not persuaded that the shape of the TR is part of the meaning of over.

1. (23) Sam threw the rope over the limb. (= (10)) (Dewell Reference Dewell1994: 359)

2. (24)

   1. a. He leaned over the rail. (= (11a)) (Dewell Reference Dewell1994: 359)

   2. b. We stretched the rope over the yard. (= (11b)) (Dewell Reference Dewell1994: 359)

   3. c. We dropped the rope down over the edge. (= (11c)) (Dewell Reference Dewell1994: 357)

3. (25) A line of soldiers marched over the ridge. (= (12)) (Dewell Reference Dewell1994: 362)

4. (26) He draped the sheet over the clothesline. (= (13)) (Dewell Reference Dewell1994: 363)

5. (27)

   1. a. She poured the syrup out over the pancakes. (= (14a)) (Dewell Reference Dewell1994: 363)

   2. b. He spread the cloth out over the table. (= (14b)) (Dewell Reference Dewell1994: 363)

As was shown in the last section, Dewell (Reference Dewell1994) proposed “edge-trajector” to explain the planar shape of the TR of (25). However, as Ando (Reference Ando2007) points out, one can see a line of soldiers as a single individual. Under that view, the meaning of over in (25) is the same as that of over in (28).

1. (28) The dog jumped over the fence. (= (3)) (Dewell Reference Dewell1994: 353)

This is based on the idea that the shape of TRs is not involved in meanings of over.

3.8 Problem 8: radial category

Dewell (Reference Dewell1994) states that if we take a semicircular path to be the central schema of over, we can account for the interrelation of all of its spatial senses using only image-schema transformations and its nonspatial senses by metaphorical applications of spatial senses to other domains. However, he does not argue that the senses of over form a radial category, nor does he provide a radial category for over, as Lakoff (Reference Lakoff1987) does. A radial category which displays how all the senses of over are interrelated, as in Lakoff (Reference Lakoff1987), is required (see Geeraerts Reference Geeraerts2010 for a radial network analysis of polysemy).Footnote ⁶

4.1 The central image-schema A

We posit the central image-schema of over as a semicircular path, as in Figure 13 below (Deane Reference Deane1988, Dewell Reference Dewell1994, Lindstromberg Reference Lindstromberg1998). In Figure 13, the TR moves along the semicircular path parabolically, and no part of the path is profiled. Also, as stated in Hypothesis (29a), TRs and LMs are captured three-dimensionally (Gibbs and Colston Reference Gibbs and Colston1995, Sandra and Rice Reference Sandra and Rice1995, Zlatev Reference Zlatev, Cuyckens, Dirven and Taylor2003), and their shape and size are expandable and reducible topologically. In addition, in this case, as stated in Hypothesis (29b), contact/non-contact between TR and LM is unspecified, that is to say, it is irrelevant to senses of over.

Figure 13:

The central image-schema of over

Sentences (32)–(39) below are examples of over in this sense, used, as is very common, with action verbs of movement.

1. (32) The dog jumped over the fence. (= (3))

2. (33) Sam drove over the bridge. (= (31))

3. (34) Sam walked over the hill. (Lakoff Reference Lakoff1987: 422)

4. (35) Sam climbed over the wall.(Lakoff Reference Lakoff1987: 422)

5. (36) The rabbit hopped over the fence. (Tyler and Evans Reference Tyler and Evans2003: 79)

6. (37) She threw the rope over the limb. (= (10))

7. (38) A line of soldiers marched over the ridge.(= (12))

8. (39) He draped the sheet over the clothesline.(= (13))

Dewell (Reference Dewell1994) treats the image-schema of over in (37)–(39) as distinct from that of over in (32)–(36). In contrast, the account being developed here treats the image-schema of over in (37)–(39) as the same as that of over in (32)–(36), because the shape and size of the TR and the LM are expandable and reducible topologically, as stated in Hypothesis (29a).Footnote ⁷ Also, although Lakoff (Reference Lakoff1987) subclassifies image-schemas of over by specifying whether there is contact between TR and LM, with the schemas for over in (33)–(35) represented as in C (‘contact’), by Hypothesis (29b) we do not distinguish over in (33)–(35) from cases with no contact between TR and LM, such as (32), (36), and (37).

4.2 Segment profiling: image-schema transformation B

Here, I adopt the notion of segment profiling: the image-schema transformation of profiling part of the semicircular path.Footnote ⁸ However, the segment profiling proposed here is not the same as that of Dewell (Reference Dewell1994). Although Dewell (Reference Dewell1994) treats over in an example like (40) as profiling the region of the peak at the semicircular path, we do not adopt this view, as discussed in section 3.3.

