The complement of the preposition naarto refers to the endpoint of a complete path, with the implication that it will be reached sooner or later. The complement of the preposition tot (en met)until denotes an arbitrary point on an implied path, with the implication that this point is the endpoint of a distinct subpart of the complete path. In other words, while example (210a) suggests that both Jan and Peter will go to Groningen (see Figure 15A), example (210b) suggests that at least one of the two participants will continue his journey beyond Groningen (in Figure 15B the dotted arrow indicates the remainder of the path that either Jan or Peter will take). The difference between tot and tot en met is that in the latter case the relevant part of the path includes the position referred to by the reference object, whereas in the former case it can be excluded. Note that the (reduced version of the) phrasal preposition in de richting van only indicates the direction of the path, without implying that the reference object will ever be reached (see Figure 15C).

PPs headed by the prepositions naarto and in de richting vantowards are special in that they also allow an orientation reading. This is illustrated in (211). The two examples differ in that only in (211a) is the reference object actually pointed at.

The PPs can be used as attributive modifiers with a similar distinction: according to (212a) the road will lead up to the church, while this need not be the case in (212b). Note that PPs headed by tot cannot usually be used as attributive modifiers; we will return to this in our discussion of example (217).

The prepositions van, vanaf, and vanuit take a nominal complement that refers to the starting point of (a subpart of) the implied path; in Figure 16 we indicate this by drawing several arrows from the reference object.

Van is the most neutral of these three prepositions; it simply expresses that there is a path starting from the reference object without necessarily implying that the reference object is included in the path; vanuit, on the other hand, expresses that (a area within) the reference object is included in the path; vanaf indicates that the path may have started at another location, but that only the part from the reference object onward is considered relevant; in this respect, this preposition is similar to tot (en met).

The prepositions van, vanaf, and vanuit leave the endpoint of the path, and thus also the direction of the path, unspecified; to specify the direction, we have to add a PP that refers to the endpoint of (the relevant part of) the path. A comparison of the examples in (213) and (214) shows that the two PPs are strictly ordered: PPs denoting the starting point must precede PPs denoting the endpoint of the path.

The examples in (215) show that this holds not only for their relative position in the middle field of the clause, but also for their relative orderings under topicalization (although contrastive focus on the topicalized part may improve the orderings in the primed examples, especially in generic contexts).

In the examples discussed above, the located object actually traverses the path denoted by the spatial PPs. This need not always be the case, as can be seen from the primeless examples in (216), which involve extent readings of the directional PPs. The same extent readings are found in the primed examples in which the PPs function as modifiers of a noun phrase.

Example (217a) shows that PPs headed by the directional preposition vanaf cannot easily be used as modifiers of the noun phrase. In Subsection 1, we noted the same thing for the preposition tot; this is illustrated again in (217b). This strongly suggests that PPs referring to a subpart of some larger implied path cannot be used as modifiers in the noun phrase, although it should immediately be noted that noun phrases modified by tot-PPs are common when the reference object is abstract, as in (217b').

The nominal objects of the prepositions over, via, and voorbij do not refer to the beginning or the end of the path, but just simply to an arbitrary point on the path. In a sense, these prepositions locate the path with respect to the reference object. This could be described by dividing the relevant path into two subparts, with the reference object being the endpoint of the first subpart and the starting part of the second subpart. This is shown in Figure 17 for the examples in (218).

Example (218b) contains three PPs: a van-PP referring to the starting point of the path, which is followed by the via/over-PP referring to a specific intermediate point, and a naar-PP referring to the endpoint. The examples in (219) show that, with a non-contrastive intonation pattern, these PPs must be placed in this order, i.e. the orders in the primed examples are severely degraded; cf. also the discussion of (214).

Finally, the examples in (220) show that the located object need not actually traverse the path denoted by the spatial PPs; these PPs can also receive an extent reading.

Subsection I has shown that the prepositions achterbehind, naastnext to and voorin front of can be used both deictically and inherently. The inherent uses of these prepositions in the examples in (222) indicate that the object is (put) in the positions indicated in Figure 18.