1. (40) The plane should be over Baltimore by now.(= (16))

I propose to analyze over in an example like (40) as the profiled central region of the arc, as in section 4.2.1 below.

4.2.1 Profiled central region of the semicircular path: image-schema transformation B1

Consider (41)–(44). In these examples, over profiles the central region of the semicircular path.

1. (41) The plane flew over the hill.(= (4a))

2. (42) The bird flew over the yard. (= (4b))

3. (43) We stretched the rope over the yard. (= (11b))

4. (44) Lisa just tapped the golf ball, but it still rolled over the cup. (Tyler and Evans Reference Tyler and Evans2003: 83)

The sense of over in these examples can be illustrated as in Figure 14.

Figure 14:

Profiled central region

The dotted line in Figure 14 represents the backgrounded part of the path. As stated in Hypothesis (29c), whether the TR actually moves along this part or not is unspecified.

4.2.2 Profiled upward region of the semicircular path: image-schema transformation B2

Consider (45) and (46). In these examples, over profiles the upward region of the semicircular path.

1. (45) The sun came up over the mountains. (= (5))

2. (46) The plane climbed high over the city. (Dewell Reference Dewell1994: 356)

The sense of over in examples like these can be illustrated as in Figure 15.

Figure 15:

Profiled upward trajectory

The dotted downward trajectory in Figure 15 represents the backgrounded part of the path. As stated in Hypothesis (29c), whether the TR actually moves along this part or not is unspecified. In examples (45) and (46), the TRs (the sun and the plane) actually move along the downward dotted trajectory. However, this is provided by our common knowledge about the sun (it sets) and planes (they land).

4.2.3 Profiled downward region of the semicircular path: image-schema transformation B3

Consider (47)–(51). In these examples, over profiles the downward region of the semicircular path, as shown in Figure 16.

1. (47) Sam fell over the cliff. (= (6))

2. (48) We dropped the rope down over the edge. (= (11c))

3. (49) He leaned over the rail. (= (11a))

4. (50) He stumbled over a stone.

5. (51) Bill: “Mum! Joe tripped me with his foot.”

   Joe: “No, I didn't, Mum. Bill just tripped over my foot.” (Radden and Dirven Reference Radden and Dirven2007: 24)

Figure 16:

Profiled downward trajectory

The dotted upward trajectory in Figure 16 above represents the backgrounded part of the path. As stated in Hypothesis (29c), whether the TR actually moves along this part or not is unspecified. In (47)–(51), the TR does not actually move along the upward dotted trajectory.

Note again that, as stated in Hypothesis (29a), the shape and size of TRs and LMs are expandable and reducible topologically. This means that the TR in (49), he, is captured topologically. We can therefore assert that over in (49) profiles the downward region of the semicircular path. This account of example (49) is more accurate than Dewell's.

4.2.4 Profiled endpoint of the semicircular path: image-schema transformation B4

In (52), over profiles the endpoint of the semicircular path, as illustrated in Figure 17.

1. (52) Sam is over the bridge now. (= (8))

The dotted arc in Figure 17 represents the backgrounded part of the path. As stated in Hypothesis (29c), whether the TR actually moves along this part is unspecified. As we will see in detail later, over in this case suggests actual movement (Ekberg Reference Ekberg2001 notes that (52) denotes the actual path of the TR).

Figure 17:

Profiled endpoint location

4.3 Profiled endpoint of the access path: image-schema transformation C

Consider (53)–(55) below. For Dewell (Reference Dewell1994), these examples profile the endpoint reached after subjective motion (Langacker Reference Langacker1990). Here, there is no suggestion of actual physical movement. According to Lakoff (Reference Lakoff1987) and Ekberg (Reference Ekberg2001), over in these examples can be interpreted as “on the other side of” – or, as Blomberg (Reference Blomberg2015) and Blomberg and Zlatev (Reference Blomberg and Zlatev2015) put it, as the phenomenology of “non-actual motion.”Footnote ⁹ With respect to over in examples like these, the speaker/interpreter mentally traces the path using the cognitive operation called mental scanning.

1. (53) Sam lives over the bridge. (= (9))

2. (54) Sausalito is over the bridge. (Lakoff Reference Lakoff1987: 424)

3. (55) The mansion is situated over that wall. (Tyler and Evans Reference Tyler and Evans2003: 82)

The sense of over in examples like these can be represented as in Figure 18. Since in these examples, the TR (Sam, Sausalito, and the mansion) do not actually move, the dotted line in Figure 18 is drawn more finely than the one in Figure 17.

Figure 18:

Profiled endpoint of the access path

Talmy (Reference Talmy, Bloom, Garrett, Nadel and Peterson1996, Reference Talmy2000) and Matsumoto (Reference Matsumoto and Goldberg1996) call path expressions like these access paths.Footnote ¹⁰ Adopting this term, we can say that over in (53)–(55) profiles the endpoint of the access path. For Lakoff (Reference Lakoff1987) and Taylor (Reference Taylor2012: 237), over in these examples and in example (52) has this sense as a result of end-point focus (see section 2.1). However, since the special cognitive process of mental scanning is operating with examples (53)–(55), I distinguish between over in (52) and that in (53)–(55). Linguistic evidence in support of this claim comes from sentences like (56).

1. (56) Sam is safely over the bridge now.

This sentence profiles the endpoint of the over-path, and suggests actual movement. In fact, in this sentence safely is used. The interpretation of the sentence does not involve subjective motion.

A similar phenomenon can also be seen with across and through, as in (57)–(62).

1. (57) The child hurried across the street. (Langacker Reference Langacker1999: 301)

2. (58) The child is safely across the street. (Langacker Reference Langacker1999: 301)

3. (59) Last night there was a fire across the street. (Langacker Reference Langacker1999: 301)

According to Langacker (Reference Langacker1999), (57) profiles objective movement. Across in (58) shows static location resulting from actual movement. In (59) no physical movement is suggested at all. Rather, across in (59) profiles the endpoint as a goal reached after mentally following the path using mental scanning. In this way, a distinction is already made between the senses of across in (58) and (59). This corresponds to the distinction between over in (52) and that in (53)–(55). The same holds for through, as shown in (60)–(62).

1. (60) The train rushed through the tunnel. (Lee Reference Lee2001: 39)

2. (61) Tom is safely through the tunnel now.

3. (62) My office is located just through that door. (Tyler and Evans Reference Tyler and Evans2003: 222)

Through in (60) represents actual physical movement, while in (61) it shows the location resulting from actual movement of the TR Tom. In (62), through suggests no actual movement, but should be analyzed as profiling the endpoint as goal reached after the speaker/interpreter mentally follows the path. In this way, a distinction can be drawn between through in (61) and that in (62).

From what we have seen above, we can conclude that a distinction should be made between over in (52), which suggests movement of the TR, and that in (53)–(55), which does not.

4.4 The ‘above’ sense: image-schema transformation D

In sentences like (63)–(68) below, over has no sense of following a semicircular path. For sentences like these, Tyler and Evans (Reference Tyler and Evans2003) state that it does not seem possible to form an interpretation in which the TR is following a trajectory. Thus, it seems that over in these examples has a sense distinct from sense A, shown in Figure 13, or sense B1, shown in Figure 14. In (63)–(68), the TR is located physically above the LM, and the semicircular path is excluded. Under my approach, a path is excluded if there is no image in which the TR follows it.

1. (63) Hang the painting over the fireplace. (= (17b))

2. (64) The helicopter is hovering over the hill. (Lakoff Reference Lakoff1987: 425)

3. (65) The helicopter hovered over the city. (Brugman Reference Brugman1981: 40; Tyler and Evans Reference Tyler and Evans2003: 75)

4. (66) The picture is over the mantel.(= (17a))

5. (67) The lamp hangs over the table. (Taylor Reference Taylor2003: 113)

6. (68) The clothesline is suspended over the yard. (Dewell Reference Dewell1994: 360)

Over in this sense, which I term the ‘above’ sense, seems to involve a transformation of the semicircular path represented in Figure 13. We posit the relevant image-schema transformation as follows: the peak of the semicircular path is profiled, and the rest of the semicircular path is excluded, giving the representation in Figure 19.

Figure 19:

‘Above’

According to Lakoff (Reference Lakoff1987), over marking this sense is roughly equivalent in meaning to above. However, as shown in (69), sometimes above cannot be replaced by over (Deane Reference Deane, Hampe and Grady2005).

1. (69)

   1. a. There are birds somewhere above us. (Kreitzer Reference Kreitzer1997: 308)

   2. b. *There are birds somewhere over us. (Kreitzer Reference Kreitzer1997: 308)

Also, (70a) and (70b) have different meanings. According to Tyler and Evans (Reference Tyler and Evans2003), in (70a) the TR ‘Nora’ is in contact with the LM ‘the polished floor’, whereas in (70b), the TR is not in contact with the LM. A salient interpretation of (70b), but not of (70a), is that Nora refers to some fantastical creature, perhaps a fairy, capable of dancing in the air without actually touching the floor. Thus, over marking the ‘above’ sense in (70a) differs in meaning from above.