The computation of the position of the located object depends on what is considered to be the back or the front of the reference object. This is largely a matter of convention, in the sense that the dimensional properties of the reference object do not matter. Some examples: the front of a car is determined by the direction in which the car normally drives, the front of a building is usually determined by its main entrance, and the front of a television is determined by the placement of the screen. Other factors may also be involved, as can be seen by comparing the examples in (223).

Although the examples in (223) imply that Jan is in similar positions with respect to the two screens, antonymous prepositions are used. This is because achter is often used to in contexts where one is operating the reference object, as in the following examples.

Another preposition that belongs to this group of inherent prepositions is the compound tegenoveropposite. It differs from prepositions like achter, naast, and voor in that it refers not only to the orientation of the reference object, but also to that of the located object; the reference and the located object must be facing each other. This is illustrated in example (225a), which refers to the situation in Figure 19A, where Jan and Peter are facing each other. Note that this situation can also be described by example (225b), but the difference between the two cases is that the orientation of the located object is not relevant in the case of voor; Figure 19B shows that (225b) can be applied to a wider range of situations than (225a).

Related to this difference between tegenover and voor is that the relation expressed by tegenover is one of equivalence, in that we can conclude from (226a) that (226a') also holds, and vice versa. The difference between the two cases is mainly one of topichood: the subject is taken to be the topic of the discourse. Equivalence does not apply to the relation expressed by voor: we cannot infer from (226b) that (226b') holds (and vice versa).

Note, however, that there are cases in which the usage conditions of tegenover seem less stringent than in (225a). For instance, example (227a) seems acceptable even though a tree is not usually thought of as an object with a front and a back. One could even use (227b) in a situation where the front of the car is not facing the church.

Perhaps we should conclude from these examples that it is only the orientation of the reference object that ultimately matters, and consider (225a) to be the special case. We leave this open for future research.

As shown in the previous subsection, the interpretation of achter, naast and voor is independent of the dimensional properties of the reference object. This is not true for all prepositions. For example, the preposition langsalong is generally interpreted in terms of the length dimension of the reference object (which is obviously related to the fact that langs is diachronically related to the adjective langlong; cf. etymologiebank.nl/trefwoord/langs). In terms of vectors, we could say that langs denotes a set of vectors that are more or less parallel, i.e. that are all perpendicular to the exterior of the reference object. The examples in (228) show that like achter, naast and voor, the preposition langs can be used to denote either a location or a change of location.

Note, however, that there are also cases in which the importance of the length dimension is reduced, or in which there may be actual contact between the located and reference object (i.e. where the length of the vector is zero); cf. Cuyckens (1995) for a discussion of these different readings of langs. The first case is illustrated by the examples in (229).

According to Cuyckens, there are also cases where langs refers to a path that is located on the reference object. One of his examples is given in (230a). It is not clear whether this is a generally accepted structure: we prefer the alternative with over in (230b). That this preference is more general is shown by a Google search (July 11, 2023) for the strings [vervoerd langs de rivieren/het spoor] and [vervoerd over de rivieren/het spoor]: while the first returned no matching results, the second returned 10 hits for de rivieren and 95 hits for het spoor. This contrast is expressed by the percentage sign.

Cuyckens’ examples in (231) seem more common, but they do not really involve a path located on the reference object, but seem to express that the located object “closely follows the [reference object] along (one of) its significantly extended dimension(s)” (p.200). This formulation suggests that there is a minimal distance between the path followed by the located object and the reference object, which may not be really different from the core use of langs illustrated in (228).

Fore completeness, note that langs can also be used directionally; this will be discussed in Section 32.3.1.3, sub II, example (271)

Other prepositions, with an interpretation depending on the physical properties of their reference object, are binneninside/within, buitenoutside and bijnear, which Zwarts (1997b) calls topological prepositions. They require that the reference object divides space into an inner and an outer area. A PP headed by binnen indicates that the located object has a position in the inner area of the reference object, whereas a PP headed by buiten locates it in the outer area. In this respect, bij is the same as buiten, but it has the additional requirement that the position is in the vicinity of the reference object (where the meaning of “in the vicinity” is contextually determined). In Figure 21, the PPs in (232) denote a position within the gray area.