1. (70)

   1. a. Nora twirled over the polished floor. (Tyler and Evans Reference Tyler and Evans2003: 112)

   2. b. Nora twirled above the polished floor. (Tyler and Evans Reference Tyler and Evans2003: 112)

As we have seen, examples (69) and (70) suggest that over is not completely equivalent in meaning to above. Incidentally, although Taylor (Reference Taylor2003) states that in over indicating the ‘above’ sense, the TR is not in contact with the LM, the TR in (70a) is in contact with the LM.

4.5 The ‘covering’ sense: image-schema transformation E

Consider (71)–(75). The sense of over in these examples involves ‘covering.’ While Lakoff (Reference Lakoff1987) treats this over as a variant of the ‘above’ sense, Taylor (Reference Taylor2003, Reference Taylor2012), Tyler and Evans (Reference Tyler and Evans2003) and Zlatev (Reference Zlatev, Cuyckens, Dirven and Taylor2003) take ‘covering’ to be a separate sense of over.

1. (71) The board is over the hole. (Lakoff Reference Lakoff1987: 427)

2. (72) They laid a board down over the hole. (Dewell Reference Dewell1994: 367)

3. (73) He spread the cloth out over the table. (= (22b))

4. (74) The tablecloth is over the table. (Tyler and Evans Reference Tyler and Evans2003: 90)

5. (75) She poured the syrup out over the pancakes.(= (22a))

Some sentences with over mark the sense of ‘covering’ explicitly. In (76)–(80), the spatial relation between the TR and the LM has nothing to do with the vector of actual up versus down. For example, in (79), the transparent plastic sheet is attached to the ceiling and is located below it, while in (80), the hands are at the same level as the face. Examples (76)–(80) thus suggest that we should take the TR and the LM to be in a ‘covering’ relation.Footnote ¹¹ I therefore call the sense of over in examples like (71)–(80) the ‘covering’ sense. Again, as stated in Hypothesis (29a), the shape and size of the TR and the LM are expandable and reducible topologically. Therefore, even if the TR (the syrup) in (75) does not completely cover the LM (the pancakes), and even if the TR (his hands) in (80) is usually smaller than the LM (his face), we can take over in these examples as expressing the ‘covering’ sense.

1. (76) She put the coat on over her dress. (Dewell Reference Dewell1994: 368)

2. (77) She held her hands over her eyes.

3. (78) He hung a curtain over the picture.

4. (79) They put a transparent plastic sheet over the painted ceiling of the chapel during repairs.(Tyler and Evans Reference Tyler and Evans2003: 91)

5. (80) He put his hands over his face. (Taylor Reference Taylor2003: 114)

The ‘covering’ sense is derived by a transformation of the semicircular path that is the central image-schema of over. I assume that the image-schema transformation is an extension from the semicircular path-trajectory traced by the TR to an image of covering. Such an image-schema transformation is motivated by the nature of the TR, the shape and size of which are expandable topologically. Since the TR is captured topologically, in this sense of over the TR is perceived as a continuous mass. The sense of over in examples such as (71)–(80) can thus be illustrated as in Figure 20.

Figure 20:

Covering

The ‘covering’ sense of over is closely related to the function of the TR (Huddleston and Pullum Reference Huddleston and Pullum2002: 650).Footnote ¹² In (74), for instance, the function of tablecloths is to cover tables, while in (76) and (78), the function of a coat and a curtain is to cover a dress and a picture, respectively. In this way, the ‘covering’ sense of over is motivated by the function of the TR as well.

4.6 Metaphorical senses: Mapping F

In what follows, we will consider some metaphorical extensions of over not discussed by Lakoff and Johnson (Reference Lakoff and Johnson1980, Reference Lakoff and Johnson1999) and Lakoff (Reference Lakoff1987, Reference Lakoff1990, Reference Lakoff and Ortony1993) (see Hypothesis (29d).Footnote ¹³ Lakoff (Reference Lakoff1990) postulated the Invariance Hypothesis, according to which metaphorical mappings preserve the cognitive topology (that is, the image-schema structure) of the source domain (Rudzka-Ostyn Reference Rudzka-Ostyn, Goossens, Pauwels, Rudzka-Ostyn, Simon-Vandenbergen and Vanparys1995). Subsequently, Lakoff (Reference Lakoff and Ortony1993) refined the Invariance Hypothesis as the Invariance Principle, which states that metaphorical mappings preserve the cognitive topology (that is, the image-schema structure) of the source domain, in a way consistent with the inherent structure of the target domain. The Invariance Principle thus guarantees that the cognitive topology of the source domain is invariant across metaphorical mappings (Deignan Reference Deignan1999). Now, we will see that in three specific cases, the cognitive structure of the image-schema represented in Figure 13 is preserved.