To conclude the discussion of this group of prepositions, it should be noted that it is not easy to fill in the idea that these prepositions denote a set of vectors. First of all, it is not clear what the starting point of the vectors is. Of course, we could make the idealization that the reference object is a point in space, which the vectors take as their starting point, but this would not help us in the case of binnen. Another possibility would be to assume that the positions in the relevant area are defined in terms of the shortest vectors from the outside of the reference object to the positions in question; cf. Figure 22. This would solve the problem that, despite the fact that the magnitudes of the vectors and are identical, the location of position B but not position C can be properly described by (233a), and (233b) can be used to describe position C but not position B. This is due to the fact that there is a shorter vector from the outside of the reference object, which is part of the denotation of vlak bij, so that position C but not position B can be properly described by (233b).

However, this solution to the problem does not solve the problem that neither the direction nor the magnitude of the vectors denoted by binneninside can be modified. For this reason, it has been assumed that binnen actually involves the null vector as well. We refer the reader to Subsection B for a discussion of the difference between in/uit and binnen/buiten.

The preposition inin differs from binneninside in that it requires physical contact between the reference object and the located object; in involves a null vector. This is illustrated for the examples in (234) by the images in Figure 23. The preposition binnen in (234a) does not imply any physical contact between Jan and the hedge; Jan just has to be somewhere in the gray area in Figure 23A. The preposition in in (234b), on the other hand, requires physical contact, so that the situation must be as shown in Figure 23B.

A caveat is in order, however. Example (234a) can be represented by using only two dimensions. If we are dealing with a three-dimensional object, however, the situation is slightly different. Since it is the preposition in, and not binnen, that is used in the examples in (235), we conclude that the inside of a three-dimensional object is mentally construed as a part of the reference object, rather than as its inner area.

Like in but unlike buitenoutside, uitout of implies that there is some physical contact with the reference object. For this reason, buiten (but not uit) can be used to refer to the situation in Figure 24A. In fact, example (236b) shows that uit cannot be used at all; if there is physical contact with the reference object, in takes precedence over uit; cf. Jan zit in de haag.

Buiten also seems to be preferred in the case of three-dimensional objects, although uit can sometimes also be used. It is not clear to us under what conditions uit can or cannot be used with three-dimensional objects.

The discussion above shows that the preposition buiten is usually preferred to uit with (static) location verbs. However, example (238b) shows that the preposition uit is possible with change-of-location verbs such as halento get, whereas buiten is not allowed in this context. This seems to be due to the fact that this verb expresses that the contact between the located and the reference object is broken; this would be consistent with the fact, illustrated in (238a), that the antonym of halen, stoppento put, only allows in.

The prepositions in and uit imply physical contact between the located object and the reference object at some point in time. However, the preposition in does not imply that the located object is completely physically enclosed by the reference object; this may only be partially the case. Similarly, the preposition uit implies that only a part of the located object protrudes from the reference object. This is illustrated by the examples in (239); the arrows in Figure 25 indicate the points that are relevant to the interpretation of the examples in (239).

In and uit differ in that the former is compatible with full inclusion, whereas the latter necessarily implies partial inclusion; this is clear from the fact that the adverbial phrase helemaalcompletely can be used with in, but not with uit (unless we are dealing with exaggeration). Note that, as expected, substituting bijna helemaalnearly completely for helemaal in (239b) would produce a fully acceptable result. The modifier een klein stukjea small piece expresses that the encompassment is not complete and is possible with both PPs, as expected.

The examples in (238) have already shown that in and uit can also be used to denote a change of location; cf. Figure 26. Some more examples are given in (241): in (241a) the reference object refers to the new position of the located object, and in (241b) it refers to its original position. In this case, the adverbial phrase helemaalcompletely can easily be used with both PPs; helemaal in (241b) expresses that the contact between the located and the reference object is completely broken.

In a sense, the preposition door combines the meanings of in and uit. In (242a), the PP door het speldenkussen expresses that the located object sticks both in and out of the reference object; in other words, both points indicated by the arrows in Figure 27A are relevant. In (242b), the PP indicates that the located object ends up in the position in Figure 27A as a result of Janʼs action; this is shown in Figure 27B.