4.6.3 Metaphorical sense F3: Control

Consider examples (89)–(93):

1. (89) She has a strange power over me. (Lakoff Reference Lakoff1987: 435)

2. (90) I have no control over what he does.

3. (91) He has no authority over me.(Taylor Reference Taylor2003: 115)

4. (92) He rules over a large kingdom.

5. (93) Henry VIII reigned over England from 1509 to 1547.

Lakoff and Johnson argue that over in these examples is a metaphorical extension of the ‘above’ sense (Lakoff and Johnson Reference Lakoff and Johnson1980, Lakoff Reference Lakoff1987). Lakoff and Johnson (Reference Lakoff and Johnson1980) state that the relevant metaphor is: “HAVING CONTROL OR FORCE IS UP; BEING SUBJECT TO CONTROL OR FORCE IS DOWN” (Lakoff and Johnson Reference Lakoff and Johnson1980: 15). Indeed, over in (89)–(93) at first appears to be metaphorically extended from the ‘above’ sense in section 4.4, but I challenge this view. Although I agree with the inclusion of ‘above in physical space’ as a sense of over, and accept the conceptual metaphor of “HAVING CONTROL OR FORCE IS UP; BEING SUBJECT TO CONTROL OR FORCE IS DOWN”, I nonetheless claim that the sense of over in (89)–(93) should not be analyzed as a metaphorically extended ‘above’ sense. The reasons for this claim are as follows. First, in examples (89)–(93) the lexical items used in the verb phrases are fixed to some extent, and the verb phrases constitute verbal idioms (Huddleston and Pullum Reference Huddleston and Pullum2002: 273, 288). Second, compared with the sentences in (94), which Lakoff and Johnson (Reference Lakoff and Johnson1980) adduce as examples of the metaphor HAVING CONTROL OR FORCE IS UP; BEING SUBJECT TO CONTROL OR FORCE IS DOWN, it is less clear that over in (89)–(93) involves this metaphor. The reason that this metaphor seems to be operating on over in (89)–(93) is that in each of the verb phrases one of the lexical items power, control, authority, rule, and reign is used.

1. (94)

   1. a. He's at the height of his power.

   2. b. He is in the upper echelon.

   3. c. His power rose.

   4. d. He fell from power.(Lakoff and Johnson Reference Lakoff and Johnson1980: 15)

While Lakoff and Johnson (Reference Lakoff and Johnson1980) describe the metaphor involved in (89) as HAVING CONTROL OR FORCE IS UP; BEING SUBJECT TO CONTROL OR FORCE IS DOWN, Lakoff (Reference Lakoff1987) describes it differently, as CONTROL IS UP; LACK OF CONTROL IS DOWN (see also Murphy Reference Murphy1996). We must therefore carefully examine the use of over in examples like (89).

I claim that the sense of over found in (89)–(93) is a metaphorical extension from the central image-schema in Figure 13. I call this metaphorical sense of over ‘control.’Footnote ¹⁶ I will show that as Lakoff's (Reference Lakoff and Ortony1993) Invariance Principle requires, the cognitive topology of the source domain is preserved in these examples. As will be argued in detail in the next section, the source domain is physical space, the target domain is a dominion, and the cognitive topology preserved is the image of the structure wherein a TR moves parabolically above and across a LM in physical space.

In this section we have seen that the preposition over has eleven distinct senses, labelled above as A–F, with their subtypes. I will now argue that the senses of the preposition over form a radial category in which A is central, and B–F are derived from A, as shown in Figure 21. More specifically, the senses within this network result from ten transformations or extensions of the central sense: segment profiling (B1–B4), profiling the endpoint of a path that the speaker/interpreter mentally traces (C), profiling the peak of the semicircular path and excluding the rest (D), extending the semicircular path-trajectory to an image of covering (E), and other metaphorical extensions (F1–F3).

Figure 21:

The radial category of the preposition over

We take the radial network in Figure 21 as a cognitive model of how categories of lexical meanings are organized. According to Lakoff (Reference Lakoff1987: 438–444), the radial structure is psychologically real and motivates the spatial polysemy of the lexical item independently of the context in which the word appears (Zlatev Reference Zlatev, Cuyckens, Dirven and Taylor2003). The radial structure in Figure 21 is simpler than the radial structures shown by Lakoff (Reference Lakoff1987) and other previous studies. This section has thus provided a natural semantic analysis of the preposition over from a cognitive perspective.