The prepositions in and uit seem to differ from the preposition door in that the former can only be used in constructions involving a (change of) location, whereas the latter can also occur in directional constructions. This is clear from the fact that the examples in (243) with the verb of traversing rijdento drive are at best marginal with in and uit, but perfectly acceptable with door; cf. Section 32.1.2, sub II. The primed examples are added to show that all three adpositions can be used to express directional meanings when they are used as postpositions.

However, there is a slight difference in meaning between (243b) and (243b') that is hard to pinpoint. Perhaps another example may clarify this. If Jan drives through a meadow from one from one side to the other, door will be appear as a preposition, not as a postposition. This is shown in the (a)-examples in (244); the acceptability contrast becomes even clearer when the reference object is relatively small, like a puddle of rainwater. However, if Jan drives right through a forest from one end to the other, it is also possible to use door as a postposition, as shown in (244b'). This suggests that in order to use door as a postposition, the located object must be completely surrounded by the reference object (i.e. in all three dimensions), whereas this is not necessary when it is used as a preposition. We leave this to future research.

Whereas in, uit and door imply that the located object is at least partly located in the reference object, the prepositions aan, op, over and tegen in (245) merely require that there should be some contact between the two.

The four prepositions differ with respect to the kind of contact they imply. The preposition aan is compatible with minimal contact: the lamp in (245a) is connected to the ceiling only by its wire. The preposition op suggests more extended contact between the located object and the reference object; the stain in (245b), of course, has maximum contact with the ceiling. The preposition over also suggests more extended contact, but now it is the reference object that has more extended contact with the located object.

In (245), the PPs headed by aan, op, over are used with a location verb; however, the examples in (246) show that they can also be used with the causative counterparts of these verbs indicating a change of location.

The examples in (245) deserve further discussion. It has been claimed that the preposition aan expresses minimal distance, not minimal contact. Examples supporting this are provided in (247): they do not imply physical contact between the ship and the quay, or the house and the lake. If minimal distance is the correct characterization, aan must be assumed to denote a set of vectors which are smaller than some contextually determined size, just like bijnear shown in (232); aan and bij differ, however, in that only aan seems compatible with actual physical contact.

The examples in (245b&c) and (246b&c) may suggest that op and over imply some notion of full contact of the located object with the reference object or vice versa. This is not always the case, as the examples in (248) make clear; (248a) suggests that only the bottom of the lamp is in contact with the table (cf. Figure 7A) and (248b) is compatible with a situation in which the chair is only partly covered by the coat. This use is again not restricted to location verbs but can also be used with the change-of-location verbs in the primed examples.

The difference between op and over seems to be that the locational relation is more point-like in the case of op and more area-like in the case of over. The adverbial phrase kriskras in (249a) implies that the path traversed by the player covers an extended area of the field, leading to a clear preference for the use of over. Similarly, the verb verspreiden implies that the end positions of the players are spread over a larger area of the field, and again over is the preferred option. Note that op in (249a) is possible without the adverbial phrase kriskras; it is then simply used to indicate where the action of running takes place; cf. Geeraerts (2023) for a detailed discussion of the role of the notion of area in the semantic structure of over.

The meaning of the preposition tegenagainst is difficult to characterize. It is often used in the sense of “touching the side surface of the reference object”, as in (245d), but resultative constructions such as (250) are also possible.

These examples suggest that tegen means (or can mean) something like “touching the reference object while exerting force on it”, which would fit in well with the non-locational uses of tegen in examples such as (251).

If the notion of exerting force is indeed appropriate in characterizing the preposition tegen, it may be the case that tegen and aan act as antonyms with respect to the direction of the exerted force (at least in some cases). The examples in (252) may make this clear. The verbs duwento push and trekkento pull both express that a force is exerted on the complement of the (non-spatial) prepositional complement of the verb: in the first case the force is directed towards it, and only the preposition tegen can be used, but in the second case the direction of the force is reversed, and only the preposition aan is possible. This is illustrated in Figure 29, where the arrow indicates the direction of the force exerted by Jan.